{"id":97087,"date":"2021-10-13T14:22:13","date_gmt":"2021-10-13T19:22:13","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=97087"},"modified":"2026-03-28T12:21:05","modified_gmt":"2026-03-28T17:21:05","slug":"adding-fractions-with-whole-numbers","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/adding-fractions-with-whole-numbers\/","title":{"rendered":"Adding Fractions with Whole Numbers Overview"},"content":{"rendered":"<p>A mixed number is a number that has a whole number part and a fractional part.<\/p>\n<p>Here is a visual representation of a mixed number.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-196025\" role=\"img\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/Adding-fractions-02.svg\" alt=\"\" width=\"489.024\" height=\"103.68\" \/><\/p>\n<p>This model shows two rectangles that are shaded completely, which represents whole numbers, and one rectangle that is shaded partially, which represents a fraction.<\/p>\n<p>This fraction model represents the mixed number \\(2\\frac{3}{8}\\).<\/p>\n<div class=\"buttonlinks\"><a href=\"#pqs\">Sample Questions<\/a><\/div>\n<h3>Example 1<\/h3>\n<p>When adding a mixed number with a whole number, we first add the whole numbers, then include the fraction.<\/p>\n<p>What is the sum of \\(11\\frac{2}{3}\\) and \\(19\\)?<\/p>\n<p>We will start by adding the whole numbers, which is \\(11+19=30\\). Then we add the fractional part to the end.<\/p>\n<p>Therefore, the sum of \\(11\\frac{2}{3}\\) and \\(19\\) is \\(30\\frac{2}{3}\\).<\/p>\n<h3 id=\"pqs\">Example 2<\/h3>\n<p>Monica picks two bags of peaches to buy at the Farmer\u2019s Market. She places each bag on the scale and the first bag weighs \\(5\\) lbs. and the second bag weighs \\(6\\frac{2}{3}\\) lbs. How many pounds of peaches does Monica buy?<\/p>\n<p>When adding a whole number and a fraction we first add the whole numbers, then we include the fraction.<\/p>\n<p>\\(5+6=11\\), now we include \\(\\frac{2}{3}\\), therefore, Monica buys a total of \\(11\\frac{2}{3}\\) lbs. of peaches.<\/p>\n<a href=\"https:\/\/www.mometrix.com\/university\/mathcr\/?utm_source=academy&amp;utm_medium=inline&amp;utm_campaign=academy-mu-ads&amp;utm_content=mathcr-test\" class=\"class_names\" style=\"color:black;\" onclick=\"_paq.push(['trackEvent', 'Course Button', 'Course Click', 'MathPlacement Course Click']);\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-57671 size-full\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/09\/imcr20-New.png\" alt=\"Click here for 20% off of Mometrix Math College Readiness Online Course. Use code: IMCR20\" width=\"728\" height=\"90\" \/><\/a>\n<h2 class=\"pt-page\">Adding Fractions with Whole Numbers Sample Questions<\/h2>\n<p>Here are a few sample questions going over adding fractions with whole numbers.<br \/>\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 \/>\nCalculate the sum of \\(14\\frac{5}{6}\\) and \\(38\\).<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(54\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">\\(52\\frac{5}{6}\\)<\/div><div class=\"PQ\"  id=\"PQ-1-3\">\\(56\\frac{2}{5}\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(55\\)<\/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>When adding fractions and whole numbers, first calculate the whole number plus the whole number, and then include the remaining fraction in the answer. For example, \\(14+38=52\\), so \\(52\\frac{5}{6}\\) is the answer.<\/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 \/>\nCalculate the sum of \\(45\\) and \\(2\\frac{1}{3}\\).<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">\\(47\\frac{2}{3}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(45\\frac{2}{3}\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(46\\frac{3}{5}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-4\">\\(47\\frac{1}{3}\\)<\/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>Once again, when adding fractions and whole numbers, first calculate the whole number plus the whole number, and then include the remaining fraction in the answer. For example, \\(45+2=47\\), so \\(47\\frac{1}{3}\\) is the answer.<\/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 \/>\nAdd \\(4\\frac{3}{2}+5\\).<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(10\\frac{1}{5}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(11\\frac{3}{5}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(9\\frac{1}{5}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">\\(10\\frac{1}{2}\\)<\/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>The first step is to address the improper fraction within the mixed number \\(4\\frac{3}{2}\\). The fraction \\(\\frac{3}{2}\\) is the same thing as \\(1\\frac{1}{2}\\), so rewrite \\(4\\frac{3}{2}\\) as \\(5\\frac{1}{2}\\). Now, simply combine \\(5\\frac{1}{2}\\) and \\(5\\) to get \\(10\\frac{1}{2}\\).<\/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 \/>\nAdd \\(3+3\\frac{5}{4}\\).<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\\(6\\frac{1}{4}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-2\">\\(7\\frac{1}{4}\\)<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(6\\frac{3}{4}\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\(7\\frac{3}{4}\\)<\/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>The first step is to address the improper fraction within the mixed number \\(3\\frac{5}{4}\\). The fraction \\(\\frac{5}{4}\\) is the same thing as \\(1\\frac{1}{4}\\), so rewrite \\(3\\frac{5}{4}\\) as \\(4\\frac{1}{4}\\). Now, simply combine \\(3\\) and \\(4\\frac{1}{4}\\) to get \\(7\\frac{1}{4}\\).<\/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 \/>\nFill in the missing value in order to make the following equation true:<\/p>\n<div class=\"yellow-math-quote\">\\(3\\frac{4}{5}+\\) ______\\(=18\\frac{4}{5}\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(13\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(14\\frac{1}{5}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">\\(15\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(16\\frac{1}{5}\\)<\/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>In order to create a balanced equation, the mixed number \\(18\\frac{4}{5}\\) must be on each side. Adding \\(3\\frac{4}{5}+15=18\\frac{4}{5}\\), so \\(15\\) is the missing value.<\/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><\/p>\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/math-sample-questions\/\">Return to Math Sample Questions<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>A mixed number is a number that has a whole number part and a fractional part. Here is a visual representation of a mixed number. This model shows two rectangles that are shaded completely, which represents whole numbers, and one rectangle that is shaded partially, which represents a fraction. This fraction model represents the mixed &#8230; <a title=\"Adding Fractions with Whole Numbers Overview\" class=\"read-more\" href=\"https:\/\/www.mometrix.com\/academy\/adding-fractions-with-whole-numbers\/\" aria-label=\"Read more about Adding Fractions with Whole Numbers Overview\">Read more<\/a><\/p>\n","protected":false},"author":13,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-97087","1":"page","2":"type-page","3":"status-publish","5":"page_category-math-advertising-group","6":"page_category-math-non-video-pages","7":"page_type-topic-overview","8":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/97087","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\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=97087"}],"version-history":[{"count":7,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/97087\/revisions"}],"predecessor-version":[{"id":281891,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/97087\/revisions\/281891"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=97087"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}