{"id":156100,"date":"2022-03-26T01:22:53","date_gmt":"2022-03-25T19:52:53","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/dividing-fractions-steps-and-solved-examples\/"},"modified":"2022-12-22T21:37:02","modified_gmt":"2022-12-22T16:07:02","slug":"dividing-fractions-steps-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/dividing-fractions\/","title":{"rendered":"Dividing Fractions \u2013 Steps and Solved Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dividing-fractions\/#Explain_in_Detail_Steps_For_Fraction_Divided_By_Fractions\" title=\"Explain in Detail :Steps For Fraction Divided By Fractions\">Explain in Detail :Steps For Fraction Divided By Fractions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dividing-fractions\/#What_are_Fractions\" title=\"What are Fractions?\">What are Fractions?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dividing-fractions\/#What_is_Meant_by_Dividing_Fractions\" title=\"What is Meant by Dividing Fractions?\">What is Meant by Dividing Fractions?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dividing-fractions\/#How_to_Divide_Fractions\" title=\"How to Divide Fractions?\">How to Divide Fractions?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dividing-fractions\/#Dividing_Fraction_by_a_Fraction\" title=\"Dividing Fraction by a Fraction\">Dividing Fraction by a Fraction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dividing-fractions\/#Dividing_Fraction_by_a_Whole_Number\" title=\"Dividing Fraction by a Whole Number\">Dividing Fraction by a Whole Number<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dividing-fractions\/#Dividing_Fractions_by_a_Mixed_Fraction\" title=\"Dividing Fractions by a Mixed Fraction\">Dividing Fractions by a Mixed Fraction<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dividing-fractions\/#Dividing_Decimals_as_Fractions\" title=\"Dividing Decimals as Fractions\">Dividing Decimals as Fractions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dividing-fractions\/#General_Solution\" title=\"General Solution:\">General Solution:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/dividing-fractions\/#Steps_For_Dividing_Fractions_By_Whole_Numbers\" title=\"Steps For Dividing Fractions By Whole Numbers\">Steps For Dividing Fractions By Whole Numbers<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Explain_in_Detail_Steps_For_Fraction_Divided_By_Fractions\"><\/span>Explain in Detail :Steps For Fraction Divided By Fractions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To divide fractions by fractions, you need to use the reciprocal of the divisor fraction.<\/p>\n<p>For example, to divide 1\/4 by 2\/3, you would use the reciprocal of 2\/3, which is 3\/2.<\/p>\n<p>To divide fractions, you simply multiply the numerators and denominators of the fractions together.<\/p>\n<p>In the example above, you would multiply 1\/4 by 3\/2 to get the answer of 3\/8.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156099 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/dividing-fractions-steps-and-solved-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/dividing-fractions-steps-and-solved-examples.jpg?v=1648237970 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/dividing-fractions-steps-and-solved-examples-300x212.jpg?v=1648237970 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_are_Fractions\"><\/span>What are Fractions?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A fraction is a part of a whole value or number. It is represented by p\/q or a\/b or m\/n, etc. The upper part of a fraction is called the numerator and the lower part is the denominator. Examples of fractions are \u00bd, \u00bc, \u2154, \u2157, etc.<\/p>\n<p>All the arithmetic operations such as addition, subtraction, multiplication and division can be performed upon the fractions. Let us learn here how to divide a fraction by a fraction, by a whole number and by a mixed number with the help of examples, with simple steps.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Meant_by_Dividing_Fractions\"><\/span>What is Meant by Dividing Fractions?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Dividing fractions is nothing but multiplying the fractions by reversing one of the two fraction numbers or by writing the reciprocal of one of the fractions. By reciprocal we mean, if a fraction is given as a\/b, then the reciprocal of it will b\/a. Thus, interchanging the position of numerator and denominator with each other.<\/p>\n<div class=\"table-responsive\">\n<table>\n<tbody>\n<tr>\n<td>a\/b \u00f7 c\/d = a\/b \u00d7 d\/c<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Divide_Fractions\"><\/span>How to Divide Fractions?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The division of fractions can be classified into three different ways. They are<\/p>\n<ul>\n<li>Dividing fractions by a fraction<\/li>\n<li>Dividing fractions by whole number<\/li>\n<li>Dividing fractions by mixed fraction<\/li>\n<\/ul>\n<p>Let us discuss all these three methods in a detailed way<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dividing_Fraction_by_a_Fraction\"><\/span><strong>Dividing Fraction by a Fraction<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p align=\"justify\">In three simple steps, we can solve the division of fractions by converting them into the multiplication of fractions. Let us learn one by one.<\/p>\n<p align=\"justify\"><strong>Step 1:<\/strong> Write the reciprocal of the second fraction number and multiply it with the first fraction number<\/p>\n<p align=\"justify\"><strong>Step 2:<\/strong> Multiply the numerators and denominators of both fractions<\/p>\n<p align=\"justify\"><strong>Step 3:<\/strong> Simplify the fraction number<\/p>\n<p>In general, if a\/b is a fraction which is divided by c\/d. Then we can solve the division as;<\/p>\n<ul>\n<li>a\/b \u00f7 c\/d = a\/b \u00d7 d\/c<\/li>\n<li>a\/b \u00f7 c\/d = a\u00d7d \/ b\u00d7c<\/li>\n<li>a\/b \u00f7 c\/d = ad\/bc<\/li>\n<\/ul>\n<p>You can see from the above expressions. The a\/b is divided by c\/d, then we can write it as a\/b multiplied by d\/c (reciprocal of c\/d). And in the next step, we have to multiply both the numerator a &amp; d and both the denominator, c &amp; d. Hence, we can simplify the rest calculation.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dividing_Fraction_by_a_Whole_Number\"><\/span><strong>Dividing Fraction by a Whole Number<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>While dividing the fractions with whole numbers, the process of division is very easy. Follow the procedure given below.<\/p>\n<p><strong>Step 1:<\/strong> The whole number is converted into a fraction by applying the denominator value is 1<\/p>\n<p><strong>Step 2:<\/strong> Take the reciprocal of the number<\/p>\n<p><strong>Step 3:<\/strong> Now, multiply the fractional value by a given fraction<\/p>\n<p><strong>Step 4:<\/strong> Simplify the given expression<\/p>\n<p><b>Example:<\/b> Divide 6\/5 by 10<\/p>\n<p>Step 1: Convert 10 into a fraction: 10\/1<\/p>\n<p>Step 2: Take reciprocal: 1\/10<\/p>\n<p>Step 3: Multiply 6\/5 and 1\/10: (6\/5)\u00d7(1\/10)<\/p>\n<p>Step 4: Simplify: 3\/25<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dividing_Fractions_by_a_Mixed_Fraction\"><\/span><strong>Dividing Fractions by a Mixed Fraction<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The process of dividing fractions by a mixed fraction is almost similar to dividing fractions by a fraction. The steps to perform the division of a fraction by a mixed fraction are as follows:<\/p>\n<p><strong>Step 1:<\/strong> Convert the mixed fraction into the improper fraction<\/p>\n<p><strong>Step 2:<\/strong> Now, take the reciprocal for the improper fraction<\/p>\n<p><strong>Step 3:<\/strong> Multiply the obtained fraction by a given fraction<\/p>\n<p><strong>Step 3:<\/strong> Simplify the fractions<\/p>\n<p><b>Example:<\/b> Divide \u2156 by 3\u00bd.<\/p>\n<p>Step 1: Convert 3\u00bd into an improper fraction, we get 7\/2<\/p>\n<p>Step 2: Take reciprocal for improper fraction: 2\/7<\/p>\n<p>Step 3: Multiply \u2156 and 2\/7<\/p>\n<p>Step 4: Simplify: 4\/35<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Dividing_Decimals_as_Fractions\"><\/span>Dividing Decimals as Fractions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>We have learned to divide fractions using three simple steps. Now with the help of these steps let us learn how to divide decimals with examples.<\/p>\n<p><strong>Example:<\/strong> Divide 0.5 \u00f7 0.2<\/p>\n<p><strong>Solution:<\/strong> To divide these decimal numbers, we have to convert both the decimal number into natural numbers by multiplying numerator and denominator by 10.<\/p>\n<p>Therefore, 0.5 \u00d7 10 \/ 0.2 \u00d7 10<\/p>\n<p>We get, 5\/2 = <strong>2.5<\/strong><\/p>\n<p>Also, we can use the dividing fractions method to solve the above problem.<\/p>\n<p>We can write 0.5 and 0.2 as 5\/10 and 2\/10.<\/p>\n<p>So for 5\/10 \u00f7 2\/10, we can use the same steps fraction\u2019s division.<\/p>\n<p>5\/10 \u00d7 10\/2<\/p>\n<p>= 5 \u00d7 10 \/ 10 \u00d7 2<\/p>\n<p>= 50\/20<\/p>\n<p>= 5\/2<\/p>\n<p>= <strong>2.5<\/strong><\/p>\n<p><strong>Note:<\/strong> These are the simple method of dividing decimals. You can also use the direct division method to divide decimals. The only difference is to place the decimal into the right place of the quotient. Let us take an example of this.<\/p>\n<p><strong>Example:<\/strong> Divide 13.2 \u00f7 2<\/p>\n<p><strong>Solution: <\/strong>2) 13.2 (6.6)<\/p>\n<p>Therefore, 13.2 \u00f7 2 = <strong>6.6<\/strong><\/p>\n<p>Dividing the natural numbers or whole numbers is an easy task but dividing the fractions is a little complex one. The operations performed on natural numbers and whole consist of simple calculations, which one can easily solve. But the operations performed on fractions are sometimes typical and also time-consuming. The simple division has four parts divisor, dividend, quotient and remainder. Also, know some of the divisibility rules for the whole number here.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"General_Solution\"><\/span>General Solution:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There is no general solution to this problem.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Steps_For_Dividing_Fractions_By_Whole_Numbers\"><\/span>Steps For Dividing Fractions By Whole Numbers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. Determine the whole number divisor.<\/p>\n<p>2. Place the divisor above the dividend (fraction) with a line drawn through the two.<\/p>\n<p>3. Divide the top number of the dividend (the numerator) by the divisor.<\/p>\n<p>4. Write the answer below the dividend line.<\/p>\n<p>5. Repeat steps 3 and 4 until there is no remainder.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Explain in Detail :Steps For Fraction Divided By Fractions To divide fractions by fractions, you need to use the reciprocal [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Dividing Fractions \u2013 Steps and Solved Examples","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Dividing Fractions topic of maths in details explained by subject experts on infinitylearn.com. 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