Fractions are written to describe the part of the whole number. We can perform all arithmetic operations like addition, subtraction, multiplication, and division. On this page, we will discuss the fraction of a fraction which means multiplication of a fraction with another fraction.<\/p>\n
Let us find the fraction of a fraction involving fractions like proper fraction, improper fraction, unit fraction, Equivalent fraction, Like and Unline fraction, and mixed fraction. Read the entire article to know how to solve a fraction of a fraction with example questions and answers provided.<\/p>\n
Do Refer:<\/strong><\/p>\n The fraction of a fraction is not like the addition and subtraction of the fractions where the denominator is the same. The method is different for the multiplication of fractions. Let us learn the steps to know how to find the fraction of a fraction. Also Read Articles:<\/strong><\/p>\n Example 1.<\/strong> Example 2.<\/strong> Example 3.<\/strong> Example 4.<\/strong> Example 5.<\/strong> 1. How do I find a fraction of a fraction?<\/strong><\/p>\n I can find the fraction of a fraction by multiplying the top numbers of the two fractions and multiply the bottom numbers of the fractions and then write the result.<\/p>\n 2. Write an example of the multiplication of a unit fraction with a unit fraction.<\/strong><\/p>\n Suppose let us consider two unit fractions \\(\\frac{1}{3}\\) and \\(\\frac{1}{10}\\). 3. What are six kinds of fractions?<\/strong><\/p>\n There are 6 types of fractions. They are proper fraction, improper fraction, mixed fraction, like fraction, unlike fraction and equivalent fraction.<\/p>\n","protected":false},"excerpt":{"rendered":" Fractions are written to describe the part of the whole number. We can perform all arithmetic operations like addition, subtraction, multiplication, and division. On this page, we will discuss the fraction of a fraction which means multiplication of a fraction with another fraction. Let us find the fraction of a fraction involving fractions like proper … Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":118474,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/07\/Fraction-of-a-Fraction.png","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/118438"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=118438"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/118438\/revisions"}],"predecessor-version":[{"id":135400,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/118438\/revisions\/135400"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media\/118474"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=118438"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=118438"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=118438"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
How to Solve a Fraction of a Fraction?<\/h3>\n
\n1. Multiplication of whole numbers and a fraction:<\/strong> The whole number of a fraction is very easy. All you have to do is to multiply the whole number with the numerator of the fraction and then write the denominator as it is. Let us see one example for the multiplication of a whole number and a fraction.
\nExample: Multiply 3 and \\(\\frac{1}{5}\\)
\nSolution:
\n3 \u00d7 \\(\\frac{1}{5}\\)
\nMultiply the whole number and numerator.
\n3 \u00d7 1 = 3
\n\\(\\frac{3}{5}\\)
\n2. Multiplication of proper fraction:<\/strong> In this concept, you have to multiply the numerator with the numerator and the denominator with the denominator of the given fractions.
\nFor example let us take \\(\\frac{2}{3}\\) and \\(\\frac{4}{6}\\)
\nSolution:
\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{4}{6}\\)
\nMultiply the numerators together: 2 \u00d7 4 = 8
\nMultiply the denominator together: 3 \u00d7 6 = 18
\n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{4}{6}\\) = \\(\\frac{8}{18}\\)
\n3. Multiplication of Improper fraction:<\/strong> The multiplication of improper fraction is similar to Multiplication of proper fraction. In this concept, we have to multiply the numerator with the numerator and the denominator with the denominator of the given fractions. And then convert the improper fraction to the mixed fraction.
\nExample:<\/strong> Multiply \\(\\frac{4}{3}\\) and \\(\\frac{6}{5}\\)
\nSolution:<\/strong>
\n\\(\\frac{4}{3}\\) \u00d7 \\(\\frac{6}{5}\\)
\nMultiply the numerators together: 4 \u00d7 6 = 24
\nMultiply the denominator together: 3 \u00d7 5 = 15
\n\\(\\frac{4}{3}\\) \u00d7 \\(\\frac{6}{5}\\) = \\(\\frac{24}{15}\\)
\nNow convert this improper fraction to the mixed fraction.
\n\\(\\frac{24}{15}\\) = 1 \\(\\frac{3}{5}\\)
\n4. Multiplication of Mixed Fraction:<\/strong> The mixed fraction is a combination of a whole number and a fraction. In this concept, we can change the mixed fraction to the improper fraction and then find the multiplication of a fraction.
\nFor example multiply 2 \\(\\frac{2}{3}\\) and 3 \\(\\frac{1}{4}\\).
\nSolution: <\/strong>
\nChange the given mixed fractions to the improper fraction
\n\\(\\frac{8}{3}\\) \u00d7 \\(\\frac{13}{4}\\) = \\(\\frac{104}{12}\\) = \\(\\frac{26}{3}\\)
\nNow convert the improper fraction to the mixed fraction 8 \\(\\frac{2}{3}\\)
\nThus the product of 2 \\(\\frac{2}{3}\\) and 3 \\(\\frac{1}{4}\\) is 8 \\(\\frac{2}{3}\\).<\/p>\n\n
Fraction of a Fraction Solved Problems<\/h3>\n
\nFind the fraction of a fraction for \\(\\frac{1}{2}\\) and \\(\\frac{1}{6}\\).
\nSolution:<\/strong>
\nGiven the fractions \\(\\frac{1}{2}\\) and \\(\\frac{1}{6}\\).
\nThe two fractions are unit fractions.
\nNow find the product of two unit fractions.
\nMultiply the numerator and denominators of the unit fractions.
\n\\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{6}\\) = \\(\\frac{1\u00d71}{2\u00d76}\\) = \\(\\frac{1}{12}\\)
\nThus the unit fraction of a fraction for \\(\\frac{1}{2}\\) and \\(\\frac{1}{6}\\) is \\(\\frac{1}{12}\\).<\/p>\n
\nFind the fraction of a fraction for \\(\\frac{4}{7}\\) and \\(\\frac{2}{5}\\).
\nSolution:<\/strong>
\nGiven the fractions \\(\\frac{4}{7}\\) and \\(\\frac{2}{5}\\).
\nMultiply the numerator with the numerator and denominator with the denominator of the given fractions.
\n\\(\\frac{4}{7}\\) \u00d7 \\(\\frac{2}{5}\\)
\nMultiply the numerators together: 4 \u00d7 2 = 8
\nMultiply the denominator together: 7 \u00d7 5 = 35
\n\\(\\frac{4}{7}\\) \u00d7 \\(\\frac{2}{5}\\) = \\(\\frac{8}{35}\\)
\nThus the fraction of a fraction for \\(\\frac{4}{7}\\) and \\(\\frac{2}{5}\\) is \\(\\frac{8}{35}\\)<\/p>\n
\nFind the fraction of a fraction for \\(\\frac{3}{8}\\) and \\(\\frac{4}{9}\\).
\nSolution:<\/strong>
\nGiven the fractions \\(\\frac{3}{8}\\) and \\(\\frac{4}{9}\\).
\nMultiply the numerator with the numerator and denominator with the denominator of the given fractions.
\n\\(\\frac{3}{8}\\) \u00d7 \\(\\frac{4}{9}\\)
\nMultiply the numerators together: 3 \u00d7 4 = 12
\nMultiply the denominator together: 8 \u00d7 9 = 72
\n\\(\\frac{3}{8}\\) \u00d7 \\(\\frac{4}{9}\\) = \\(\\frac{12}{72}\\) = \\(\\frac{1}{6}\\)
\nThus the fraction of a fraction for \\(\\frac{3}{8}\\) and \\(\\frac{4}{9}\\) is \\(\\frac{12}{72}\\) or \\(\\frac{1}{6}\\).<\/p>\n
\nFind the fraction of a fraction for \\(\\frac{7}{2}\\) and \\(\\frac{9}{5}\\).
\nSolution:<\/strong>
\nGiven the fractions \\(\\frac{7}{2}\\) and \\(\\frac{9}{5}\\).
\nMultiply the numerator with the numerator and denominator with the denominator of the given fractions.
\nWe have to multiply the numerator with the numerator and the denominator with the denominator of the given fractions.
\nAnd then convert the improper fraction to the mixed fraction.
\n\\(\\frac{7}{2}\\) \u00d7 \\(\\frac{9}{5}\\)
\nMultiply the numerators together: 7 \u00d7 9 = 63
\nMultiply the denominator together: 2 \u00d7 5 = 10
\n\\(\\frac{7}{2}\\) \u00d7 \\(\\frac{9}{5}\\) = \\(\\frac{63}{10}\\)
\nNow convert this improper fraction to the mixed fraction.
\n\\(\\frac{63}{10}\\) = 6 \\(\\frac{3}{10}\\)
\nTherefore the fraction of a fraction for \\(\\frac{7}{2}\\) and \\(\\frac{9}{5}\\) is \\(\\frac{63}{10}\\) or 6 \\(\\frac{3}{10}\\)<\/p>\n
\nFind the fraction of a fraction for 1 \\(\\frac{1}{4}\\) and 2 \\(\\frac{1}{5}\\).
\nSolution:<\/strong>
\nGiven the fractions 1 \\(\\frac{1}{4}\\) and 2 \\(\\frac{1}{5}\\).
\nChange the given mixed fractions to the improper fraction.
\nWe have to multiply the numerator with the numerator and the denominator with the denominator of the given fractions.
\nAnd then convert the improper fraction to the mixed fraction.
\n1 \\(\\frac{1}{4}\\) = 4 \u00d7 1 + 1 = 5 = \\(\\frac{5}{4}\\)
\n2 \\(\\frac{1}{5}\\) = 5 \u00d7 2 + 1 = 11 = \\(\\frac{11}{5}\\)
\nNow multiply the fractions.
\n\\(\\frac{5}{4}\\) \u00d7 \\(\\frac{11}{5}\\)
\nMultiply the numerators together: 5 \u00d7 11 = 55
\nMultiply the denominator together: 4 \u00d7 5 = 20
\n\\(\\frac{5}{4}\\) \u00d7 \\(\\frac{11}{5}\\) = \\(\\frac{55}{20}\\)
\nNow convert this improper fraction to the mixed fraction.
\n\\(\\frac{55}{20}\\) = 2 \\(\\frac{3}{4}\\)
\nTherefore the fraction of a fraction for 1 \\(\\frac{1}{4}\\) and 2 \\(\\frac{1}{5}\\) is \\(\\frac{55}{20}\\) or 2 \\(\\frac{3}{4}\\)<\/p>\nFAQs on Fraction of a Fraction<\/h3>\n
\nSolution:<\/strong>
\nNow find the product of two unit fractions.
\nMultiply the numerator and denominators of the fractions.
\n\\(\\frac{1}{3}\\) \u00d7 \\(\\frac{1}{10}\\) = \\(\\frac{1\u00d71}{3\u00d710}\\) = \\(\\frac{1\u00d71}{30}\\)<\/p>\n