{"id":340,"date":"2023-02-17T17:28:29","date_gmt":"2023-02-17T17:28:29","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=340"},"modified":"2024-10-18T20:52:01","modified_gmt":"2024-10-18T20:52:01","slug":"measurement-background-youll-need-page-1","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/measurement-background-youll-need-page-1\/","title":{"raw":"Measurement:  Background You'll Need - Page 1","rendered":"Measurement:  Background You&#8217;ll Need &#8211; Page 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Understand different types of fractions<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Converting Mixed Numbers and Improper Fractions<\/h2>\r\n<h3>Convert an Improper Fraction to a Mixed Number<\/h3>\r\n<p>Switching between mixed numbers and improper fractions is a handy skill in math, especially when it comes to adding or subtracting fractions. A mixed number combines a whole number with a fraction, while an improper fraction has a numerator larger than its denominator. Here\u2019s a quick guide on how to transform an improper fraction into a mixed number, breaking it down into simpler, more understandable parts.<\/p>\r\n<section class=\"textbox questionHelp\">\r\n<p><strong>How To: Convert an Improper Fraction to a Mixed Number<\/strong><\/p>\r\n<ol id=\"eip-241\" class=\"stepwise\">\r\n\t<li>Divide the denominator into the numerator.<\/li>\r\n\t<li>Identify the quotient, remainder, and divisor.<\/li>\r\n\t<li>Write the mixed number as [latex] \\text{quotient} {\\Large\\frac{\\text{remainder}}{\\text{divisor}}}[\/latex] .<\/li>\r\n<\/ol>\r\n<\/section>\r\n<section class=\"textbox example\">Convert the improper fraction [latex]{\\Large\\frac{33}{8}}[\/latex] to a mixed number.<br \/>\r\n[reveal-answer q=\"584602\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"584602\"]\r\n\r\n\r\n<table id=\"eip-id1168469862094\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"A division symbol is shown with a 33 on the inside. An 8 is on the outside and is labeled as the divisor. A 32 is below the 33. Below the 32 is a 1 that is labeled as the remainder. Above the division sign, a 4 is labeled as the quotient.\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]{\\Large\\frac{33}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide the denominator into the numerator.<\/td>\r\n<td>Remember, [latex]{\\Large\\frac{33}{8}}[\/latex] means [latex]8\\overline{)33}[\/latex] .<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Identify the quotient, remainder, and divisor.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220741\/CNX_BMath_Figure_04_01_032_img-01.png\" alt=\"33 divided by 8 using long division. 4 is the quotient, 8 is the divisor. 32 is under the 33. Then below the 31 is a bar and the number 1 labeled as &quot;remainder&quot;.\" width=\"269\" height=\"85\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the mixed number as [latex] \\text{quotient} {\\Large\\frac{\\text{remainder}}{\\text{divisor}}}[\/latex] .<\/td>\r\n<td>[latex]4{\\Large\\frac{1}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>So, [latex]{\\Large\\frac{33}{8}}=4{\\Large\\frac{1}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2939[\/ohm2_question]<\/section>\r\n<h3>Convert a Mixed Number to an Improper Fraction<\/h3>\r\n<p>Converting a mixed number to an improper fraction is just as straightforward as the reverse process we've covered. It\u2019s about combining the whole number and the fraction part into one fraction. This conversion is crucial for performing various arithmetic operations with mixed numbers. Let\u2019s go through the simple steps to make this transformation.<\/p>\r\n<section class=\"textbox questionHelp\">\r\n<p><strong>How To: Convert a Mixed Number to an Improper Fraction<\/strong><\/p>\r\n<ol id=\"eip-id1168467427407\" class=\"stepwise\">\r\n\t<li>Multiply the whole number by the denominator.<\/li>\r\n\t<li>Add the numerator to the product found in Step [latex]1[\/latex].<\/li>\r\n\t<li>Write the final sum over the original denominator.<\/li>\r\n<\/ol>\r\n<\/section>\r\n<section class=\"textbox example\">Convert the mixed number [latex]10{\\Large\\frac{2}{7}}[\/latex] to an improper fraction.<br \/>\r\n[reveal-answer q=\"474296\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"474296\"]\r\n\r\n\r\n<table id=\"eip-id1168466244930\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The mixed number 10 and 2 sevenths is shown. The first step says, \">\r\n<tbody>\r\n<tr>\r\n<td>[latex]10{\\Large\\frac{2}{7}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the whole number by the denominator.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The whole number is [latex]10[\/latex] and the denominator is [latex]7[\/latex].<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220746\/CNX_BMath_Figure_04_01_069_img-01.png\" alt=\"A fraction with the numerator showing &quot;10 dot 7 + empty box&quot; and the denominator showing &quot;empty box&quot;.\" width=\"88\" height=\"54\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220747\/CNX_BMath_Figure_04_01_069_img-02.png\" alt=\"A fraction with the numerator showing &quot;70 + empty box&quot; and the denominator showing &quot;empty box&quot;.\" width=\"88\" height=\"53\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the numerator to the product.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The numerator of the mixed number is [latex]2[\/latex].<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220748\/CNX_BMath_Figure_04_01_069_img-03.png\" alt=\"A fraction with the numerator showing &quot;70 + 2&quot; and the denominator showing &quot;empty box&quot;.\" width=\"88\" height=\"48\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220749\/CNX_BMath_Figure_04_01_069_img-04.png\" alt=\"A fraction with the numerator showing &quot;72&quot; and the denominator showing &quot;empty box&quot;.\" width=\"88\" height=\"49\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the final sum over the original denominator.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The denominator is [latex]7[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{72}{7}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2942[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Understand different types of fractions<\/li>\n<\/ul>\n<\/section>\n<h2>Converting Mixed Numbers and Improper Fractions<\/h2>\n<h3>Convert an Improper Fraction to a Mixed Number<\/h3>\n<p>Switching between mixed numbers and improper fractions is a handy skill in math, especially when it comes to adding or subtracting fractions. A mixed number combines a whole number with a fraction, while an improper fraction has a numerator larger than its denominator. Here\u2019s a quick guide on how to transform an improper fraction into a mixed number, breaking it down into simpler, more understandable parts.<\/p>\n<section class=\"textbox questionHelp\">\n<p><strong>How To: Convert an Improper Fraction to a Mixed Number<\/strong><\/p>\n<ol id=\"eip-241\" class=\"stepwise\">\n<li>Divide the denominator into the numerator.<\/li>\n<li>Identify the quotient, remainder, and divisor.<\/li>\n<li>Write the mixed number as [latex]\\text{quotient} {\\Large\\frac{\\text{remainder}}{\\text{divisor}}}[\/latex] .<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox example\">Convert the improper fraction [latex]{\\Large\\frac{33}{8}}[\/latex] to a mixed number.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q584602\">Show Solution<\/button><\/p>\n<div id=\"q584602\" class=\"hidden-answer\" style=\"display: none\">\n<table id=\"eip-id1168469862094\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"A division symbol is shown with a 33 on the inside. An 8 is on the outside and is labeled as the divisor. A 32 is below the 33. Below the 32 is a 1 that is labeled as the remainder. Above the division sign, a 4 is labeled as the quotient.\">\n<tbody>\n<tr>\n<td>[latex]{\\Large\\frac{33}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide the denominator into the numerator.<\/td>\n<td>Remember, [latex]{\\Large\\frac{33}{8}}[\/latex] means [latex]8\\overline{)33}[\/latex] .<\/td>\n<\/tr>\n<tr>\n<td>Identify the quotient, remainder, and divisor.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220741\/CNX_BMath_Figure_04_01_032_img-01.png\" alt=\"33 divided by 8 using long division. 4 is the quotient, 8 is the divisor. 32 is under the 33. Then below the 31 is a bar and the number 1 labeled as &quot;remainder&quot;.\" width=\"269\" height=\"85\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write the mixed number as [latex]\\text{quotient} {\\Large\\frac{\\text{remainder}}{\\text{divisor}}}[\/latex] .<\/td>\n<td>[latex]4{\\Large\\frac{1}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>So, [latex]{\\Large\\frac{33}{8}}=4{\\Large\\frac{1}{8}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2939\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2939&theme=lumen&iframe_resize_id=ohm2939&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h3>Convert a Mixed Number to an Improper Fraction<\/h3>\n<p>Converting a mixed number to an improper fraction is just as straightforward as the reverse process we&#8217;ve covered. It\u2019s about combining the whole number and the fraction part into one fraction. This conversion is crucial for performing various arithmetic operations with mixed numbers. Let\u2019s go through the simple steps to make this transformation.<\/p>\n<section class=\"textbox questionHelp\">\n<p><strong>How To: Convert a Mixed Number to an Improper Fraction<\/strong><\/p>\n<ol id=\"eip-id1168467427407\" class=\"stepwise\">\n<li>Multiply the whole number by the denominator.<\/li>\n<li>Add the numerator to the product found in Step [latex]1[\/latex].<\/li>\n<li>Write the final sum over the original denominator.<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox example\">Convert the mixed number [latex]10{\\Large\\frac{2}{7}}[\/latex] to an improper fraction.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q474296\">Show Solution<\/button><\/p>\n<div id=\"q474296\" class=\"hidden-answer\" style=\"display: none\">\n<table id=\"eip-id1168466244930\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The mixed number 10 and 2 sevenths is shown. The first step says,\">\n<tbody>\n<tr>\n<td>[latex]10{\\Large\\frac{2}{7}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the whole number by the denominator.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The whole number is [latex]10[\/latex] and the denominator is [latex]7[\/latex].<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220746\/CNX_BMath_Figure_04_01_069_img-01.png\" alt=\"A fraction with the numerator showing &quot;10 dot 7 + empty box&quot; and the denominator showing &quot;empty box&quot;.\" width=\"88\" height=\"54\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220747\/CNX_BMath_Figure_04_01_069_img-02.png\" alt=\"A fraction with the numerator showing &quot;70 + empty box&quot; and the denominator showing &quot;empty box&quot;.\" width=\"88\" height=\"53\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add the numerator to the product.<\/td>\n<\/tr>\n<tr>\n<td>The numerator of the mixed number is [latex]2[\/latex].<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220748\/CNX_BMath_Figure_04_01_069_img-03.png\" alt=\"A fraction with the numerator showing &quot;70 + 2&quot; and the denominator showing &quot;empty box&quot;.\" width=\"88\" height=\"48\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220749\/CNX_BMath_Figure_04_01_069_img-04.png\" alt=\"A fraction with the numerator showing &quot;72&quot; and the denominator showing &quot;empty box&quot;.\" width=\"88\" height=\"49\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write the final sum over the original denominator.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The denominator is [latex]7[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{72}{7}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2942\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2942&theme=lumen&iframe_resize_id=ohm2942&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":16,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"OpenStax\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":62,"module-header":"background_you_need","content_attributions":[{"type":"cc-attribution","description":"Prealgebra","author":"OpenStax","organization":"","url":"","project":"","license":"cc-by","license_terms":"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757"}],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/340"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/16"}],"version-history":[{"count":28,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/340\/revisions"}],"predecessor-version":[{"id":15274,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/340\/revisions\/15274"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/62"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/340\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=340"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=340"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=340"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}