chơi xổ số keno trực tuyến

{"appState":{"pageLoadApiCallsStatus":true},"authorState":{"author":{"headers":{"timestamp":"2025-04-01T08:49:13+00:00"},"authorId":9399,"data":{"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" Angie Papple Johnston joined the U.S. Army in 2006 as a Chemical, Biological, Radiological, and Nuclear Specialist. During her second deployment as part of Operation Iraqi Freedom, Angie became her battalion&#8217;s public affairs representative. She also served as the Lead Cadre for the Texas Army National Guard&#8217;s Recruit Sustainment program. ","photo":{"src":null,"width":0,"height":0}}},"authorLoadedStatus":"success"},"listState":{"list":{"count":10,"total":269,"items":[{"headers":{"creationTime":"2017-03-26T13:42:37+00:00","modifiedTime":"2025-03-20T14:29:48+00:00","timestamp":"2025-03-20T15:01:18+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"Important Operations that Make Math Problems Easier","strippedTitle":"important operations that make math problems easier","slug":"inverse-operations-and-commutative-associative-and-distributive-properties","canonicalUrl":"","百度搜指数擎推广":{"metaDescription":"Understand math operations, including inverse operations, the commutative property, the associative property, and the distributive property.","noIndex":0,"noFollow":0},"content":"The Big Four math operations — addition, subtraction, multiplication, and division — let you combine numbers and perform calculations. Certain operations possess properties that enable you to manipulate the numbers in the problem, which comes in handy, especially when you get into higher math like algebra. The important properties you need to know are the commutative property, the associative property, and the distributive property. Understanding what an inverse operation is is also helpful.\r\n<h2 id=\"tab1\" >Inverse operations</h2>\r\n<i>Inverse operations</i> are pairs of operations that you can work \"backward\" to cancel each other out. Two pairs of the Big Four operations — addition, subtraction, multiplication, and division —are inverses of each other:\r\n<ul class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\"><b>Addition and subtraction are inverse operations of each other.</b> When you start with any value, then add a number to it and subtract the same number from the result, the value you started with remains unchanged. For example:</p>\r\n\r\n<blockquote>2 + 3 = 5 so 5 – 3 = 2</blockquote>\r\n<blockquote>7 – 1 = 6 so 6 + 1 = 7</blockquote>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\"><b>Multiplication and division are inverse operations of each other. </b>When you start with any value, then multiply it by a number and divide the result by the same number (except zero), the value you started with remains unchanged. For example:</p>\r\n\r\n<blockquote>3 × 4 = 12 so 12 ÷ 4 = 3</blockquote>\r\n<blockquote>10 ÷ 2 = 5 so 5 × 2 = 10</blockquote>\r\n</li>\r\n</ul>\r\n<h2 id=\"tab2\" >The commutative property</h2>\r\nAn operation is <i>commutative</i> when you apply it to a pair of numbers either forwards or backwards and expect the same result. The two Big Four that are commutative are addition and subtraction.\r\n\r\nAddition is commutative because, for example, 3 + 5 is the same as 5 + 3. In other words\r\n<blockquote>3 + 5 = 5 + 3</blockquote>\r\nMultiplication is <i>commutative</i> because 2 × 7 is the same as 7 × 2. In other words\r\n<blockquote>2 × 7 = 7 × 2</blockquote>\r\n<h2 id=\"tab3\" >The associative property</h2>\r\nAn operation is <i>associative</i> when you can apply it, using parentheses, in different groupings of numbers and still expect the same result. The two Big Four operations that are associative are addition and multiplication.\r\n\r\nAddition is associative because, for example, the problem (2 + 4) + 7 produces the same result as does the problem 2 + (4 + 7). In other words,\r\n<blockquote>(2 + 4) + 7 = 2 + (4 + 7)</blockquote>\r\nNo matter which pair of numbers you add together first, the answer is the same: 13.\r\n\r\nMultiplication is associative because, for example, the problem 3 × (4 × 5) produces the same result as the problem (3 × 4) × 5. In other words,\r\n<blockquote>3 × (4 × 5) = (3 × 4) × 5</blockquote>\r\nAgain, no matter which pair of numbers you multiply first, both problems yield the same answer: 60.\r\n<h2 id=\"tab4\" >The distributive property</h2>\r\nThe <i>distributive property</i> connects the operations of multiplication and addition. When multiplication is described as \"distributive over addition,\" you can split a multiplication problem into two smaller problems and then add the results.\r\n\r\nFor example, suppose you want to multiply 27 × 6. You know that 27 equals 20 + 7, so you can do this multiplication in two steps:\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">First multiply 20 × 6; then multiply 7 × 6.</p>\r\n<p class=\"child-para\">20 × 6 = 1207 × 6 = 42</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Then add the results.</p>\r\n<p class=\"child-para\">120 + 42 = 162</p>\r\n</li>\r\n</ol>\r\nTherefore, 27 × 6 = 162.","description":"The Big Four math operations — addition, subtraction, multiplication, and division — let you combine numbers and perform calculations. Certain operations possess properties that enable you to manipulate the numbers in the problem, which comes in handy, especially when you get into higher math like algebra. The important properties you need to know are the commutative property, the associative property, and the distributive property. Understanding what an inverse operation is is also helpful.\r\n<h2 id=\"tab1\" >Inverse operations</h2>\r\n<i>Inverse operations</i> are pairs of operations that you can work \"backward\" to cancel each other out. Two pairs of the Big Four operations — addition, subtraction, multiplication, and division —are inverses of each other:\r\n<ul class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\"><b>Addition and subtraction are inverse operations of each other.</b> When you start with any value, then add a number to it and subtract the same number from the result, the value you started with remains unchanged. For example:</p>\r\n\r\n<blockquote>2 + 3 = 5 so 5 – 3 = 2</blockquote>\r\n<blockquote>7 – 1 = 6 so 6 + 1 = 7</blockquote>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\"><b>Multiplication and division are inverse operations of each other. </b>When you start with any value, then multiply it by a number and divide the result by the same number (except zero), the value you started with remains unchanged. For example:</p>\r\n\r\n<blockquote>3 × 4 = 12 so 12 ÷ 4 = 3</blockquote>\r\n<blockquote>10 ÷ 2 = 5 so 5 × 2 = 10</blockquote>\r\n</li>\r\n</ul>\r\n<h2 id=\"tab2\" >The commutative property</h2>\r\nAn operation is <i>commutative</i> when you apply it to a pair of numbers either forwards or backwards and expect the same result. The two Big Four that are commutative are addition and subtraction.\r\n\r\nAddition is commutative because, for example, 3 + 5 is the same as 5 + 3. In other words\r\n<blockquote>3 + 5 = 5 + 3</blockquote>\r\nMultiplication is <i>commutative</i> because 2 × 7 is the same as 7 × 2. In other words\r\n<blockquote>2 × 7 = 7 × 2</blockquote>\r\n<h2 id=\"tab3\" >The associative property</h2>\r\nAn operation is <i>associative</i> when you can apply it, using parentheses, in different groupings of numbers and still expect the same result. The two Big Four operations that are associative are addition and multiplication.\r\n\r\nAddition is associative because, for example, the problem (2 + 4) + 7 produces the same result as does the problem 2 + (4 + 7). In other words,\r\n<blockquote>(2 + 4) + 7 = 2 + (4 + 7)</blockquote>\r\nNo matter which pair of numbers you add together first, the answer is the same: 13.\r\n\r\nMultiplication is associative because, for example, the problem 3 × (4 × 5) produces the same result as the problem (3 × 4) × 5. In other words,\r\n<blockquote>3 × (4 × 5) = (3 × 4) × 5</blockquote>\r\nAgain, no matter which pair of numbers you multiply first, both problems yield the same answer: 60.\r\n<h2 id=\"tab4\" >The distributive property</h2>\r\nThe <i>distributive property</i> connects the operations of multiplication and addition. When multiplication is described as \"distributive over addition,\" you can split a multiplication problem into two smaller problems and then add the results.\r\n\r\nFor example, suppose you want to multiply 27 × 6. You know that 27 equals 20 + 7, so you can do this multiplication in two steps:\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">First multiply 20 × 6; then multiply 7 × 6.</p>\r\n<p class=\"child-para\">20 × 6 = 1207 × 6 = 42</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Then add the results.</p>\r\n<p class=\"child-para\">120 + 42 = 162</p>\r\n</li>\r\n</ol>\r\nTherefore, 27 × 6 = 162.","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":33726,"title":"Pre-Algebra","slug":"pre-algebra","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33726"}},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Inverse operations","target":"#tab1"},{"label":"The commutative property","target":"#tab2"},{"label":"The associative property","target":"#tab3"},{"label":"The distributive property","target":"#tab4"}],"relatedArticles":{"fromBook":[{"articleId":207780,"title":"Basic Math & Pre-Algebra For Dummies Cheat Sheet","slug":"basic-math-pre-algebra-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/207780"}},{"articleId":194384,"title":"How to Write Numbers in Scientific Notation","slug":"how-to-write-numbers-in-scientific-notation","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/194384"}},{"articleId":158567,"title":"Converting Metric Units to English Units","slug":"converting-metric-units-to-english-units","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/158567"}},{"articleId":158560,"title":"Working with Exponents, Radicals, & Absolute Value","slug":"a-guide-to-working-with-exponents-radicals-and-absolute-value","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/158560"}},{"articleId":158557,"title":"Conversion Guide for Fractions, Decimals, and Percents","slug":"a-quick-conversion-guide-for-fractions-decimals-and-percents","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/158557"}}],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/291491"}},{"articleId":253710,"title":"Pre-Algebra: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/253710"}},{"articleId":249996,"title":"Solving Simple Equations in Pre-Algebra Problems","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249986"}},{"articleId":249980,"title":"Rearranging Algebraic Equations to Isolate X","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249980"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281978,"slug":"basic-math-pre-algebra-for-dummies-2nd-edition","isbn":"9781119293637","categoryList":["academics-the-arts","math","basic-math"],"amazon":{"default":"//www.amazon.com/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"//www.amazon.ca/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"//www.tkqlhce.com/click-9208661-13710633?url=//www.chapters.indigo.ca/en-ca/books/product/1119293634-item.html&cjsku=978111945484","gb":"//www.amazon.co.uk/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"//www.amazon.de/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"//coursofppt.com/wp-content/uploads/basic-math-and-pre-algebra-for-dummies-2nd-edition-cover-9781119293637-203x255.jpg","width":203,"height":255},"title":"Basic Math & Pre-Algebra For Dummies","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"<p><p><b><b data-author-id=\"9399\">Mark Zegarelli</b></b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com.</p>","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"_links":{"self":"//dummies-api.coursofppt.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119293637&quot;]}]\" id=\"du-slot-65fafa3ee0db9\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = 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years","lifeExpectancySetFrom":"2024-07-10T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":158569},{"headers":{"creationTime":"2017-03-26T13:42:34+00:00","modifiedTime":"2025-03-20T14:27:39+00:00","timestamp":"2025-03-20T15:01:18+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"Conversion Guide for Fractions, Decimals, and Percents","strippedTitle":"conversion guide for fractions, decimals, and percents","slug":"a-quick-conversion-guide-for-fractions-decimals-and-percents","canonicalUrl":"","百度搜指数擎推广":{"metaDescription":"Learn the mathematical equivalents of fractions, decimals, and percents.","noIndex":0,"noFollow":0},"content":"Fractions, decimals, and percents are the three most common ways to give a mathematical description of parts of a whole object. <i>Fractions </i>are common in baking and carpentry when you're using English measurement units (such as cups, gallons, feet, and inches). <i>Decimals </i>are used with dollars and cents, the metric system, and in scientific notation. <i>Percents </i>are used in business when figuring profit and interest rates, as well as in statistics.\r\n\r\nUse the following table as a handy guide when you need to make basic conversions among the three.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th>Fraction</th>\r\n<th>Decimal</th>\r\n<th>Percent</th>\r\n</tr>\r\n<tr>\r\n<td>1/100</td>\r\n<td>0.01</td>\r\n<td>1%</td>\r\n</tr>\r\n<tr>\r\n<td>1/20</td>\r\n<td>0.05</td>\r\n<td>5%</td>\r\n</tr>\r\n<tr>\r\n<td>1/10</td>\r\n<td>0.1</td>\r\n<td>10%</td>\r\n</tr>\r\n<tr>\r\n<td>1/5</td>\r\n<td>0.2</td>\r\n<td>20%</td>\r\n</tr>\r\n<tr>\r\n<td>1/4</td>\r\n<td>0.25</td>\r\n<td>25%</td>\r\n</tr>\r\n<tr>\r\n<td>3/10</td>\r\n<td>0.3</td>\r\n<td>30%</td>\r\n</tr>\r\n<tr>\r\n<td>2/5</td>\r\n<td>0.4</td>\r\n<td>40%</td>\r\n</tr>\r\n<tr>\r\n<td>1/2</td>\r\n<td>0.5</td>\r\n<td>50%</td>\r\n</tr>\r\n<tr>\r\n<td>3/5</td>\r\n<td>0.6</td>\r\n<td>60%</td>\r\n</tr>\r\n<tr>\r\n<td>7/10</td>\r\n<td>0.7</td>\r\n<td>70%</td>\r\n</tr>\r\n<tr>\r\n<td>3/4</td>\r\n<td>0.75</td>\r\n<td>75%</td>\r\n</tr>\r\n<tr>\r\n<td>4/5</td>\r\n<td>0.8</td>\r\n<td>80%</td>\r\n</tr>\r\n<tr>\r\n<td>9/10</td>\r\n<td>0.9</td>\r\n<td>90%</td>\r\n</tr>\r\n<tr>\r\n<td>1</td>\r\n<td>1.0</td>\r\n<td>100%</td>\r\n</tr>\r\n<tr>\r\n<td>2</td>\r\n<td>2.0</td>\r\n<td>200%</td>\r\n</tr>\r\n<tr>\r\n<td>10</td>\r\n<td>10.0</td>\r\n<td>1,000%</td>\r\n</tr>\r\n</tbody>\r\n</table>","description":"Fractions, decimals, and percents are the three most common ways to give a mathematical description of parts of a whole object. <i>Fractions </i>are common in baking and carpentry when you're using English measurement units (such as cups, gallons, feet, and inches). <i>Decimals </i>are used with dollars and cents, the metric system, and in scientific notation. <i>Percents </i>are used in business when figuring profit and interest rates, as well as in statistics.\r\n\r\nUse the following table as a handy guide when you need to make basic conversions among the three.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th>Fraction</th>\r\n<th>Decimal</th>\r\n<th>Percent</th>\r\n</tr>\r\n<tr>\r\n<td>1/100</td>\r\n<td>0.01</td>\r\n<td>1%</td>\r\n</tr>\r\n<tr>\r\n<td>1/20</td>\r\n<td>0.05</td>\r\n<td>5%</td>\r\n</tr>\r\n<tr>\r\n<td>1/10</td>\r\n<td>0.1</td>\r\n<td>10%</td>\r\n</tr>\r\n<tr>\r\n<td>1/5</td>\r\n<td>0.2</td>\r\n<td>20%</td>\r\n</tr>\r\n<tr>\r\n<td>1/4</td>\r\n<td>0.25</td>\r\n<td>25%</td>\r\n</tr>\r\n<tr>\r\n<td>3/10</td>\r\n<td>0.3</td>\r\n<td>30%</td>\r\n</tr>\r\n<tr>\r\n<td>2/5</td>\r\n<td>0.4</td>\r\n<td>40%</td>\r\n</tr>\r\n<tr>\r\n<td>1/2</td>\r\n<td>0.5</td>\r\n<td>50%</td>\r\n</tr>\r\n<tr>\r\n<td>3/5</td>\r\n<td>0.6</td>\r\n<td>60%</td>\r\n</tr>\r\n<tr>\r\n<td>7/10</td>\r\n<td>0.7</td>\r\n<td>70%</td>\r\n</tr>\r\n<tr>\r\n<td>3/4</td>\r\n<td>0.75</td>\r\n<td>75%</td>\r\n</tr>\r\n<tr>\r\n<td>4/5</td>\r\n<td>0.8</td>\r\n<td>80%</td>\r\n</tr>\r\n<tr>\r\n<td>9/10</td>\r\n<td>0.9</td>\r\n<td>90%</td>\r\n</tr>\r\n<tr>\r\n<td>1</td>\r\n<td>1.0</td>\r\n<td>100%</td>\r\n</tr>\r\n<tr>\r\n<td>2</td>\r\n<td>2.0</td>\r\n<td>200%</td>\r\n</tr>\r\n<tr>\r\n<td>10</td>\r\n<td>10.0</td>\r\n<td>1,000%</td>\r\n</tr>\r\n</tbody>\r\n</table>","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":33726,"title":"Pre-Algebra","slug":"pre-algebra","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33726"}},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":207780,"title":"Basic Math & Pre-Algebra For Dummies Cheat Sheet","slug":"basic-math-pre-algebra-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/207780"}},{"articleId":194384,"title":"How to Write Numbers in Scientific Notation","slug":"how-to-write-numbers-in-scientific-notation","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/194384"}},{"articleId":158569,"title":"Important Operations that Make Math Problems Easier","slug":"inverse-operations-and-commutative-associative-and-distributive-properties","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/158569"}},{"articleId":158567,"title":"Converting Metric Units to English Units","slug":"converting-metric-units-to-english-units","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/158567"}},{"articleId":158560,"title":"Working with Exponents, Radicals, & Absolute Value","slug":"a-guide-to-working-with-exponents-radicals-and-absolute-value","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/158560"}}],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/291491"}},{"articleId":253710,"title":"Pre-Algebra: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/253710"}},{"articleId":249996,"title":"Solving Simple Equations in Pre-Algebra Problems","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249986"}},{"articleId":249980,"title":"Rearranging Algebraic Equations to Isolate X","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249980"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281978,"slug":"basic-math-pre-algebra-for-dummies-2nd-edition","isbn":"9781119293637","categoryList":["academics-the-arts","math","basic-math"],"amazon":{"default":"//www.amazon.com/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"//www.amazon.ca/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"//www.tkqlhce.com/click-9208661-13710633?url=//www.chapters.indigo.ca/en-ca/books/product/1119293634-item.html&cjsku=978111945484","gb":"//www.amazon.co.uk/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"//www.amazon.de/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"//coursofppt.com/wp-content/uploads/basic-math-and-pre-algebra-for-dummies-2nd-edition-cover-9781119293637-203x255.jpg","width":203,"height":255},"title":"Basic Math & Pre-Algebra For Dummies","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"<p><p><b><b data-author-id=\"9399\">Mark Zegarelli</b></b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com.</p>","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"_links":{"self":"//dummies-api.coursofppt.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119293637&quot;]}]\" id=\"du-slot-65fafa3ed7d57\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119293637&quot;]}]\" id=\"du-slot-65fafa3ed854d\"></div></div>"},"articleType":{"articleType":"Articles","articleList":null,"content":null,"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2024-06-06T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":158557},{"headers":{"creationTime":"2017-03-26T13:42:36+00:00","modifiedTime":"2025-03-20T14:26:53+00:00","timestamp":"2025-03-20T15:01:18+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"Converting Metric Units to English Units","strippedTitle":"converting metric units to english units","slug":"converting-metric-units-to-english-units","canonicalUrl":"","百度搜指数擎推广":{"metaDescription":"Discover common metric-to-English conversions, including meter to feet, kilometer to mile, liter to gallons, and more.","noIndex":0,"noFollow":0},"content":"The English system of measurements is most commonly used in the United States. In contrast, the metric system is used throughout most of the rest of the world. Converting measurements between the English and metric systems is a common everyday reason to know math. This article gives you some precise metric-to-English conversions, as well as some easy-to-remember conversions that are good enough for most situations.\r\n<table border=\"0\"><caption>Metric-to-English Conversion Table</caption>\r\n<tbody>\r\n<tr>\r\n<th>Metric-to-English Conversions</th>\r\n<th>Metric Units in Plain English</th>\r\n</tr>\r\n<tr>\r\n<td>1 meter ≈ 3.28 feet</td>\r\n<td>A meter is about 3 feet (1 yard).</td>\r\n</tr>\r\n<tr>\r\n<td>1 kilometer ≈ 0.62 miles</td>\r\n<td>A kilometer is about 1/2 mile.</td>\r\n</tr>\r\n<tr>\r\n<td>1 liter ≈ 0.26 gallons</td>\r\n<td>A liter is about 1 quart (1/4 gallon).</td>\r\n</tr>\r\n<tr>\r\n<td>1 kilogram ≈ 2.20 pounds</td>\r\n<td>A kilo is about 2 pounds.</td>\r\n</tr>\r\n<tr>\r\n<td>0°C = 32°F</td>\r\n<td>0°C is cold.</td>\r\n</tr>\r\n<tr>\r\n<td>10°C = 50°F</td>\r\n<td>10°C is cool.</td>\r\n</tr>\r\n<tr>\r\n<td>20°C = 68°F</td>\r\n<td>20°C is warm.</td>\r\n</tr>\r\n<tr>\r\n<td>30°C = 86°</td>\r\n<td>30°C is hot.</td>\r\n</tr>\r\n</tbody>\r\n</table>\r\n<p class=\"Tip\">Here's an easy temperature conversion to remember: 16°C = 61°F.</p>","description":"The English system of measurements is most commonly used in the United States. In contrast, the metric system is used throughout most of the rest of the world. Converting measurements between the English and metric systems is a common everyday reason to know math. This article gives you some precise metric-to-English conversions, as well as some easy-to-remember conversions that are good enough for most situations.\r\n<table border=\"0\"><caption>Metric-to-English Conversion Table</caption>\r\n<tbody>\r\n<tr>\r\n<th>Metric-to-English Conversions</th>\r\n<th>Metric Units in Plain English</th>\r\n</tr>\r\n<tr>\r\n<td>1 meter ≈ 3.28 feet</td>\r\n<td>A meter is about 3 feet (1 yard).</td>\r\n</tr>\r\n<tr>\r\n<td>1 kilometer ≈ 0.62 miles</td>\r\n<td>A kilometer is about 1/2 mile.</td>\r\n</tr>\r\n<tr>\r\n<td>1 liter ≈ 0.26 gallons</td>\r\n<td>A liter is about 1 quart (1/4 gallon).</td>\r\n</tr>\r\n<tr>\r\n<td>1 kilogram ≈ 2.20 pounds</td>\r\n<td>A kilo is about 2 pounds.</td>\r\n</tr>\r\n<tr>\r\n<td>0°C = 32°F</td>\r\n<td>0°C is cold.</td>\r\n</tr>\r\n<tr>\r\n<td>10°C = 50°F</td>\r\n<td>10°C is cool.</td>\r\n</tr>\r\n<tr>\r\n<td>20°C = 68°F</td>\r\n<td>20°C is warm.</td>\r\n</tr>\r\n<tr>\r\n<td>30°C = 86°</td>\r\n<td>30°C is hot.</td>\r\n</tr>\r\n</tbody>\r\n</table>\r\n<p class=\"Tip\">Here's an easy temperature conversion to remember: 16°C = 61°F.</p>","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. 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They are useful in more advanced math, such as algebra, but they also have real-world applications, especially in geometry and measurement.\r\n\r\n<i>Exponents </i>(powers) are repeated multiplication: When you raise a number to the power of an exponent, you multiply that number by itself the number of times indicated by the exponent. For example:\r\n<blockquote>7<sup>2</sup> = 7 × 7 = 49</blockquote>\r\n<blockquote>2<sup>5</sup> = 2 × 2 × 2 × 2 × 2 = 32</blockquote>\r\n<i>Square roots </i>(radicals) are the inverse of exponent 2 — that is, the number that, when multiplied by itself, gives you the indicated value.\r\n\r\n<i>Absolute value </i>is the positive value of a number — that is, the value of a negative number when you drop the minus sign. For example:\r\n\r\nAbsolute value is used to describe numbers that are always positive, such as the distance between two points or the area inside a polygon.","description":"Exponents, radicals, and absolute value are mathematical operations that go beyond addition, subtraction, multiplication, and division. They are useful in more advanced math, such as algebra, but they also have real-world applications, especially in geometry and measurement.\r\n\r\n<i>Exponents </i>(powers) are repeated multiplication: When you raise a number to the power of an exponent, you multiply that number by itself the number of times indicated by the exponent. For example:\r\n<blockquote>7<sup>2</sup> = 7 × 7 = 49</blockquote>\r\n<blockquote>2<sup>5</sup> = 2 × 2 × 2 × 2 × 2 = 32</blockquote>\r\n<i>Square roots </i>(radicals) are the inverse of exponent 2 — that is, the number that, when multiplied by itself, gives you the indicated value.\r\n\r\n<i>Absolute value </i>is the positive value of a number — that is, the value of a negative number when you drop the minus sign. For example:\r\n\r\nAbsolute value is used to describe numbers that are always positive, such as the distance between two points or the area inside a polygon.","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. 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He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com.</p>","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"_links":{"self":"//dummies-api.coursofppt.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119293637&quot;]}]\" id=\"du-slot-65fafa3eb2dad\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119293637&quot;]}]\" id=\"du-slot-65fafa3eb3966\"></div></div>"},"articleType":{"articleType":"Articles","articleList":null,"content":null,"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2024-06-06T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":158560},{"headers":{"creationTime":"2017-03-27T16:56:07+00:00","modifiedTime":"2024-10-05T20:38:44+00:00","timestamp":"2024-10-05T21:01:03+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Study Skills & Test Prep","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33772"},"slug":"study-skills-test-prep","categoryId":33772},{"name":"SAT","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33794"},"slug":"sat","categoryId":33794}],"title":"Digital SAT Math Prep For Dummies Cheat Sheet","strippedTitle":"digital sat math prep for dummies cheat sheet","slug":"sat-math-for-dummies-cheat-sheet","canonicalUrl":"","百度搜指数擎推广":{"metaDescription":"This Cheat Sheet summarizes valuable information on the SAT's Math section, including topics and difficulty of questions, and some helpful advice.","noIndex":0,"noFollow":0},"content":"Although there's no shortcut to success on the math sections of the SAT, you can study and prepare in order to get the best SAT score you possibly can. Knowing what will be on the test (and what won't be) is key so you know what to brush up on.\r\n\r\nAlso, some basic strategy goes a long way toward helping you get the best score you can. Finally, mapping out a time-management plan to answer (and skip!) the right questions can really boost your score.","description":"Although there's no shortcut to success on the math sections of the SAT, you can study and prepare in order to get the best SAT score you possibly can. Knowing what will be on the test (and what won't be) is key so you know what to brush up on.\r\n\r\nAlso, some basic strategy goes a long way toward helping you get the best score you can. Finally, mapping out a time-management plan to answer (and skip!) the right questions can really boost your score.","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is an instructor and math and test prep tutor in New Jersey. He is the author of <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, ACT Math For Dummies, Logic For Dummies,</i> and <i>Calculus II For Dummies</i>. In his spare time, he enjoys traveling and learning foreign languages.</p> ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33794,"title":"SAT","slug":"sat","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33794"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[],"fromCategory":[{"articleId":299987,"title":"Digital SAT Prep 2024 For Dummies Cheat Sheet","slug":"digital-sat-prep-2024-for-dummies-cheat-sheet","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/299987"}},{"articleId":293029,"title":"SAT Prep 2023 For Dummies Cheat Sheet","slug":"sat-prep-2023-for-dummies-cheat-sheet","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/293029"}},{"articleId":277844,"title":"10 Ways to Get the Most from the Practice SATs","slug":"10-ways-to-get-the-most-from-the-practice-sats","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/277844"}},{"articleId":277839,"title":"10 Mistakes You Won’t Make on the SAT","slug":"10-mistakes-you-wont-make-on-the-sat","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/277839"}},{"articleId":277836,"title":"Strategies for the SAT Reading Test","slug":"strategies-for-the-sat-reading-test","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/277836"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":288189,"slug":"sat-math-for-dummies-with-online-practice-2nd-edition","isbn":"9781394207381","categoryList":["academics-the-arts","study-skills-test-prep","sat"],"amazon":{"default":"//www.amazon.com/gp/product/1394207387/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"//www.amazon.ca/gp/product/1394207387/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"//www.tkqlhce.com/click-9208661-13710633?url=//www.chapters.indigo.ca/en-ca/books/product/1394207387-item.html&cjsku=978111945484","gb":"//www.amazon.co.uk/gp/product/1394207387/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"//www.amazon.de/gp/product/1394207387/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"//coursofppt.com/wp-content/uploads/digital-sat-math-prep-for-dummies-3rd-edition-cover-9781394207381-199x255.jpg","width":199,"height":255},"title":"Digital SAT Math Prep For Dummies","testBankPinActivationLink":"//testbanks.wiley.com","bookOutOfPrint":true,"authorsInfo":"<p><b><b data-author-id=\"9399\">Mark Zegarelli</b></b> is an instructor and math and test prep tutor in New Jersey. He is the author of <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, ACT Math For Dummies, Logic For Dummies,</i> and <i>Calculus II For Dummies</i>. In his spare time, he enjoys traveling and learning foreign languages.</p>","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is an instructor and math and test prep tutor in New Jersey. He is the author of <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, ACT Math For Dummies, Logic For Dummies,</i> and <i>Calculus II For Dummies</i>. In his spare time, he enjoys traveling and learning foreign languages.</p> ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"_links":{"self":"//dummies-api.coursofppt.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;study-skills-test-prep&quot;,&quot;sat&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781394207381&quot;]}]\" id=\"du-slot-651f240f35623\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;study-skills-test-prep&quot;,&quot;sat&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781394207381&quot;]}]\" id=\"du-slot-651f240f35eed\"></div></div>"},"articleType":{"articleType":"Cheat Sheet","articleList":[{"articleId":192329,"title":"Topics Covered in the Math Sections of the SAT","slug":"topics-covered-in-the-math-sections-of-the-sat","categoryList":[],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/192329"}},{"articleId":192327,"title":"Managing Time on the SAT Math Sections","slug":"managing-time-on-the-sat-math-sections","categoryList":[],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/192327"}},{"articleId":192326,"title":"Using Calculators on the SAT","slug":"using-calculators-on-the-sat","categoryList":[],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/192326"}}],"content":[{"title":"Overview of SAT math topics","thumb":null,"image":null,"content":"<p>The math covered on the SAT is very closely tracked to what&#8217;s covered in most U.S. high school math classes. So if you’re a current or recent U.S. high school student, you’re probably familiar with most of this curriculum.</p>\n<p>The SAT breaks this down into four general areas of study: algebra, problem solving and data analysis, advanced math, and geometry and trigonometry. In this section, I give you an overview of each of these topics.</p>\n<ul>\n<li><strong>Algebra</strong> centers on the linear function and other information covered in a typical high school Algebra I class. To answer SAT math questions in this area, you’ll need to feel comfortable working with the following:\n<ul>\n<li>Evaluating, simplifying, and factoring algebra expressions</li>\n<li>Solving algebraic equations and inequalities</li>\n<li>Working with linear functions in four complementary ways: words, tables, graphs, and equations</li>\n<li>Solving systems of equations (both linear and non-linear), and identifying when such systems have either no solution or infinitely many solutions</li>\n</ul>\n</li>\n<li><strong>Problem Solving and Data Analysis</strong> focuses on a relatively short list of problem-solving techniques:\n<ul>\n<li>Working with ratios, proportional equations, and percentages</li>\n<li>Relying on a basic understanding of statistics and probability</li>\n<li>Applying these techniques to information presented visually in tables and graphs</li>\n</ul>\n</li>\n<li><strong>Advanced Math</strong> requires you to understand a core of information covered in high school Algebra II:\n<ul>\n<li>Working with functions using notation, and knowing how to graph a core of basic functions and their most elementary transformations</li>\n<li>Understanding how to work with and graph polynomials, especially linear, quadratic, cubic, and quartic polynomials</li>\n<li>Graphing quadratic functions using standard, vertex, and factored forms</li>\n<li>Graphing exponential and radical equations</li>\n</ul>\n</li>\n<li><strong>Geometry and Trigonometry</strong> covers math that focuses on shapes and solids in two and three dimensions:\n<ul>\n<li>Solving problems using basic geometry and circles on the <em>xy</em>-plane</li>\n<li>Working in-depth with right triangles, the Pythagorean theorem, and trigonometric ratios such as sine, cosine, and tangent</li>\n</ul>\n</li>\n</ul>\n<p>Almost as important as knowing which math topics are covered on the SAT is knowing the topics you can safely avoid. Here’s a list of the math skills that you don’t need for the SAT:</p>\n<ul>\n<li>Doing big number-crunching — large numbers or endless calculations, such as standard deviations</li>\n<li>Writing geometry proofs</li>\n<li>The base<em> e</em></li>\n<li>Logarithms and the natural log ln</li>\n<li>The complex plane and the irrational number <em>i</em></li>\n<li>Limits, derivatives, and integrals</li>\n<li>Summations using sigma notation Σ</li>\n</ul>\n"},{"title":"SAT math strategy Q&A","thumb":null,"image":null,"content":"<p>When it comes to doing well on the SAT, your test-taking strategy is a small but important piece of the puzzle. And this strategy also extends to knowing which questions to answer and which to skip, depending on the score you’re currently striving for.</p>\n<p>These questions and answers will fill you in on this essential information.</p>\n<p><a name=\"_Toc78452623\"></a><strong>Isn’t there some way to get a good SAT Math score without actually knowing math?</strong></p>\n<p>No. I’d love to tell you otherwise, but no.</p>\n<p>If the key to getting a great score were, say, choosing Answer C on every question, the name of this article would be &#8220;Answer C Math For Dummies Cheat Sheet&#8221; and it would be a <em>lot</em> shorter.</p>\n<p>While you fully absorb that difficult truth, I will add that there’s a reasonable amount of strategy you should absolutely know before taking your first SAT. And while you may think that lots of students already know this stuff, plenty of others don’t — yet.</p>\n<p>I don’t want you to be one of them. So read on.</p>\n<p><a name=\"_Toc78452624\"></a><strong>Is there a penalty for guessing?</strong></p>\n<p>If you have an older brother or sister who took the SAT before 2016, they may remember the old format, which had a penalty for filling in a wrong answer.</p>\n<p>So please take note: <strong>The SAT in its current form has no penalty for filling in a wrong answer. </strong>This goes for all four sections, the Reading and Writing as well as the Math sections.</p>\n<p>Obviously, then, you want to make sure that you fill in at least some answer for each multiple-choice question on the two math sections. That’s 33 questions, so by pure chance, you can expect to get about 8 of these questions right just by making wild guesses.</p>\n<p>Let’s take that thinking a step further: If you <em>don’t</em> fill in guesses for all the questions you don’t have time to think about, you’ll be competing against a ton of other students who <em>are</em> guessing. So, bottom line, you can’t afford <em>not</em> to guess every multiple-choice question you don’t know the answer to.</p>\n<p>What about the fill-in-the-blank questions? Well, because these questions are entirely open ended, you don’t have much chance of answering them correctly with a wild guess. But if you have any idea what the answer might be, go ahead and enter it. Worst case, doing this won’t lose you any points.</p>\n<p><a name=\"_Toc78452625\"></a><strong>Are some questions harder than others?</strong></p>\n<p>Generally speaking, SAT Math questions fall into three categories of difficulty: easy, medium, and hard. Both sections of the new SAT are identical in this regard. The table below shows the rough breakdown of questions by difficulty levels.</p>\n<p><strong>Easy, Medium, and Hard Questions</strong></p>\n<table>\n<tbody>\n<tr>\n<td width=\"78\"><strong>Difficulty Level</strong></td>\n<td width=\"78\"><strong>Question Number</strong></td>\n</tr>\n<tr>\n<td width=\"78\">Easy</td>\n<td width=\"78\">1-7</td>\n</tr>\n<tr>\n<td width=\"78\">Medium</td>\n<td width=\"78\">8-16</td>\n</tr>\n<tr>\n<td width=\"78\">Hard</td>\n<td width=\"78\">16-22</td>\n</tr>\n</tbody>\n</table>\n<p>Remember that <em>every</em> question counts for one point toward your raw score, which directly affects your scaled score (200–800). So, unlike the tests you take in school, the easiest and hardest questions on the SAT both have the same value.<a name=\"_Toc78452626\"></a></p>\n<p><strong>Do I have to answer every question?</strong></p>\n<p>The short answer is, no, you don’t have to answer every SAT math question to get a good score. In fact, depending on your current performance level on practice tests, it may very well be to your benefit <strong><em>not</em></strong> to answer all of the questions.</p>\n<p>This piece of strategy definitely goes against a lot of your training as a high school student. After all, in most of your classes, you can’t get an A or even a B on a test without answering just about all of the questions. If you only answer 75 percent and skip the rest, even if you answer perfectly, probably the best you can hope for is a C.</p>\n<p>However, the situation with the SAT is entirely different. On the SAT, you can get a 500 math score by answering only about half of the questions on the test correctly. Think about it — a respectable score on the SAT would be a failing grade on a math test at school!</p>\n<p>For now — and this goes double if you’re a perfectionist — simply let go of the compulsive need to answer all 44 math questions on the SAT. Until you’re already scoring 740+ on your practice tests, answering all of the questions would be a poor allocation of your time.</p>\n<p>If you’re answering all of the questions, you’re probably rushing through questions that are within your reach, getting them wrong, and losing points you should be getting as a result.</p>\n<p><strong>When’s the latest I can take the SAT and still get into school?</strong></p>\n<p>Most students take the SAT with their class in May or June of their junior year. They may try it out before that, but somehow, it doesn’t feel real until their whole class is doing it, too.</p>\n<p>But if that’s the beginning, it doesn’t have to be the end. Usually, December of your senior year is your last shot at the SAT if you want to start college the following fall. Unless you’re applying for early acceptance, most colleges don’t make their final decisions until after the December SAT scores have been posted.</p>\n"},{"title":"How many SAT math questions should I answer?","thumb":null,"image":null,"content":"<p>The answer to this question depends on your current score, which I break down into three basic scenarios:</p>\n<h3><a name=\"_Toc78452628\"></a>Clearing 500</h3>\n<p>Most schools prefer to enroll students who have an SAT composite score of at least 1,000, which is approximately 500 on both the Reading and Writing and the Math tests.</p>\n<p>If your Reading and Writing score is 550 or higher, you may be able to get away with a Math score that’s slightly less than 500. Even so, a good first goal would be to break 500 on the Math test.</p>\n<p>To get this score, you need to answer about 22 of the 44 SAT math questions correctly. To this end, refer to the table above and then plan to do the following:</p>\n<ul>\n<li>Attempt to answer <em>all</em> 14 easy questions correctly.</li>\n<li>Choose 8 out of 16 medium questions to answer correctly and guess the rest.</li>\n<li>Guess on the 14 hard questions.</li>\n</ul>\n<p>I know it seems weird to guess so many questions. But the SAT is different from the tests you take in school, where you need to get at least 80 percent right to get a decent grade.</p>\n<p>Choosing 22 easy and medium questions to focus on gives you almost three minutes per question, which increases your changes of answering more questions correctly. And remember that you have a 25 percent chance of guessing each hard multiple-choice question correctly, which will give you some wiggle room to make a few mistakes along the way with the easier questions.</p>\n<p>Believe me, in my experience working with hundreds of students, if you’re simply trying to break 500, you probably need to give yourself <em>more </em>time by answering <em>fewer</em> questions.</p>\n<h3><a name=\"_Toc78452629\"></a>Breaking solidly beyond 600</h3>\n<p>At the next level are students applying for colleges that strongly encourage a composite SAT score of 1,200 or more. That means aiming for at least a 600 score in math, which requires approximately 30 correct answers.</p>\n<p>Here’s what I recommend (again, referring to the table for question difficulty):</p>\n<ul>\n<li>Attempt to answer <em>all</em> 14 easy questions correctly.</li>\n<li>Attempt to answer <em>all </em>16 medium questions correctly.</li>\n<li>Guess on the 14 hard questions.</li>\n</ul>\n<p>As when breaking 500, you still have a 25 percent shot at answering each hard multiple-choice question.</p>\n<h3><a name=\"_Toc78452630\"></a>Reaching 700 and beyond</h3>\n<p>If you’re striving to break 1,400 or even 1,500 on your SAT composite score, you know that there’s no easy answer. You’ll want to get a math score of 700 or more, with a little wiggle room if you’re confident of scoring 750 or more on the Reading and Writing test. This means answering about 38 out of 44 math questions correctly.</p>\n<ul>\n<li>Attempt to answer <em>all</em> 14 easy questions correctly.</li>\n<li>Attempt to answer <em>all </em>16 medium questions correctly.</li>\n<li>Choose 8 of the 14 hard questions to attempt to answer and guess the rest.</li>\n</ul>\n<p>OK, we both know that if you’re aiming to break 700, you may not feel comfortable strictly “guessing” 8 hard questions. But please, please, please don’t feel you have to answer every question! With limited time to allocate, almost every student will do better to focus on a subset of the hard questions and <em>get them right</em> rather than waste time on the two or three hardest questions <em>they&#8217;ll</em> <em>probably get wrong anyway.</em></p>\n<p>The good news is that you’re obviously a strong student with a well-practiced set of study skills. I recommend getting a private tutor if you don’t already have one (but you already have one, don’t you?.</p>\n<p>Take as many practice tests as you can, and then comb through your wrong answers and do your best to figure out where you went wrong. If your math teacher is supportive, bring especially hard SAT problems to them — they’ll almost certainly be willing to help!<a name=\"_Toc78452631\"></a></p>\n"}],"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"One year","lifeExpectancySetFrom":"2024-10-05T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":208986},{"headers":{"creationTime":"2019-02-13T02:02:54+00:00","modifiedTime":"2024-08-07T14:56:15+00:00","timestamp":"2024-08-07T15:01:03+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"Pre-Algebra Practice Questions: Finding the Volume of Prisms and Cylinders","strippedTitle":"pre-algebra practice questions: finding the volume of prisms and cylinders","slug":"pre-algebra-practice-questions-finding-volume-prisms-cylinders","canonicalUrl":"","百度搜指数擎推广":{"metaDescription":"To find the volume of a prism or cylinder, you can use the following formula, where A b is the area of the base and h is the height: V = A b x h --> Practice qu","noIndex":0,"noFollow":0},"content":"To find the volume of a prism or cylinder, you can use the following formula, where <em>A<sub>b</sub></em> is the area of the base and <em>h</em> is the height:\r\n<pre><em>V</em> = <em>A<sub>b</sub></em> x <em>h</em></pre>\r\n<!--<img class=\"alignnone size-full wp-image-249965\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_3401.gif\" alt=\"PREALGEBRA_3401\" width=\"75\" height=\"27\" />-->\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n \t<li>Find the volume of a prism with a base that has an area of 6 square centimeters and a height of 3 centimeters.</li>\r\n \t<li>Figure out the approximate volume of a cylinder whose base has a radius of 7 millimeters and whose height is 16 millimeters.</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n \t<li>18 cubic centimeters\r\n \t<pre><em>V</em> = <em>A<sub>b</sub></em> x <em>h</em> = 6cm<sup>2</sup> x 3cm = 18cm<sup>3</sup></pre>\r\n<!--<img class=\"alignnone size-full wp-image-249966\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_3402.gif\" alt=\"PREALGEBRA_3402\" width=\"244\" height=\"28\" />--></li>\r\n \t<li>Approximately 2,461.76 cubic millimeters\r\n<p>First, use the area formula for a circle to find the area of the base:</p>\r\n \t <pre><em>A<sub>b</sub></em> = <em>π</em> x <em>r<sup>2</sup>\r\n ≅ 3.14 x (7mm)<sup>2</sup>\r\n = 3.14 x 49mm<sup>2</sup>\r\n = 153.86mm<sup>2</sup></pre>\r\n<!--<img class=\"alignnone size-full wp-image-249967\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_3403.gif\" alt=\"PREALGEBRA_3403\" width=\"144\" height=\"120\" />-->\r\n\r\nPlug this result into the formula for the volume of a cylinder:\r\n \t<pre><em>V</em> = <em>A<sub>b</sub></em> x <em>h\r\n = 153.86mm<sup>2</sup> x 16mm\r\n = 2,461.76mm<sup>3</sup></pre>\r\n<!--<img class=\"alignnone size-full wp-image-249968\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_3404.gif\" alt=\"PREALGEBRA_3404\" width=\"185\" height=\"84\" />--></li>\r\n</ol>","description":"To find the volume of a prism or cylinder, you can use the following formula, where <em>A<sub>b</sub></em> is the area of the base and <em>h</em> is the height:\r\n<pre><em>V</em> = <em>A<sub>b</sub></em> x <em>h</em></pre>\r\n<!--<img class=\"alignnone size-full wp-image-249965\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_3401.gif\" alt=\"PREALGEBRA_3401\" width=\"75\" height=\"27\" />-->\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n \t<li>Find the volume of a prism with a base that has an area of 6 square centimeters and a height of 3 centimeters.</li>\r\n \t<li>Figure out the approximate volume of a cylinder whose base has a radius of 7 millimeters and whose height is 16 millimeters.</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n \t<li>18 cubic centimeters\r\n \t<pre><em>V</em> = <em>A<sub>b</sub></em> x <em>h</em> = 6cm<sup>2</sup> x 3cm = 18cm<sup>3</sup></pre>\r\n<!--<img class=\"alignnone size-full wp-image-249966\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_3402.gif\" alt=\"PREALGEBRA_3402\" width=\"244\" height=\"28\" />--></li>\r\n \t<li>Approximately 2,461.76 cubic millimeters\r\n<p>First, use the area formula for a circle to find the area of the base:</p>\r\n \t <pre><em>A<sub>b</sub></em> = <em>π</em> x <em>r<sup>2</sup>\r\n ≅ 3.14 x (7mm)<sup>2</sup>\r\n = 3.14 x 49mm<sup>2</sup>\r\n = 153.86mm<sup>2</sup></pre>\r\n<!--<img class=\"alignnone size-full wp-image-249967\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_3403.gif\" alt=\"PREALGEBRA_3403\" width=\"144\" height=\"120\" />-->\r\n\r\nPlug this result into the formula for the volume of a cylinder:\r\n \t<pre><em>V</em> = <em>A<sub>b</sub></em> x <em>h\r\n = 153.86mm<sup>2</sup> x 16mm\r\n = 2,461.76mm<sup>3</sup></pre>\r\n<!--<img class=\"alignnone size-full wp-image-249968\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_3404.gif\" alt=\"PREALGEBRA_3404\" width=\"185\" height=\"84\" />--></li>\r\n</ol>","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":33726,"title":"Pre-Algebra","slug":"pre-algebra","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33726"}},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Practice questions","target":"#tab1"},{"label":"Answers and explanations","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":253710,"title":"Pre-Algebra: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/253710"}},{"articleId":249996,"title":"Solving Simple Equations in Pre-Algebra Problems","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249986"}},{"articleId":249980,"title":"Rearranging Algebraic Equations to Isolate X","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249980"}},{"articleId":249971,"title":"Pre-Algebra: Cross-Multiply to Solve Equations","slug":"pre-algebra-practice-questions-cross-multiply-solve-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249971"}}],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/291491"}},{"articleId":253710,"title":"Pre-Algebra: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/253710"}},{"articleId":249996,"title":"Solving Simple Equations in Pre-Algebra Problems","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249986"}},{"articleId":249980,"title":"Rearranging Algebraic Equations to Isolate X","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249980"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281980,"slug":"basic-math-and-pre-algebra-workbook-for-dummies-with-online-practice-3rd-edition","isbn":"9781119357513","categoryList":["academics-the-arts","math","basic-math"],"amazon":{"default":"//www.amazon.com/gp/product/1119357519/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"//www.amazon.ca/gp/product/1119357519/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"//www.tkqlhce.com/click-9208661-13710633?url=//www.chapters.indigo.ca/en-ca/books/product/1119357519-item.html&cjsku=978111945484","gb":"//www.amazon.co.uk/gp/product/1119357519/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"//www.amazon.de/gp/product/1119357519/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"//coursofppt.com/wp-content/uploads/basic-math-and-pre-algebra-workbook-for-dummies-3rd-edition-cover-9781119357513-204x255.jpg","width":204,"height":255},"title":"Basic Math & Pre-Algebra Workbook For Dummies with Online Practice","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p><b data-author-id=\"9399\">Mark Zegarelli</b> is a math and test prep teacher who has written a wide variety of basic math and pre-algebra books in the <i>For Dummies</i> series. </p>","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"_links":{"self":"//dummies-api.coursofppt.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119357513&quot;]}]\" id=\"du-slot-64d1072f6f6ab\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119357513&quot;]}]\" id=\"du-slot-64d1072f6fb69\"></div></div>"},"articleType":{"articleType":"Articles","articleList":null,"content":null,"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2024-08-07T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":249964},{"headers":{"creationTime":"2017-03-26T18:17:12+00:00","modifiedTime":"2024-07-14T13:05:10+00:00","timestamp":"2024-07-14T15:01:02+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Calculus","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33723"},"slug":"calculus","categoryId":33723}],"title":"Finding the Area of a Surface of Revolution","strippedTitle":"finding the area of a surface of revolution","slug":"finding-the-area-of-a-surface-of-revolution","canonicalUrl":"","百度搜指数擎推广":{"metaDescription":"The nice thing about finding the area of a surface of revolution is that there’s a formula you can use. Memorize it and you’re halfway done. To find the area of","noIndex":0,"noFollow":0},"content":"<p>The nice thing about finding the area of a surface of revolution is that there’s a formula you can use. Memorize it and you’re halfway done.</p>\r\n<p>To find the area of a surface of revolution between <i>a</i> and <i>b</i><i>,</i> watch this video tutorial or follow the steps below:</p>\r\n<div class='x2 x2-top'><div class=\"video-player-organism\"></div></div>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314778.image0.png\" width=\"153\" height=\"57\" alt=\"image0.png\"/>\r\n<p>This formula looks long and complicated, but it makes more sense when you spend a minute thinking about it. The integral is made from two pieces:</p>\r\n<ul class=\"level-one\">\r\n <li><p class=\"first-para\">The arc-length formula, which measures the length along the surface </p>\r\n </li>\r\n <li><p class=\"first-para\">The formula for the circumference of a circle, which measures the length around the surface</p>\r\n </li>\r\n</ul>\r\n<p>So multiplying these two pieces together is similar to multiplying length and width to find the area of a rectangle. In effect, the formula allows you to measure surface area as an infinite number of little rectangles.</p>\r\n<p>When you’re measuring the surface of revolution of a function <i>f</i>(<i>x</i>) around the <i>x</i>-axis, substitute <i>r</i> = <i>f</i>(<i>x</i>) into the formula:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314779.image1.png\" width=\"188\" height=\"53\" alt=\"image1.png\"/>\r\n<p>For example, suppose that you want to find the area of revolution that’s shown in this figure.</p>\r\n<div class=\"imageBlock\" style=\"width:286px;\"><img src=\"//coursofppt.com/wp-content/uploads/314780.image2.jpg\" width=\"286\" height=\"400\" alt=\"Measuring the surface of revolution of <i>y</i> = <i>x</i><sup>3</sup> between <i>x</i> = 0 and <i>\"/><div class=\"imageCaption\">Measuring the surface of revolution of <i>y</i> = <i>x</i><sup>3</sup> between <i>x</i> = 0 and <i>x</i> = 1.</div></div>\r\n<p>To solve this problem, first note that for </p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314781.image3.png\" width=\"149\" height=\"29\" alt=\"image3.png\"/>\r\n<p>So set up the problem as follows:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314782.image4.png\" width=\"168\" height=\"52\" alt=\"image4.png\"/>\r\n<p>To start off, simplify the problem a bit:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314783.image5.png\" width=\"135\" height=\"52\" alt=\"image5.png\"/>\r\n<p>You can solve this problem by using the following variable substitution:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314784.image6.png\" width=\"100\" height=\"51\" alt=\"image6.png\"/>\r\n<p>Now substitute <i>u</i> for 1+ 9<i>x</i><sup>4</sup> and </p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314785.image7.png\" width=\"41\" height=\"37\" alt=\"image7.png\"/>\r\n<p>for <i>x</i><sup>3</sup> <i>dx </i>into the equation:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314786.image8.png\" width=\"112\" height=\"52\" alt=\"image8.png\"/>\r\n<p>Notice that you change the limits of integration: When <i>x</i> = 0, <i>u</i> = 1. And when <i>x</i> = 1, <i>u</i> = 10.</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314787.image9.png\" width=\"96\" height=\"52\" alt=\"image9.png\"/>\r\n<p>Now you can perform the integration:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314788.image10.png\" width=\"117\" height=\"119\" alt=\"image10.png\"/>\r\n<p>Finally, evaluate the definite integral:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314789.image11.png\" width=\"136\" height=\"115\" alt=\"image11.png\"/>","description":"<p>The nice thing about finding the area of a surface of revolution is that there’s a formula you can use. Memorize it and you’re halfway done.</p>\r\n<p>To find the area of a surface of revolution between <i>a</i> and <i>b</i><i>,</i> watch this video tutorial or follow the steps below:</p>\r\n<div class='x2 x2-top'><div class=\"video-player-organism\"></div></div>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314778.image0.png\" width=\"153\" height=\"57\" alt=\"image0.png\"/>\r\n<p>This formula looks long and complicated, but it makes more sense when you spend a minute thinking about it. The integral is made from two pieces:</p>\r\n<ul class=\"level-one\">\r\n <li><p class=\"first-para\">The arc-length formula, which measures the length along the surface </p>\r\n </li>\r\n <li><p class=\"first-para\">The formula for the circumference of a circle, which measures the length around the surface</p>\r\n </li>\r\n</ul>\r\n<p>So multiplying these two pieces together is similar to multiplying length and width to find the area of a rectangle. In effect, the formula allows you to measure surface area as an infinite number of little rectangles.</p>\r\n<p>When you’re measuring the surface of revolution of a function <i>f</i>(<i>x</i>) around the <i>x</i>-axis, substitute <i>r</i> = <i>f</i>(<i>x</i>) into the formula:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314779.image1.png\" width=\"188\" height=\"53\" alt=\"image1.png\"/>\r\n<p>For example, suppose that you want to find the area of revolution that’s shown in this figure.</p>\r\n<div class=\"imageBlock\" style=\"width:286px;\"><img src=\"//coursofppt.com/wp-content/uploads/314780.image2.jpg\" width=\"286\" height=\"400\" alt=\"Measuring the surface of revolution of <i>y</i> = <i>x</i><sup>3</sup> between <i>x</i> = 0 and <i>\"/><div class=\"imageCaption\">Measuring the surface of revolution of <i>y</i> = <i>x</i><sup>3</sup> between <i>x</i> = 0 and <i>x</i> = 1.</div></div>\r\n<p>To solve this problem, first note that for </p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314781.image3.png\" width=\"149\" height=\"29\" alt=\"image3.png\"/>\r\n<p>So set up the problem as follows:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314782.image4.png\" width=\"168\" height=\"52\" alt=\"image4.png\"/>\r\n<p>To start off, simplify the problem a bit:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314783.image5.png\" width=\"135\" height=\"52\" alt=\"image5.png\"/>\r\n<p>You can solve this problem by using the following variable substitution:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314784.image6.png\" width=\"100\" height=\"51\" alt=\"image6.png\"/>\r\n<p>Now substitute <i>u</i> for 1+ 9<i>x</i><sup>4</sup> and </p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314785.image7.png\" width=\"41\" height=\"37\" alt=\"image7.png\"/>\r\n<p>for <i>x</i><sup>3</sup> <i>dx </i>into the equation:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314786.image8.png\" width=\"112\" height=\"52\" alt=\"image8.png\"/>\r\n<p>Notice that you change the limits of integration: When <i>x</i> = 0, <i>u</i> = 1. And when <i>x</i> = 1, <i>u</i> = 10.</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314787.image9.png\" width=\"96\" height=\"52\" alt=\"image9.png\"/>\r\n<p>Now you can perform the integration:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314788.image10.png\" width=\"117\" height=\"119\" alt=\"image10.png\"/>\r\n<p>Finally, evaluate the definite integral:</p>\r\n<img src=\"//coursofppt.com/wp-content/uploads/314789.image11.png\" width=\"136\" height=\"115\" alt=\"image11.png\"/>","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33723,"title":"Calculus","slug":"calculus","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33723"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":208670,"title":"Calculus II For Dummies Cheat Sheet","slug":"calculus-ii-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","calculus"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/208670"}},{"articleId":179236,"title":"Computing Integrals and Representing Integrals as Functions","slug":"computing-integrals-and-representing-integrals-as-functions","categoryList":["academics-the-arts","math","calculus"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/179236"}},{"articleId":179235,"title":"Drawing with 3-D Cartesian Coordinates","slug":"drawing-with-3-d-cartesian-coordinates","categoryList":["academics-the-arts","math","calculus"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/179235"}},{"articleId":179234,"title":"Evaluating Triple Integrals","slug":"evaluating-triple-integrals","categoryList":["academics-the-arts","math","calculus"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/179234"}},{"articleId":179233,"title":"Find the Area Between Two Functions","slug":"find-the-area-between-two-functions","categoryList":["academics-the-arts","math","calculus"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/179233"}}],"fromCategory":[{"articleId":256336,"title":"Solve a Difficult Limit Problem Using the Sandwich Method","slug":"solve-a-difficult-limit-problem-using-the-sandwich-method","categoryList":["academics-the-arts","math","calculus"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/256336"}},{"articleId":255765,"title":"Solve Limit Problems on a Calculator Using Graphing Mode","slug":"solve-limit-problems-on-a-calculator-using-graphing-mode","categoryList":["academics-the-arts","math","calculus"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/255765"}},{"articleId":255755,"title":"Solve Limit Problems on a Calculator Using the Arrow-Number","slug":"solve-limit-problems-on-a-calculator-using-the-arrow-number","categoryList":["academics-the-arts","math","calculus"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/255755"}},{"articleId":255261,"title":"Limit and Continuity Graphs: Practice Questions","slug":"limit-and-continuity-graphs-practice-questions","categoryList":["academics-the-arts","math","calculus"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/255261"}},{"articleId":255255,"title":"Use the Vertical Line Test to Identify a Function","slug":"use-the-vertical-line-test-to-identify-a-function","categoryList":["academics-the-arts","math","calculus"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/255255"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282046,"slug":"calculus-ii-for-dummies-2nd-edition","isbn":"9781119986614","categoryList":["academics-the-arts","math","calculus"],"amazon":{"default":"//www.amazon.com/gp/product/1119986613/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"//www.amazon.ca/gp/product/1119986613/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"//www.tkqlhce.com/click-9208661-13710633?url=//www.chapters.indigo.ca/en-ca/books/product/1119986613-item.html&cjsku=978111945484","gb":"//www.amazon.co.uk/gp/product/1119986613/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"//www.amazon.de/gp/product/1119986613/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"//coursofppt.com/wp-content/uploads/calculus-ii-for-dummies-3rd-edition-cover-1119986613-203x255.jpg","width":203,"height":255},"title":"Calculus II For Dummies","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"<p><p><b><b data-author-id=\"9399\">Mark Zegarelli</b></b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com.</p>","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"_links":{"self":"//dummies-api.coursofppt.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;calculus&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119986614&quot;]}]\" id=\"du-slot-64b1632edf82d\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;calculus&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119986614&quot;]}]\" id=\"du-slot-64b1632ee0108\"></div></div>"},"articleType":{"articleType":"Videos","articleList":null,"content":null,"videoInfo":{"videoId":"694655204001","name":"How to Find the Surface Area of a Surface Revolution","accountId":"622696558001","playerId":"default","thumbnailUrl":"//cf-images.us-east-1.prod.boltdns.net/v1/static/622696558001/76f0595c-da6a-42d9-ac74-6f5d34e4edc9/a0a533ae-7b93-47e8-a41c-befd77598689/160x90/match/image.jpg","description":"The surface area of a surface of revolution applies to many three-dimensional, radially symmetrical shapes. Formulas in this calculus video tutorial reveal how to estimate, measure, and solve for the surface area of a three-dimensional object like a","uploadDate":"2023-07-15T08:18:07.281Z"}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2024-07-13T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":178407},{"headers":{"creationTime":"2017-03-26T11:06:08+00:00","modifiedTime":"2024-07-10T19:00:07+00:00","timestamp":"2024-07-10T21:01:03+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"Evaluating an Expression with Only Multiplication & Division","strippedTitle":"evaluating an expression with only multiplication & division","slug":"applying-order-of-operations-to-expressions-with-only-multiplication-and-division","canonicalUrl":"","百度搜指数擎推广":{"metaDescription":"Some expressions contain only multiplication and division. When this is the case, the rule for evaluating the expression is pretty straightforward. When an expr","noIndex":0,"noFollow":0},"content":"Some expressions contain only multiplication and division. When this is the case, the rule for evaluating the expression is pretty straightforward. When an expression contains only multiplication and division, evaluate it step by step from left to right.\r\n<h2 id=\"tab1\" >The Three Types of Big Four Expressions</h2>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th>Expression</th>\r\n<th>Example</th>\r\n<th>Rule</th>\r\n</tr>\r\n<tr>\r\n<td>Contains only addition and subtraction</td>\r\n<td>12 + 7 – 6 – 3 + 8</td>\r\n<td>Evaluate left to right.</td>\r\n</tr>\r\n<tr>\r\n<td>Contains only multiplication and division</td>\r\n<td>18 ÷ 3 x 7 ÷ 14</td>\r\n<td>Evaluate left to right.</td>\r\n</tr>\r\n<tr>\r\n<td>Mixed-operator expression: contains a combination of\r\naddition/subtraction and multiplication/division</td>\r\n<td>9 + 6 ÷ 3</td>\r\n<td>1. Evaluate multiplication and division left to right.\r\n2. Evaluate addition and subtraction left to right.</td>\r\n</tr>\r\n</tbody>\r\n</table>\r\n<p class=\"Remember\">Suppose you want to evaluate this expression:</p>\r\n\r\n<blockquote>9 × 2 ÷ 6 ÷ 3 × 2</blockquote>\r\nAgain, the expression contains only multiplication and division, so you can move from left to right, starting with 9 x 2:\r\n<blockquote>= 18 ÷ 6 ÷ 3 × 2\r\n= 3 ÷ 3 × 2\r\n= 1 × 2\r\n= 2</blockquote>\r\nNotice that the expression shrinks one number at a time until all that’s left is 2. So\r\n<blockquote>9 × 2 ÷ 6 ÷ 3 × 2 = 2</blockquote>\r\nHere’s another quick example:\r\n<blockquote>−2 × 6 ÷ −4</blockquote>\r\nEven though this expression has some negative numbers, the only operations it contains are multiplication and division. So you can evaluate it in two steps from left to right (remembering the rules for multiplying and dividing with negative numbers):\r\n<blockquote>= −2 × 6 ÷ −4\r\n= −12 ÷ −4\r\n= 3</blockquote>\r\nThus,\r\n<blockquote>−2 × 6 ÷ −4 = 3</blockquote>","description":"Some expressions contain only multiplication and division. When this is the case, the rule for evaluating the expression is pretty straightforward. When an expression contains only multiplication and division, evaluate it step by step from left to right.\r\n<h2 id=\"tab1\" >The Three Types of Big Four Expressions</h2>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th>Expression</th>\r\n<th>Example</th>\r\n<th>Rule</th>\r\n</tr>\r\n<tr>\r\n<td>Contains only addition and subtraction</td>\r\n<td>12 + 7 – 6 – 3 + 8</td>\r\n<td>Evaluate left to right.</td>\r\n</tr>\r\n<tr>\r\n<td>Contains only multiplication and division</td>\r\n<td>18 ÷ 3 x 7 ÷ 14</td>\r\n<td>Evaluate left to right.</td>\r\n</tr>\r\n<tr>\r\n<td>Mixed-operator expression: contains a combination of\r\naddition/subtraction and multiplication/division</td>\r\n<td>9 + 6 ÷ 3</td>\r\n<td>1. Evaluate multiplication and division left to right.\r\n2. Evaluate addition and subtraction left to right.</td>\r\n</tr>\r\n</tbody>\r\n</table>\r\n<p class=\"Remember\">Suppose you want to evaluate this expression:</p>\r\n\r\n<blockquote>9 × 2 ÷ 6 ÷ 3 × 2</blockquote>\r\nAgain, the expression contains only multiplication and division, so you can move from left to right, starting with 9 x 2:\r\n<blockquote>= 18 ÷ 6 ÷ 3 × 2\r\n= 3 ÷ 3 × 2\r\n= 1 × 2\r\n= 2</blockquote>\r\nNotice that the expression shrinks one number at a time until all that’s left is 2. So\r\n<blockquote>9 × 2 ÷ 6 ÷ 3 × 2 = 2</blockquote>\r\nHere’s another quick example:\r\n<blockquote>−2 × 6 ÷ −4</blockquote>\r\nEven though this expression has some negative numbers, the only operations it contains are multiplication and division. So you can evaluate it in two steps from left to right (remembering the rules for multiplying and dividing with negative numbers):\r\n<blockquote>= −2 × 6 ÷ −4\r\n= −12 ÷ −4\r\n= 3</blockquote>\r\nThus,\r\n<blockquote>−2 × 6 ÷ −4 = 3</blockquote>","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":33726,"title":"Pre-Algebra","slug":"pre-algebra","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33726"}},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"The Three Types of Big Four Expressions","target":"#tab1"}],"relatedArticles":{"fromBook":[{"articleId":207780,"title":"Basic Math & Pre-Algebra For Dummies Cheat Sheet","slug":"basic-math-pre-algebra-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/207780"}},{"articleId":194384,"title":"How to Write Numbers in Scientific Notation","slug":"how-to-write-numbers-in-scientific-notation","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/194384"}},{"articleId":158569,"title":"Important Operations that Make Math Problems Easier","slug":"inverse-operations-and-commutative-associative-and-distributive-properties","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/158569"}},{"articleId":158567,"title":"Converting Metric Units to English Units","slug":"converting-metric-units-to-english-units","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/158567"}},{"articleId":158560,"title":"Working with Exponents, Radicals, & Absolute Value","slug":"a-guide-to-working-with-exponents-radicals-and-absolute-value","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/158560"}}],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/291491"}},{"articleId":253710,"title":"Pre-Algebra: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/253710"}},{"articleId":249996,"title":"Solving Simple Equations in Pre-Algebra Problems","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249986"}},{"articleId":249980,"title":"Rearranging Algebraic Equations to Isolate X","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249980"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281978,"slug":"basic-math-pre-algebra-for-dummies-2nd-edition","isbn":"9781119293637","categoryList":["academics-the-arts","math","basic-math"],"amazon":{"default":"//www.amazon.com/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"//www.amazon.ca/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"//www.tkqlhce.com/click-9208661-13710633?url=//www.chapters.indigo.ca/en-ca/books/product/1119293634-item.html&cjsku=978111945484","gb":"//www.amazon.co.uk/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"//www.amazon.de/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"//coursofppt.com/wp-content/uploads/basic-math-and-pre-algebra-for-dummies-2nd-edition-cover-9781119293637-203x255.jpg","width":203,"height":255},"title":"Basic Math & Pre-Algebra For Dummies","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"<p><p><b><b data-author-id=\"9399\">Mark Zegarelli</b></b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com.</p>","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"_links":{"self":"//dummies-api.coursofppt.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119293637&quot;]}]\" id=\"du-slot-64ac718f5cb21\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;basic-math&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119293637&quot;]}]\" id=\"du-slot-64ac718f5ddb5\"></div></div>"},"articleType":{"articleType":"Articles","articleList":null,"content":null,"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Advance","lifeExpectancy":"Five years","lifeExpectancySetFrom":"2023-10-03T00:00:00+00:00","dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":150507},{"headers":{"creationTime":"2019-06-25T23:01:36+00:00","modifiedTime":"2024-07-10T18:47:24+00:00","timestamp":"2024-07-10T21:01:03+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Basic Math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33722"},"slug":"basic-math","categoryId":33722}],"title":"Pre-Algebra: Comparing Fractions Using Cross-Multiplication","strippedTitle":"pre-algebra: comparing fractions using cross-multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","canonicalUrl":"","百度搜指数擎推广":{"metaDescription":"Cross-multiplication is a handy tool for finding the common denominator for two fractions, which is important for many operations involving fractions. In the fo","noIndex":0,"noFollow":0},"content":"Cross-multiplication is a handy tool for finding the common denominator for two fractions, which is important for many operations involving fractions. In the following practice questions, you are asked to cross-multiply to compare fractions to find out which is greater or less.\r\n<h2 style=\"padding-left: 30px;\">Practice questions</h2>\r\n<p style=\"padding-left: 30px;\"><strong>1.</strong> Find the lesser fraction:</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253711\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0101.gif\" alt=\"PREALGEBRA_0101\" width=\"65\" height=\"45\" /></p>\r\n<p style=\"padding-left: 30px;\"><strong>2.</strong> Among these three fractions, which is greatest:</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253712\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0102.gif\" alt=\"PREALGEBRA_0102\" width=\"116\" height=\"45\" /></p>\r\n\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<p style=\"padding-left: 30px;\"><strong>1.</strong> Of the two fractions,</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253713\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0103.gif\" alt=\"PREALGEBRA_0103\" width=\"79\" height=\"45\" /></p>\r\n<p style=\"padding-left: 30px;\">Cross-multiply to compare the two fractions:</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253714\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0104-FINAL.gif\" alt=\"PREALGEBRA_0104\" width=\"59\" height=\"71\" /></p>\r\n<p style=\"padding-left: 30px;\">Because 35 is less than 36,</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253715\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0105.gif\" alt=\"PREALGEBRA_0105\" width=\"131\" height=\"45\" /></p>\r\n<p style=\"padding-left: 30px;\"><strong>2.</strong> Of the three fractions,</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253716\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0106.gif\" alt=\"PREALGEBRA_0106\" width=\"217\" height=\"45\" /></p>\r\n<p style=\"padding-left: 30px;\">Use cross-multiplication to compare the first two fractions.</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253717\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0107-FINAL.gif\" alt=\"PREALGEBRA_0107\" width=\"64\" height=\"71\" /></p>\r\n<p style=\"padding-left: 30px;\">Because 21 is greater than 20, this means that 1/10 is greater than 2/21, so you can rule out 2/21. Next, compare 1/10 and 3/29 by cross-multiplying.</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253718\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0108-FINAL.gif\" alt=\"PREALGEBRA_0108\" width=\"67\" height=\"71\" /></p>\r\n<p style=\"padding-left: 30px;\">Because 30 is greater than 29, 3/29 is greater than 1/10. Therefore, 3/29 is the greatest of the three fractions.</p>","description":"Cross-multiplication is a handy tool for finding the common denominator for two fractions, which is important for many operations involving fractions. In the following practice questions, you are asked to cross-multiply to compare fractions to find out which is greater or less.\r\n<h2 style=\"padding-left: 30px;\">Practice questions</h2>\r\n<p style=\"padding-left: 30px;\"><strong>1.</strong> Find the lesser fraction:</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253711\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0101.gif\" alt=\"PREALGEBRA_0101\" width=\"65\" height=\"45\" /></p>\r\n<p style=\"padding-left: 30px;\"><strong>2.</strong> Among these three fractions, which is greatest:</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253712\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0102.gif\" alt=\"PREALGEBRA_0102\" width=\"116\" height=\"45\" /></p>\r\n\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<p style=\"padding-left: 30px;\"><strong>1.</strong> Of the two fractions,</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253713\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0103.gif\" alt=\"PREALGEBRA_0103\" width=\"79\" height=\"45\" /></p>\r\n<p style=\"padding-left: 30px;\">Cross-multiply to compare the two fractions:</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253714\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0104-FINAL.gif\" alt=\"PREALGEBRA_0104\" width=\"59\" height=\"71\" /></p>\r\n<p style=\"padding-left: 30px;\">Because 35 is less than 36,</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253715\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0105.gif\" alt=\"PREALGEBRA_0105\" width=\"131\" height=\"45\" /></p>\r\n<p style=\"padding-left: 30px;\"><strong>2.</strong> Of the three fractions,</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253716\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0106.gif\" alt=\"PREALGEBRA_0106\" width=\"217\" height=\"45\" /></p>\r\n<p style=\"padding-left: 30px;\">Use cross-multiplication to compare the first two fractions.</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253717\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0107-FINAL.gif\" alt=\"PREALGEBRA_0107\" width=\"64\" height=\"71\" /></p>\r\n<p style=\"padding-left: 30px;\">Because 21 is greater than 20, this means that 1/10 is greater than 2/21, so you can rule out 2/21. Next, compare 1/10 and 3/29 by cross-multiplying.</p>\r\n<p style=\"padding-left: 30px;\"><img class=\"alignnone size-full wp-image-253718\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_0108-FINAL.gif\" alt=\"PREALGEBRA_0108\" width=\"67\" height=\"71\" /></p>\r\n<p style=\"padding-left: 30px;\">Because 30 is greater than 29, 3/29 is greater than 1/10. Therefore, 3/29 is the greatest of the three fractions.</p>","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. He is the author of a dozen books, including <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies, and Calculus II For Dummies</i>. Through online tutoring, he teaches multiplication and beyond to preschoolers in a way that sets them up for school success while keeping the natural magic of math alive. Contact Mark at markzegarelli.com. ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":33726,"title":"Pre-Algebra","slug":"pre-algebra","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33726"}},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Practice questions","target":"#tab1"},{"label":"Answers and explanations","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":249996,"title":"Solving Simple Equations in Pre-Algebra Problems","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249986"}},{"articleId":249980,"title":"Rearranging Algebraic Equations to Isolate X","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249980"}},{"articleId":249971,"title":"Pre-Algebra: Cross-Multiply to Solve Equations","slug":"pre-algebra-practice-questions-cross-multiply-solve-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249971"}},{"articleId":249964,"title":"Pre-Algebra Practice Questions: Finding the Volume of Prisms and Cylinders","slug":"pre-algebra-practice-questions-finding-volume-prisms-cylinders","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249964"}}],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/291491"}},{"articleId":249996,"title":"Solving Simple Equations in Pre-Algebra Problems","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249986"}},{"articleId":249980,"title":"Rearranging Algebraic Equations to Isolate X","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249980"}},{"articleId":249971,"title":"Pre-Algebra: Cross-Multiply to Solve Equations","slug":"pre-algebra-practice-questions-cross-multiply-solve-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"//dummies-api.coursofppt.com/v2/articles/249971"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281980,"slug":"basic-math-and-pre-algebra-workbook-for-dummies-with-online-practice-3rd-edition","isbn":"9781119357513","categoryList":["academics-the-arts","math","basic-math"],"amazon":{"default":"//www.amazon.com/gp/product/1119357519/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"//www.amazon.ca/gp/product/1119357519/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"//www.tkqlhce.com/click-9208661-13710633?url=//www.chapters.indigo.ca/en-ca/books/product/1119357519-item.html&cjsku=978111945484","gb":"//www.amazon.co.uk/gp/product/1119357519/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"//www.amazon.de/gp/product/1119357519/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"//coursofppt.com/wp-content/uploads/basic-math-and-pre-algebra-workbook-for-dummies-3rd-edition-cover-9781119357513-204x255.jpg","width":204,"height":255},"title":"Basic Math & Pre-Algebra Workbook For Dummies with Online Practice","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p><b data-author-id=\"9399\">Mark Zegarelli</b> is a math and test prep teacher who has written a wide variety of basic math and pre-algebra books in the <i>For Dummies</i> series. </p>","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> is a math teacher and tutor with degrees in math and English from Rutgers University. 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The following practice questions ask you to use three different met","noIndex":0,"noFollow":0},"content":"When dealing with simple algebraic expressions, you don't always need algebra to solve them. The following practice questions ask you to use three different methods: inspecting, rewriting the problem, and guessing and checking.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\nIn the following questions, solve for <em>x</em> in each case just by looking at the equation.\r\n<p style=\"padding-left: 30px;\"><strong> 1. 18 – <em>x</em> = 12</strong></p>\r\n<p style=\"padding-left: 30px;\"><strong> 2. 4<em>x</em> = 44</strong></p>\r\n<p style=\"padding-left: 30px;\">In the following questions, use the correct inverse operation to rewrite and solve each problem.</p>\r\n<p style=\"padding-left: 30px;\"> <strong>3. 100 – <em>x</em> = 58</strong></p>\r\n<p style=\"padding-left: 30px;\"> <strong>4. 238/<em>x</em> = 17</strong></p>\r\n<p style=\"padding-left: 30px;\">In the following questions, find the value of <em>x</em> in each equation by guessing and checking.</p>\r\n<p style=\"padding-left: 30px;\"><strong> 5. 12<em>x</em> – 17 = 151</strong></p>\r\n<p style=\"padding-left: 30px;\"> <strong>6. 19<em>x</em> – 8 = 600</strong></p>\r\n\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n \t<li><em>x</em> = 6You can solve this problem through simple inspection. Because 18 – 6 = 12, <em>x</em> = 6.</li>\r\n \t<li><em>x</em> = 11Again, through simple inspection, because 4(11) = 44, you know that <em>x</em> = 11.</li>\r\n \t<li><em>x </em>= 42Turn the problem around by changing the subtraction to addition: 100 – <em>x = </em>58 means the same thing as 100 – 58 =<em> x</em>, so<em> x = </em>42.</li>\r\n \t<li><em>x </em>= 14Turn the problem around by switching around the division:\r\n\r\n<img class=\"alignnone size-full wp-image-249997\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_3001.gif\" alt=\"PREALGEBRA_3001\" width=\"183\" height=\"45\" />\r\n\r\nso <em>x </em>= 14.</li>\r\n \t<li><em>x</em> = 14Guess what you think the answer may be. For example, perhaps it's <em>x</em> = 10:\r\n\r\n12(10) – 17 = 120 – 17 = 103\r\n\r\n103 is less than 151, so this guess is too low. Try <em>x</em> = 20:\r\n\r\n12(20) – 17 = 240 – 17 = 223\r\n\r\n223 is greater than 151, so this guess is too high. Therefore, <em>x</em> is between 10 and 20. Try <em>x</em> = 15:\r\n\r\n12(15) – 17 = 180 – 17 = 163\r\n\r\n163 is a little greater than 151, so this guess is a little too high. Try <em>x </em>= 14:\r\n\r\n12(14) – 17 = 168 – 17 = 151\r\n\r\n151 is correct, so <em>x</em> = 14.</li>\r\n \t<li><em>x</em> = 32Again, start by guessing. First, try <em>x</em> = 10:\r\n\r\n19(10) – 8 = 190 – 8 = 182\r\n\r\n182 is much less than 600, so this guess is much too low. Try <em>x</em> = 30:\r\n\r\n19(30) – 8 = 570 – 8 = 562\r\n\r\n562 is still less than 600, so this guess is still too low. Try <em>x</em> = 35:\r\n\r\n19(35) – 8 = 665 – 8 = 657\r\n\r\n657 is greater than 600, so this guess is too high. Therefore, <em>x</em> is between 30 and 35. Try <em>x</em> = 32:\r\n\r\n19(32) – 8 = 608 – 8 = 600\r\n\r\n600 is correct, so <em>x</em> = 32.</li>\r\n</ol>\r\n ","description":"When dealing with simple algebraic expressions, you don't always need algebra to solve them. The following practice questions ask you to use three different methods: inspecting, rewriting the problem, and guessing and checking.\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\nIn the following questions, solve for <em>x</em> in each case just by looking at the equation.\r\n<p style=\"padding-left: 30px;\"><strong> 1. 18 – <em>x</em> = 12</strong></p>\r\n<p style=\"padding-left: 30px;\"><strong> 2. 4<em>x</em> = 44</strong></p>\r\n<p style=\"padding-left: 30px;\">In the following questions, use the correct inverse operation to rewrite and solve each problem.</p>\r\n<p style=\"padding-left: 30px;\"> <strong>3. 100 – <em>x</em> = 58</strong></p>\r\n<p style=\"padding-left: 30px;\"> <strong>4. 238/<em>x</em> = 17</strong></p>\r\n<p style=\"padding-left: 30px;\">In the following questions, find the value of <em>x</em> in each equation by guessing and checking.</p>\r\n<p style=\"padding-left: 30px;\"><strong> 5. 12<em>x</em> – 17 = 151</strong></p>\r\n<p style=\"padding-left: 30px;\"> <strong>6. 19<em>x</em> – 8 = 600</strong></p>\r\n\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n \t<li><em>x</em> = 6You can solve this problem through simple inspection. Because 18 – 6 = 12, <em>x</em> = 6.</li>\r\n \t<li><em>x</em> = 11Again, through simple inspection, because 4(11) = 44, you know that <em>x</em> = 11.</li>\r\n \t<li><em>x </em>= 42Turn the problem around by changing the subtraction to addition: 100 – <em>x = </em>58 means the same thing as 100 – 58 =<em> x</em>, so<em> x = </em>42.</li>\r\n \t<li><em>x </em>= 14Turn the problem around by switching around the division:\r\n\r\n<img class=\"alignnone size-full wp-image-249997\" src=\"//coursofppt.com/wp-content/uploads/PREALGEBRA_3001.gif\" alt=\"PREALGEBRA_3001\" width=\"183\" height=\"45\" />\r\n\r\nso <em>x </em>= 14.</li>\r\n \t<li><em>x</em> = 14Guess what you think the answer may be. For example, perhaps it's <em>x</em> = 10:\r\n\r\n12(10) – 17 = 120 – 17 = 103\r\n\r\n103 is less than 151, so this guess is too low. Try <em>x</em> = 20:\r\n\r\n12(20) – 17 = 240 – 17 = 223\r\n\r\n223 is greater than 151, so this guess is too high. Therefore, <em>x</em> is between 10 and 20. Try <em>x</em> = 15:\r\n\r\n12(15) – 17 = 180 – 17 = 163\r\n\r\n163 is a little greater than 151, so this guess is a little too high. Try <em>x </em>= 14:\r\n\r\n12(14) – 17 = 168 – 17 = 151\r\n\r\n151 is correct, so <em>x</em> = 14.</li>\r\n \t<li><em>x</em> = 32Again, start by guessing. First, try <em>x</em> = 10:\r\n\r\n19(10) – 8 = 190 – 8 = 182\r\n\r\n182 is much less than 600, so this guess is much too low. Try <em>x</em> = 30:\r\n\r\n19(30) – 8 = 570 – 8 = 562\r\n\r\n562 is still less than 600, so this guess is still too low. Try <em>x</em> = 35:\r\n\r\n19(35) – 8 = 665 – 8 = 657\r\n\r\n657 is greater than 600, so this guess is too high. Therefore, <em>x</em> is between 30 and 35. Try <em>x</em> = 32:\r\n\r\n19(32) – 8 = 608 – 8 = 600\r\n\r\n600 is correct, so <em>x</em> = 32.</li>\r\n</ol>\r\n ","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <p><b>Mark Zegarelli</b> earned degrees in mathematics and English from Rutgers University. He is the founder of SimpleStep Learning, an online educational platform that teaches courses in basic concepts in ten minutes or less, keeping students engaged and learning in every moment. Mark is also author of several other successful <i>For Dummies</i> books.</p> ","hasArticle":false,"_links":{"self":"//dummies-api.coursofppt.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":33726,"title":"Pre-Algebra","slug":"pre-algebra","_links":{"self":"//dummies-api.coursofppt.com/v2/categories/33726"}},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Practice questions","target":"#tab1"},{"label":"Answers and explanations","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":253710,"title":"Pre-Algebra Practice Questions: Comparing Fractions Using 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Mark Zegarelli

Angie Papple Johnston joined the U.S. Army in 2006 as a Chemical, Biological, Radiological, and Nuclear Specialist. During her second deployment as part of Operation Iraqi Freedom, Angie became her battalion’s public affairs representative. She also served as the Lead Cadre for the Texas Army National Guard’s Recruit Sustainment program.

Articles From Mark Zegarelli

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269 results
269 results
Important Operations that Make Math Problems Easier Article / Updated 03-20-2024 The Big Four math operations — addition, subtraction, multiplication, and division — let you combine numbers and perform calculations. Certain operations possess properties that enable you to manipulate the numbers in the problem, which comes in handy, especially when you get into higher math like algebra. The important properties you need to know are the commutative property, the associative property, and the distributive property. Understanding what an inverse operation is is also helpful. Inverse operations Inverse operations are pairs of operations that you can work "backward" to cancel each other out. Two pairs of the Big Four operations — addition, subtraction, multiplication, and division —are inverses of each other: Addition and subtraction are inverse operations of each other. When you start with any value, then add a number to it and subtract the same number from the result, the value you started with remains unchanged. For example: 2 + 3 = 5 so 5 – 3 = 2 7 – 1 = 6 so 6 + 1 = 7 Multiplication and division are inverse operations of each other. When you start with any value, then multiply it by a number and divide the result by the same number (except zero), the value you started with remains unchanged. For example: 3 × 4 = 12 so 12 ÷ 4 = 3 10 ÷ 2 = 5 so 5 × 2 = 10 The commutative property An operation is commutative when you apply it to a pair of numbers either forwards or backwards and expect the same result. The two Big Four that are commutative are addition and subtraction. Addition is commutative because, for example, 3 + 5 is the same as 5 + 3. In other words 3 + 5 = 5 + 3 Multiplication is commutative because 2 × 7 is the same as 7 × 2. In other words 2 × 7 = 7 × 2 The associative property An operation is associative when you can apply it, using parentheses, in different groupings of numbers and still expect the same result. The two Big Four operations that are associative are addition and multiplication. Addition is associative because, for example, the problem (2 + 4) + 7 produces the same result as does the problem 2 + (4 + 7). In other words, (2 + 4) + 7 = 2 + (4 + 7) No matter which pair of numbers you add together first, the answer is the same: 13. Multiplication is associative because, for example, the problem 3 × (4 × 5) produces the same result as the problem (3 × 4) × 5. In other words, 3 × (4 × 5) = (3 × 4) × 5 Again, no matter which pair of numbers you multiply first, both problems yield the same answer: 60. The distributive property The distributive property connects the operations of multiplication and addition. When multiplication is described as "distributive over addition," you can split a multiplication problem into two smaller problems and then add the results. For example, suppose you want to multiply 27 × 6. You know that 27 equals 20 + 7, so you can do this multiplication in two steps: First multiply 20 × 6; then multiply 7 × 6. 20 × 6 = 1207 × 6 = 42 Then add the results. 120 + 42 = 162 Therefore, 27 × 6 = 162. View Article
Conversion Guide for Fractions, Decimals, and Percents Article / Updated 03-20-2024 Fractions, decimals, and percents are the three most common ways to give a mathematical description of parts of a whole object. Fractions are common in baking and carpentry when you're using English measurement units (such as cups, gallons, feet, and inches). Decimals are used with dollars and cents, the metric system, and in scientific notation. Percents are used in business when figuring profit and interest rates, as well as in statistics. Use the following table as a handy guide when you need to make basic conversions among the three. Fraction Decimal Percent 1/100 0.01 1% 1/20 0.05 5% 1/10 0.1 10% 1/5 0.2 20% 1/4 0.25 25% 3/10 0.3 30% 2/5 0.4 40% 1/2 0.5 50% 3/5 0.6 60% 7/10 0.7 70% 3/4 0.75 75% 4/5 0.8 80% 9/10 0.9 90% 1 1.0 100% 2 2.0 200% 10 10.0 1,000% View Article
Converting Metric Units to English Units Article / Updated 03-20-2024 The English system of measurements is most commonly used in the United States. In contrast, the metric system is used throughout most of the rest of the world. Converting measurements between the English and metric systems is a common everyday reason to know math. This article gives you some precise metric-to-English conversions, as well as some easy-to-remember conversions that are good enough for most situations. Metric-to-English Conversion Table Metric-to-English Conversions Metric Units in Plain English 1 meter ≈ 3.28 feet A meter is about 3 feet (1 yard). 1 kilometer ≈ 0.62 miles A kilometer is about 1/2 mile. 1 liter ≈ 0.26 gallons A liter is about 1 quart (1/4 gallon). 1 kilogram ≈ 2.20 pounds A kilo is about 2 pounds. 0°C = 32°F 0°C is cold. 10°C = 50°F 10°C is cool. 20°C = 68°F 20°C is warm. 30°C = 86° 30°C is hot. Here's an easy temperature conversion to remember: 16°C = 61°F. View Article
Working with Exponents, Radicals, & Absolute Value Article / Updated 03-20-2024 Exponents, radicals, and absolute value are mathematical operations that go beyond addition, subtraction, multiplication, and division. They are useful in more advanced math, such as algebra, but they also have real-world applications, especially in geometry and measurement. Exponents (powers) are repeated multiplication: When you raise a number to the power of an exponent, you multiply that number by itself the number of times indicated by the exponent. For example: 72 = 7 × 7 = 49 25 = 2 × 2 × 2 × 2 × 2 = 32 Square roots (radicals) are the inverse of exponent 2 — that is, the number that, when multiplied by itself, gives you the indicated value. Absolute value is the positive value of a number — that is, the value of a negative number when you drop the minus sign. For example: Absolute value is used to describe numbers that are always positive, such as the distance between two points or the area inside a polygon. View Article
Digital SAT Math Prep For Dummies Cheat Sheet Cheat Sheet / Updated 10-05-2023 Although there's no shortcut to success on the math sections of the SAT, you can study and prepare in order to get the best SAT score you possibly can. Knowing what will be on the test (and what won't be) is key so you know what to brush up on. Also, some basic strategy goes a long way toward helping you get the best score you can. Finally, mapping out a time-management plan to answer (and skip!) the right questions can really boost your score. View Cheat Sheet
Pre-Algebra Practice Questions: Finding the Volume of Prisms and Cylinders Article / Updated 08-07-2023 To find the volume of a prism or cylinder, you can use the following formula, where Ab is the area of the base and h is the height: V = Ab x h Practice questions Find the volume of a prism with a base that has an area of 6 square centimeters and a height of 3 centimeters. Figure out the approximate volume of a cylinder whose base has a radius of 7 millimeters and whose height is 16 millimeters. Answers and explanations 18 cubic centimeters V = Ab x h = 6cm2 x 3cm = 18cm3 Approximately 2,461.76 cubic millimeters First, use the area formula for a circle to find the area of the base: Ab = π x r2 ≅ 3.14 x (7mm)2 = 3.14 x 49mm2 = 153.86mm2 Plug this result into the formula for the volume of a cylinder: V = Ab x h = 153.86mm2 x 16mm = 2,461.76mm3 View Article
Finding the Area of a Surface of Revolution Video / Updated 07-14-2023 The nice thing about finding the area of a surface of revolution is that there’s a formula you can use. Memorize it and you’re halfway done. To find the area of a surface of revolution between a and b, watch this video tutorial or follow the steps below: This formula looks long and complicated, but it makes more sense when you spend a minute thinking about it. The integral is made from two pieces: The arc-length formula, which measures the length along the surface The formula for the circumference of a circle, which measures the length around the surface So multiplying these two pieces together is similar to multiplying length and width to find the area of a rectangle. In effect, the formula allows you to measure surface area as an infinite number of little rectangles. When you’re measuring the surface of revolution of a function f(x) around the x-axis, substitute r = f(x) into the formula: For example, suppose that you want to find the area of revolution that’s shown in this figure. Measuring the surface of revolution of y = x3 between x = 0 and x = 1. To solve this problem, first note that for So set up the problem as follows: To start off, simplify the problem a bit: You can solve this problem by using the following variable substitution: Now substitute u for 1+ 9x4 and for x3 dx into the equation: Notice that you change the limits of integration: When x = 0, u = 1. And when x = 1, u = 10. Now you can perform the integration: Finally, evaluate the definite integral: Watch Video
Evaluating an Expression with Only Multiplication & Division Article / Updated 07-10-2023 Some expressions contain only multiplication and division. When this is the case, the rule for evaluating the expression is pretty straightforward. When an expression contains only multiplication and division, evaluate it step by step from left to right. The Three Types of Big Four Expressions Expression Example Rule Contains only addition and subtraction 12 + 7 – 6 – 3 + 8 Evaluate left to right. Contains only multiplication and division 18 ÷ 3 x 7 ÷ 14 Evaluate left to right. Mixed-operator expression: contains a combination of addition/subtraction and multiplication/division 9 + 6 ÷ 3 1. Evaluate multiplication and division left to right. 2. Evaluate addition and subtraction left to right. Suppose you want to evaluate this expression: 9 × 2 ÷ 6 ÷ 3 × 2 Again, the expression contains only multiplication and division, so you can move from left to right, starting with 9 x 2: = 18 ÷ 6 ÷ 3 × 2 = 3 ÷ 3 × 2 = 1 × 2 = 2 Notice that the expression shrinks one number at a time until all that’s left is 2. So 9 × 2 ÷ 6 ÷ 3 × 2 = 2 Here’s another quick example: −2 × 6 ÷ −4 Even though this expression has some negative numbers, the only operations it contains are multiplication and division. So you can evaluate it in two steps from left to right (remembering the rules for multiplying and dividing with negative numbers): = −2 × 6 ÷ −4 = −12 ÷ −4 = 3 Thus, −2 × 6 ÷ −4 = 3 View Article
Pre-Algebra: Comparing Fractions Using Cross-Multiplication Article / Updated 07-10-2023 Cross-multiplication is a handy tool for finding the common denominator for two fractions, which is important for many operations involving fractions. In the following practice questions, you are asked to cross-multiply to compare fractions to find out which is greater or less. Practice questions 1. Find the lesser fraction: 2. Among these three fractions, which is greatest: Answers and explanations 1. Of the two fractions, Cross-multiply to compare the two fractions: Because 35 is less than 36, 2. Of the three fractions, Use cross-multiplication to compare the first two fractions. Because 21 is greater than 20, this means that 1/10 is greater than 2/21, so you can rule out 2/21. Next, compare 1/10 and 3/29 by cross-multiplying. Because 30 is greater than 29, 3/29 is greater than 1/10. Therefore, 3/29 is the greatest of the three fractions. View Article
Solving Simple Equations in Pre-Algebra Problems Article / Updated 06-28-2023 When dealing with simple algebraic expressions, you don't always need algebra to solve them. The following practice questions ask you to use three different methods: inspecting, rewriting the problem, and guessing and checking. Practice questions In the following questions, solve for x in each case just by looking at the equation. 1. 18 – x = 12 2. 4x = 44 In the following questions, use the correct inverse operation to rewrite and solve each problem. 3. 100 – x = 58 4. 238/x = 17 In the following questions, find the value of x in each equation by guessing and checking. 5. 12x – 17 = 151 6. 19x – 8 = 600 Answers and explanations x = 6You can solve this problem through simple inspection. Because 18 – 6 = 12, x = 6. x = 11Again, through simple inspection, because 4(11) = 44, you know that x = 11. x = 42Turn the problem around by changing the subtraction to addition: 100 – x = 58 means the same thing as 100 – 58 = x, so x = 42. x = 14Turn the problem around by switching around the division: so x = 14. x = 14Guess what you think the answer may be. For example, perhaps it's x = 10: 12(10) – 17 = 120 – 17 = 103 103 is less than 151, so this guess is too low. Try x = 20: 12(20) – 17 = 240 – 17 = 223 223 is greater than 151, so this guess is too high. Therefore, x is between 10 and 20. Try x = 15: 12(15) – 17 = 180 – 17 = 163 163 is a little greater than 151, so this guess is a little too high. Try x = 14: 12(14) – 17 = 168 – 17 = 151 151 is correct, so x = 14. x = 32Again, start by guessing. First, try x = 10: 19(10) – 8 = 190 – 8 = 182 182 is much less than 600, so this guess is much too low. Try x = 30: 19(30) – 8 = 570 – 8 = 562 562 is still less than 600, so this guess is still too low. Try x = 35: 19(35) – 8 = 665 – 8 = 657 657 is greater than 600, so this guess is too high. Therefore, x is between 30 and 35. Try x = 32: 19(32) – 8 = 608 – 8 = 600 600 is correct, so x = 32. View Article
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