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Let us revise a bit about fractions before we know more about unlike fractions<\/span><\/p>\n <\/p>\n A fraction is a number representation by which a part of a whole object or a group of objects is described. The numerical representation of fraction is as follows:<\/span><\/p>\n \\frac{a}{b}<\/span> where \u2018a\u2019 is termed as the numerator and \u2018b\u2019 as the denominator.<\/span><\/p>\n Some examples of fractions are \\frac{2}{5}, \\frac{2}{4}, \\frac{1}{7}, \\frac{4}{9}, \\frac{3}{8}, \\frac{7}{12} .<\/span><\/span><\/p>\n The two types of fractions are Like and Unlike Fractions.<\/span><\/p>\n Like Fractions<\/b><\/p>\n A group of Fractions is like or similar fractions if all fractions have the same denominators. For Example, \\frac{2}{5}, \\frac{3}{5}, \\frac{1}{5}, \\frac{4}{5}<\/span> is a group of like fractions.<\/span><\/b><\/p>\n <\/p>\n A group of fractions is Unlike fractions or dissimilar fractions if fractions have different denominators. For example, <\/span><\/b><\/p>\n \\frac{2}{5}, \\frac{2}{4}, \\frac{1}{7}, \\frac{4}{9}, \\frac{3}{8}, \\frac{7}{12} .<\/span><\/span><\/b><\/p>\n As the denominators are different so addition and subtraction cannot be done simply. First, the fractions have to be changed to like fractions and then the required operation can be performed.<\/span><\/p>\n <\/span><\/p>\n Unlike fractions can be converted to like fractions. First, the LCM of the denominators is found out and the numerator and denominator of each fraction are multiplied by a number which changes the denominator value, such that the fractions become alike.\u00a0<\/span><\/p>\n For example, unlike fractions \\frac{2}{3} \\text { and } \\frac{3}{5}<\/span> can be converted to like fractions.<\/span><\/p>\n First, the LCM of the denominators 3, 5 needs to be calculated. The LCM is 15.<\/span><\/p>\n Now converting the fractions to like fractions.<\/span><\/p>\n \\frac{2}{3} \\times \\frac{5}{5}=\\frac{10}{15} <\/span><\/span><\/p>\n Now the fractions are \\frac{10}{15} \\text { and } \\frac{9}{15}<\/span> are like fractions.<\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n The addition and subtraction of two, unlike fractions, can be performed only when the denominators are made equal this can be done in two ways.\u00a0<\/span><\/p>\n (1)<\/b> Cross Multiplication\u00a0<\/strong><\/p>\n (2)<\/b> LCM<\/strong><\/p>\n <\/p>\n Let us understand both the methods with the help of examples:<\/span><\/p>\n Example<\/strong>:<\/strong> Add \\frac{5}{6} \\text { and } \\frac{3}{7} \\text {. }<\/span><\/span><\/p>\n Solution:<\/strong><\/p>\n By Cross Multiplication<\/b><\/p>\n The numerator of the first fraction \\frac{5}{6}<\/span> i.e., 5 is multiplied by the denominator of the second fraction \\frac{3}{7}<\/span> i.e., 7.<\/span><\/span><\/p>\n Similarly, the numerator of the second fraction is multiplied by the denominator of the first fraction, i.e., 3 is multiplied by 6.<\/span><\/p>\n Now the denominator of both the fractions is multiplied.<\/span><\/p>\n \\therefore \\frac{5}{6}+\\frac{3}{7}=\\frac{(5 \\times 7)+(3 \\times 6)}{7 \\times 6}<\/span><\/span><\/p>\n =\\frac{35+18}{42}<\/span><\/span><\/p>\n =\\frac{53}{42}<\/span><\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n By LCM method<\/b><\/p>\n The LCM of the denominators, i.e., 6 and 7, is 42.<\/span><\/p>\n Now multiply the first fraction \\frac{5}{6}<\/span> with the fraction \\frac{7}{7}<\/span> and the second fraction \\frac{3}{7}<\/span> with the fraction \\frac{6}{6}<\/span> and then add the two.<\/span><\/p>\n \\therefore \\frac{5}{6}+\\frac{3}{7}=\\left(\\frac{5}{6} \\times \\frac{7}{7}\\right)+\\left(\\frac{3}{7} \\times \\frac{6}{6}\\right)<\/span><\/span><\/p>\n =\\frac{35}{42}+\\frac{18}{42}<\/span><\/span><\/p>\n =\\frac{35+18}{42}=\\frac{53}{42}<\/span><\/span><\/p>\n Hence using both the methods the addition can be done of fractions which are unlike.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Example:<\/strong> Subtract \\frac{3}{6}<\/span> <\/span>from \\frac{3}{4}<\/span><\/span>.<\/span><\/p>\n Solution:<\/strong><\/p>\n By Cross Multiplication<\/b><\/p>\n The numerator of the first fraction \\frac{3}{6}<\/span> <\/span>i.e., 3 is multiplied by the denominator of the second fraction \\frac{3}{4}<\/span> <\/span>i.e., 4.<\/span><\/p>\n Similarly, the numerator of the second fraction is multiplied by the denominator of the first fraction, i.e., 3 is multiplied by 6.<\/span><\/p>\n Now the denominator of both the fractions is multiplied.<\/span><\/p>\n \\frac{3}{4}-\\frac{3}{6}=\\frac{(3 \\times 6)-(3 \\times 4)}{4 \\times 6}<\/span><\/span><\/p>\n =\\frac{18-12}{24}<\/span><\/span><\/p>\n =\\frac{6}{24}<\/span><\/span><\/p>\n The fraction can be simplified to \\frac{1}{4} \\text {. }<\/span>\u00a0 \u00a0 \u00a0 \u00a0[since, 24 \u00f7 6 = 4]<\/span><\/p>\n <\/b><\/p>\n By LCM method<\/b><\/p>\n The LCM of the denominators, i.e., 4 and 6, is 12. <\/span><\/p>\n Now multiply the first fraction \\frac{3}{6}<\/span> <\/span>with the fraction \\frac{2}{2}<\/span> <\/span>and the second fraction\u00a0 \\frac{3}{4}<\/span> <\/span>with the fraction \\frac{3}{3}<\/span><\/span>.<\/span><\/p>\n \\therefore \\frac{3}{4}-\\frac{3}{6}=\\frac{3}{4} \\times \\frac{3}{3}-\\left(\\frac{3}{6} \\times \\frac{2}{2}\\right)<\/span><\/span><\/p>\n =\\frac{9}{12}-\\frac{6}{12}<\/span><\/span><\/p>\n =\\frac{3}{12}<\/span><\/span><\/p>\n which can simply further as 12 \\div 3=4<\/span><\/span><\/p>\n \\therefore \\frac{3}{4}-\\frac{3}{6}=\\frac{1}{4}<\/span><\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n To multiply unlike fractions, multiply the numerators then multiply the denominators separately, and then simplify the result.<\/span><\/p>\n Example<\/strong>:<\/strong> <\/span>Multiply \\frac{2}{5}\\text{ and }\\frac{1}{3}<\/span>.<\/span><\/p>\n Solution:<\/strong><\/p>\n \\frac{2}{5} \\times \\frac{1}{3}=\\frac{2 \\times 1}{5 \\times 3}=\\frac{2}{15}<\/span><\/span><\/p>\n <\/p>\n To divide unlike fractions, replace the division sign with multiplication and take the reciprocal of the second fraction.<\/span><\/p>\n Example<\/strong>:<\/strong> \\frac{2}{3} \\div \\frac{4}{5}<\/span><\/span>.<\/span><\/p>\n Solution:\u00a0<\/strong><\/p>\n \\frac{2}{3} \\div \\frac{4}{5}=\\frac{2}{3} \\times \\frac{5}{4}<\/span><\/span><\/p>\n =\\frac{2 \\times 5}{3 \\times 4}<\/span><\/span><\/p>\n =\\frac{10}{12}<\/span><\/span><\/p>\n <\/p>\n Example 1<\/span>: Which group of fractions are like and which are unlike among the given options:<\/span><\/p>\n \\text { A. } \\frac{1}{2}, \\frac{2}{2}, \\frac{4}{2}, \\frac{7}{2}.<\/span><\/span><\/p>\n <\/span><\/p>\n\\text { B. } \\frac{2}{3}, \\frac{4}{3}, \\frac{5}{6}, \\frac{2}{4}, \\frac{6}{7}<\/span>\n <\/p>\n\\text { C. } \\frac{2}{5}, \\frac{7}{5}, \\frac{6}{5}, \\frac{4}{5}, \\frac{9}{5}<\/span>\n <\/span><\/p>\n \\text { D. } \\frac{1}{2}, \\frac{3}{4}, \\frac{5}{6}, \\frac{7}{8}, \\frac{9}{10}<\/span><\/span><\/p>\n Solution:<\/strong><\/p>\n In options (A) and (B) the denominator is the same for the full group of fractions hence they are like fractions.<\/span><\/p>\n In options (C) and (D) the denominators are different for each fraction and hence they are unlike fractions.<\/span><\/p>\n <\/span><\/p>\n Example 2<\/strong>:<\/strong> Find the sum of the unlike fractions \\frac{4}{7}<\/span> <\/span>and \\frac{3}{2}<\/span><\/span>.<\/span><\/p>\n Solution:<\/strong><\/p>\n The given fractions are unlike as the denominators are 7 and 2.<\/span><\/p>\n The LCM of the denominators 7 and 2 is 14.<\/span><\/p>\n Multiply the numerator\u00a0 and denominator of\u00a0 \\frac{4}{7} \\text { by } 2<\/span><\/span><\/p>\n \\frac{4}{7} \\times \\frac{2}{2}=\\frac{8}{14}<\/span><\/span><\/p>\nWhat is a Fraction?<\/b><\/h2>\n
Unlike Fractions<\/b><\/h2>\n
How to Convert Unlike Fractions to Like Fractions?<\/b><\/h2>\n
\\frac{3}{5} \\times \\frac{3}{3}=\\frac{9}{15}<\/span><\/span><\/p>\nDifferent Operations on unlike fractions:<\/b><\/h2>\n
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Examples<\/b><\/h2>\n