{"id":1168,"date":"2013-06-06T07:22:45","date_gmt":"2013-06-06T07:22:45","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=1168"},"modified":"2026-03-26T09:27:41","modified_gmt":"2026-03-26T14:27:41","slug":"converting-decimals-to-improper-fractions-and-mixed-numbers","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/converting-decimals-to-improper-fractions-and-mixed-numbers\/","title":{"rendered":"Converting Decimals, Improper Fractions, and Mixed Numbers"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_KPD8XtafLnc\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_KPD8XtafLnc\" data-source-videoID=\"KPD8XtafLnc\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Converting Decimals, Improper Fractions, and Mixed Numbers Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Converting Decimals, Improper Fractions, and Mixed Numbers\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_KPD8XtafLnc:hover {cursor:pointer;} img#videoThumbnailImage_KPD8XtafLnc {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/1868-thumb-final-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_KPD8XtafLnc\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_KPD8XtafLnc\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Converting Decimals, Improper Fractions, and Mixed Numbers\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_KPD8XtafLnc\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_KPD8XtafLnc\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_KPD8XtafLnc\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction jca_Function() {\n  var x = document.getElementById(\"jca\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"jca_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"jca\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Converting_a_Decimal_to_a_Fraction\" class=\"smooth-scroll\">Converting a Decimal to a Fraction<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Converting_an_Improper_Fraction_to_a_Mixed_Number\" class=\"smooth-scroll\">Converting an Improper Fraction to a Mixed Number<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Converting_Decimals,_Improper_Fractions,_and_Mixed_Numbers_Practice_Questions\" class=\"smooth-scroll\">Converting Decimals, Improper Fractions, and Mixed Numbers Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello, and welcome to this video about converting decimals, improper fractions, and mixed numbers!<\/p>\n<p>In this video, we will explore the steps to convert a decimal to a fraction and a mixed number to an improper fraction and vice versa. Let&#8217;s learn about converting decimals to fractions and mixed numbers to improper fractions!<\/p>\n<p>We use fractions and decimals daily. All our money transactions are done in decimal form. When we bake, we use half cups and one-third cups. Being able to convert between a decimal and a fraction is a math skill you will use every single day. <\/p>\n<p>The table shows a decimal, an improper fraction, and a mixed number that are all equivalent.<\/p>\n<table class=\"ATable\" style=\"margin: auto;\">\n<tbody>\n<tr>\n<td>Decimal<\/td>\n<td><span style=\"font-style:normal; font-size:90%\">\\(3.25\\)<\/span><\/td>\n<\/tr>\n<tr>\n<td>Improper fraction<\/td>\n<td><span style=\"font-style:normal; font-size:90%\">\\(\\frac{13}{4}\\)<\/span><\/td>\n<\/tr>\n<tr>\n<td>Mixed number<\/td>\n<td><span style=\"font-style:normal; font-size:90%\">\\(3\\frac{1}{4}\\)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Converting_a_Decimal_to_a_Fraction\" class=\"m-toc-anchor\"><\/span>Converting a Decimal to a Fraction<\/h2>\n<p>\nWhen converting a decimal to a fraction, we start by multiplying the decimal by a fraction that is equivalent to 1, so the value of the decimal does not change. <\/p>\n<p>For example, if there is only one number after the decimal (in other words, a number in the tenths place), the number would be multiplied by <span style=\"font-style:normal; font-size:90%\">\\(\\frac{10}{10}\\)<\/span>. If there are two numbers after the decimal (the last digit is in the hundredths place), we would multiply the number by <span style=\"font-style:normal; font-size:90%\">\\(\\frac{100}{100}\\)<\/span>, and so on. After multiplying, we simplify the fraction.<\/p>\n<h3><span id=\"Example\" class=\"m-toc-anchor\"><\/span>Example<\/h3>\n<p>\nLet\u2019s take a look at an example.<\/p>\n<p>We will convert 5.85 into fraction form. Since there are 2 numbers after the decimal, we will multiply 5.85 by <span style=\"font-style:normal; font-size:90%\">\\(\\frac{100}{100}\\)<\/span>.<\/p>\n<div class=\"examplesentence\">\\(5.58\\times\\)<span style=\"font-size: 120%;\">\\( \\frac{100}{100}=\\frac{585}{100}\\)<\/span><\/div>\n<p>\n&nbsp;<br \/>\nTo simplify the fraction, we will start by breaking down the number into its factors. Then we will cancel out the common factors in the numerator and denominator.<\/p>\n<p>Both numbers have a factor of 5, so <span style=\"font-style:normal; font-size:90%\">\\(\\frac{585}{100}\\)<\/span> can be simplified to <span style=\"font-style:normal; font-size:90%\">\\(\\frac{117}{20}\\)<\/span>.<\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\(\\frac{585}{100}=\\frac{5\\times 3\\times 3\\times 13}{5\\times 5\\times 2\\times 2}=\\frac{117}{20}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe fraction equivalent to 5.85 is <span style=\"font-style:normal; font-size:90%\">\\(\\frac{117}{20}\\)<\/span>, which is also called an improper fraction. We will now convert the improper fraction into a mixed number.<\/p>\n<h2><span id=\"Converting_an_Improper_Fraction_to_a_Mixed_Number\" class=\"m-toc-anchor\"><\/span>Converting an Improper Fraction to a Mixed Number<\/h2>\n<p>\nWe will convert the improper fraction, <span style=\"font-style:normal; font-size:90%\">\\(\\frac{117}{20}\\)<\/span>, to a mixed number by first dividing the numerator by the denominator.<\/p>\n<p>The whole number becomes the number in the front of the fraction, the remainder becomes the numerator of the fraction, and the denominator of the fraction remains the same. Therefore, <span style=\"font-style:normal; font-size:90%\">\\(\\frac{117}{20}\\)<\/span>, converted to a mixed number is <span style=\"font-style:normal; font-size:90%\">\\(5\\frac{17}{20}\\)<\/span>.<\/p>\n<h3><span id=\"Example\" class=\"m-toc-anchor\"><\/span>Example<\/h3>\n<p>\nHere\u2019s an example of how we use conversions in real life.<\/p>\n<p>Samm owns a bakery. She has <span style=\"font-style:normal; font-size:90%\">\\(5\\frac{3}{4}\\)<\/span> kg of sugar. She buys another bag with 10.75 kg of sugar. What is the total amount of sugar, in kilograms, that Samm has for baking? Give your answer in fraction form.<\/p>\n<p>First, we will start by converting 10.75 to fraction form by multiplying it by <span style=\"font-style:normal; font-size:90%\">\\(\\frac{100}{100}\\)<\/span>, which is <span style=\"font-style:normal; font-size:90%\">\\(\\frac{1,075}{100}\\)<\/span>. Once the fraction is simplified, we get <span style=\"font-style:normal; font-size:90%\">\\(\\frac{43}{4}\\)<\/span>, which when converted to a mixed number is <span style=\"font-style:normal; font-size:90%\">\\(10\\frac{3}{4}\\)<\/span>. <\/p>\n<p>Now that both numbers are in mixed number form, we can easily combine to find the total amount of sugar that Samm has for her baking. So all we\u2019re gonna do is add, <span style=\"font-style:normal; font-size:90%\">\\(5\\frac{3}{4}+10\\frac{3}{4}\\)<\/span>. When we add mixed numbers, we want to start by adding the fractional parts, so let\u2019s do <span style=\"font-style:normal; font-size:90%\">\\(\\frac{3}{4}+\\frac{3}{4}\\)<\/span>. That gives us <span style=\"font-style:normal; font-size:90%\">\\(\\frac{6}{4}\\)<\/span> because we add our numerators and our denominator stays the same.<\/p>\n<p>Now, if you notice, we have an improper fraction. So let\u2019s convert that to a mixed number. If we divide the numerator by the denominator, we\u2019ll get <span style=\"font-style:normal; font-size:90%\">\\(1\\frac{2}{4}\\)<\/span>, which can be simplified to <span style=\"font-style:normal; font-size:90%\">\\(1\\frac{1}{2}\\)<\/span>. Now we\u2019re gonna add this part to our whole number parts from earlier. So <span style=\"font-style:normal; font-size:90%\">\\(5+10=15+1\\frac{1}{2}=16\\frac{1}{2}\\)<\/span>. So Samm has <span style=\"font-style:normal; font-size:90%\">\\(16\\frac{1}{2}\\)<\/span> kg of sugar for baking.<\/p>\n<p>I hope this video on converting decimals, improper fractions, and mixed numbers was helpful. Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Converting_Decimals,_Improper_Fractions,_and_Mixed_Numbers_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Converting Decimals, Improper Fractions, and Mixed Numbers Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nConvert the decimal number 6.8 to a mixed number. <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-1-1\">\\(6\\frac{4}{5}\\)<\/div><div class=\"PQ\"  id=\"PQ-1-2\">\\(6\\frac{3}{4}\\)<\/div><div class=\"PQ\"  id=\"PQ-1-3\">\\(6\\frac{5}{8}\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(6\\frac{1}{2}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>A mixed number is a whole number along with a proper fraction next to it.<\/p>\n<p><strong>Step 1.<\/strong> Convert the decimal number to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change. The number 8 after the decimal is in the tenths place, so we can multiply our decimal number by \\(\\frac{10}{10}\\) to convert it to an improper fraction.<\/p>\n<p style=\"text-align: center;\">\\(6.8\\times\\dfrac{10}{10}=\\dfrac{68}{10}\\)<\/p>\n<p><strong>Step 2.<\/strong> Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.<\/p>\n<p style=\"text-align: center;\">\\(\\dfrac{68}{10}=\\dfrac{2\\times 2\\times 17}{2\\times 5}=\\dfrac{34}{5}\\)<\/p>\n<p><strong>Step 3.<\/strong> Convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Long-Division-Example-1.svg\" alt=\"Long division showing 34 divided by 5. The quotient is 6, 30 is subtracted from 34, leaving a remainder of 4.\" width=\"59\" height=\"100\" class=\"aligncenter size-full wp-image-287035\"  role=\"img\" \/><\/p>\n<p>The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of \\(6\\). The numerator of the proper fraction is the remainder of \\(4\\), and the denominator is the divisor of \\(5\\). So, \\(\\frac{34}{5}=6\\frac{4}{5}\\).<\/p>\n<p>Thus, \\(6.8=6\\frac{4}{5}\\). <\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nConvert the decimal number 3.25 to a mixed number. <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">\\(3\\frac{1}{8}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-2\">\\(3\\frac{1}{4}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(3\\frac{2}{5}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(3\\frac{3}{4}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>A mixed number is a whole number along with a proper fraction next to it. <\/p>\n<p><strong>Step 1.<\/strong> Convert the decimal number to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change. The number 5 after the decimal is in the hundredths place, so we can multiply our decimal number by \\(\\frac{100}{100}\\) to convert it to an improper fraction.<\/p>\n<p style=\"text-align: center;\">\\(3.25\\times\\dfrac{100}{100}=\\dfrac{325}{100}\\)<\/p>\n<p><strong>Step 2.<\/strong> Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.<\/p>\n<p style=\"text-align: center;\">\\(\\dfrac{325}{100}=\\dfrac{5\\times5\\times13}{2\\times2\\times\\times5}=\\dfrac{13}{4}\\)<\/p>\n<p><strong>Step 3.<\/strong> Convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Long-Division-Example-2.svg\" alt=\"Long division of 13 by 4, showing 4 goes into 13 three times, 12 subtracted from 13, with a remainder of 1.\" width=\"59\" height=\"100\" class=\"aligncenter size-full wp-image-287038\"  role=\"img\" \/><\/p>\n<p>The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 3. The numerator of the proper fraction is the remainder of 1, and the denominator is the divisor of 4.  So, \\(\\frac{13}{4}=3\\frac{1}{4}\\).<\/p>\n<p>Thus, \\(3.25=3\\frac{1}{4}\\). <\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nConvert the decimal number 8.275 to a mixed number. <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(8\\frac{25}{49}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(8\\frac{22}{45}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-3\">\\(8\\frac{11}{40}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(8\\frac{29}{40}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>A mixed number is a whole number along with a proper fraction next to it. <\/p>\n<p><strong>Step 1.<\/strong> Convert the decimal number to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change. The number 5 after the decimal is in the thousandths place, so we can multiply our decimal number by \\(\\frac{1{,}000}{1{,}000}\\) to convert it to an improper fraction. <\/p>\n<p style=\"text-align: center;\">\\(8.275\\times\\dfrac{1{,}000}{1{,}000}=\\dfrac{8{,}275}{1{,}000}\\)<\/p>\n<p><strong>Step 2.<\/strong> Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.<\/p>\n<p style=\"text-align: center; line-height: 60px\">\\(\\dfrac{8{,}275}{1{,}000}=\\dfrac{5\\times5\\times331}{2\\times2\\times2\\times5\\times5\\times5}\\)\\(\\:=\\dfrac{331}{40}\\)<\/p>\n<p><strong>Step 3.<\/strong> Convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Long-Division-Example-3.svg\" alt=\"Long division problem showing 331 divided by 40 equals 8, with a remainder of 11.\" width=\"85\" height=\"100\" class=\"aligncenter size-full wp-image-287041\"  role=\"img\" \/><\/p>\n<p>The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 8. The numerator of the proper fraction is the remainder of 11, and the denominator is the divisor of 40.  So, \\(\\frac{331}{40}=8\\frac{11}{40}\\).<\/p>\n<p>Thus, \\(8.275=8\\frac{11}{40}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nA fruit drink recipe that is made with several types of fruit is mixed with 20 ounces of water, 10.2 ounces of apple juice, and \\(\\frac{13}{5}\\) ounces of lemon juice. How much liquid is needed for the recipe? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">\\(32\\frac{4}{5}\\) ounces<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(32\\frac{1}{5}\\) ounces<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(32\\frac{1}{4}\\) ounces<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\(32\\frac{3}{4}\\) ounces<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>We need to combine the amounts of water, apple juice, and lemon juice to find the total amount of liquid needed to mix into the fruit drink. We will convert the amounts of apple juice and lemon juice to mixed numbers first before combining all of the amounts of liquid. A mixed number is a whole number along with a proper fraction next to it.<\/p>\n<p><strong>Step 1.<\/strong> Convert the decimal number of 10.2 to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change, before converting it to a mixed number. The number 2 after the decimal is in the tenths place, so we can multiply our decimal number by \\(\\frac{10}{10}\\) to convert it to an improper fraction. <\/p>\n<p style=\"text-align: center;\">\\(10.2\\times\\dfrac{10}{10}=\\dfrac{102}{10}\\)<\/p>\n<p><strong>Step 2.<\/strong> Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.<\/p>\n<p style=\"text-align: center;\">\\(\\dfrac{102}{10}=\\dfrac{2\\times51}{2\\times5}=\\dfrac{51}{5}\\)<\/p>\n<p><strong>Step 3.<\/strong> Convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Long-Division-Example-4.svg\" alt=\"Long division of 51 by 5, showing 10 as the quotient and 1 as the remainder.\" width=\"59\" height=\"100\" class=\"aligncenter size-full wp-image-287044\"  role=\"img\" \/><\/p>\n<p>The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 10. The numerator of the proper fraction is the remainder of 1, and the denominator is the divisor of 5. So, \\(\\frac{51}{5}=10\\frac{1}{5}\\).<\/p>\n<p><strong>Step 4.<\/strong> Next, convert \\(\\frac{13}{5}\\) to a mixed number by dividing the numerator by the denominator. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Long-Division-Example-5.svg\" alt=\"Long division of 13 by 5, with 2 as the quotient and 3 as the remainder.\" width=\"59\" height=\"100\" class=\"aligncenter size-full wp-image-287047\"  role=\"img\" \/><\/p>\n<p>The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 2. The numerator of the proper fraction is the remainder of 3, and the denominator is the divisor of 5.  So, \\(\\frac{13}{5}=2\\frac{3}{5}\\).<\/p>\n<p><strong>Step 5.<\/strong> Now that we have converted the amounts of apple juice and lemon juice to mixed numbers, we can combine the 3 amounts by adding the proper fractions for the mixed numbers, then adding the whole numbers for each mixed number. <\/p>\n<p style=\"text-align: center;\">\\(20+10\\frac{1}{5}+2\\frac{3}{5}=32\\frac{4}{5}\\)<\/p>\n<p>So, there is a total of \\(32\\frac{4}{5}\\) ounces of liquid needed for the fruit drink recipe.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nYou are on a fishing trip, hoping to catch a certain fish. The daily weight limit for keeping the fish is \\(9\\frac{1}{2}\\) pounds. You catch two fish, one weighing 4.75 pounds, and the other weighing \\(\\frac{9}{2}\\) pounds. Will you need to release one of the fish back into the water due to exceeding the daily weight limit?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">Yes, since the total weight of fish you caught is \\(9\\frac{3}{4}\\) pounds, which is greater than the daily weight limit of \\(9\\frac{1}{2}\\) pounds.<\/div><div class=\"PQ\"  id=\"PQ-5-2\">Yes, since the total weight of fish you caught is \\(9\\frac{1}{4}\\) pounds, which is greater than the daily weight limit of \\(9\\frac{1}{2}\\) pounds.<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">No, since the total weight of fish you caught is \\(9\\frac{1}{4}\\) pounds, which is less than the daily weight limit of \\(9\\frac{1}{2}\\) pounds.<\/div><div class=\"PQ\"  id=\"PQ-5-4\">No, since the total weight of fish you caught is \\(9\\frac{3}{4}\\) pounds, which is less than the daily weight limit of \\(9\\frac{1}{2}\\) pounds.<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>We will combine the total weight of the 2 fish you caught using mixed numbers and compare it with the daily weight limit to determine if one of the fish needs to be released. A mixed number is a whole number along with a proper fraction next to it. <\/p>\n<p><strong>Step 1.<\/strong> Convert the weight of the fish given as a decimal number to an improper fraction by multiplying it by some form of one, so the value of the decimal does not change, before converting it to a mixed number. The number 5 after the decimal is in the hundredths place value, so we can multiply our decimal number by \\(\\frac{100}{100}\\) to convert it to an improper fraction. <\/p>\n<p style=\"text-align: center;\">\\(4.75\\times\\dfrac{100}{100}=\\dfrac{475}{100}\\)<\/p>\n<p><strong>Step 2.<\/strong> Reduce the improper fraction by completely factoring the numerator and denominator, then cancel out any common factors between them.<\/p>\n<p style=\"text-align: center;\">\\(\\dfrac{475}{100}=\\dfrac{5 \\times 5 \\times 19}{2 \\times 2 \\times 5 \\times 5}=\\dfrac{19}{4}\\)<\/p>\n<p>Next, convert the improper fraction, in reduced form, to a mixed number by dividing the numerator by the denominator.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Long-Division-Example-6.svg\" alt=\"Long division of 19 by 4, showing 16 subtracted from 19, resulting in a remainder of 3.\" width=\"59\" height=\"100\" class=\"aligncenter size-full wp-image-287050\"  role=\"img\" \/><\/p>\n<p>The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 4. The numerator of the proper fraction is the remainder of 3, and the denominator is the divisor of 4.  So, \\(4.75=\\frac{19}{4}=4\\frac{3}{4}\\).<\/p>\n<p><strong>Step 3.<\/strong> Convert the weight of the fish given as an improper fraction to a mixed number by dividing the numerator by the denominator. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Long-Division-Example-7.svg\" alt=\"Long division problem showing 9 divided by 2. The 2 divides into 9, giving 4 with a remainder of 1.\" width=\"50\" height=\"100\" class=\"aligncenter size-full wp-image-287029\"  role=\"img\" \/><\/p>\n<p>The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 4. The numerator of the proper fraction is the remainder of 1, and the denominator is the divisor of 2.  So, \\(\\frac{9}{2}=4\\frac{1}{2}\\).<\/p>\n<p><strong>Step 4.<\/strong> Now that we have converted the weights of the two fish caught to mixed numbers, we can combine them by adding the proper fractions for each mixed number, then adding the whole numbers for each mixed number. <\/p>\n<p style=\"text-align: center;\">\\(4\\frac{3}{4}+4\\frac{1}{2}=4\\frac{3}{4}+4\\frac{2}{4}=8\\frac{5}{4}\\)<\/p>\n<p>Since the fractional part of the mixed number is an improper fraction, we need to convert it to a mixed number and add it to 8 to determine the total weight of the fish caught as a proper mixed number.<\/p>\n<p>We can convert \\(\\frac{5}{4}\\) to a mixed number by dividing the numerator by the denominator. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Long-Division-Example-8.svg\" alt=\"Long division of 5 divided by 4, showing 1 as the quotient and 1 as the remainder.\" width=\"50\" height=\"100\" class=\"aligncenter size-full wp-image-287032\"  role=\"img\" \/><\/p>\n<p>The mixed number is written using the quotient, any remainder, and the divisor. The whole number for our mixed number is the quotient of 1. The numerator of the proper fraction is the remainder of 1, and the denominator is the divisor of 4.  So, \\(\\frac{5}{4}=1\\frac{1}{4}\\).<\/p>\n<p>Therefore, the proper mixed number is:<\/p>\n<p style=\"text-align: center;\">\\(8\\frac{5}{4}=8+1\\frac{1}{4}=9\\frac{1}{4}\\)<\/p>\n<p>The total weight of the two game fish you caught is \\(9\\frac{1}{4}\\) pounds. The daily weight limit for the game fish is \\(9\\frac{1}{2}\\) pounds, or \\(9\\frac{2}{4}\\) pounds. Since your total weight for the fish caught is less than the daily weight limit, you do not need to release any of the fish.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/conversions\/\">Return to Conversions Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Conversions Videos<\/p>\n","protected":false},"author":1,"featured_media":100321,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-1168","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-conversion-videos","7":"page_category-pre-algebra-rational-numbers-videos","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/1168","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=1168"}],"version-history":[{"count":7,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/1168\/revisions"}],"predecessor-version":[{"id":287026,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/1168\/revisions\/287026"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100321"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=1168"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}