Dividing FractionsIf your friend has half a pie, how many quarterpies are in that half? Or, to put this into mathematical notation: ^{1}/2 ÷ ^{1}/4 = ? To get the answer, flip the divisor (the second fraction) over, and then multiply the fractions. (Or, to put it another way, multiply the dividend [the first fraction] by the reciprocal of the divisor [the second fraction].) In this case, that makes the problem: ^{1}/2 x ^{4}/1 = ? We begin by multiplying the numerators: 1 x 4 = 4 And then we multiply the denominators: 2 x 1 = 2 The answer has a numerator of 4 and a denominator of 2. In other words: ^{1 x 4}/2 x 1 =^{4}/2 This fraction can be reduced to lowest terms: ^{4 ÷ 2}/2 ÷ 2 =^{2}/1 = 2 There are 2 quarterpies in a halfpie. Another ExampleLet's try another: ^{4}/5 ÷ ^{6}/7 = ? We flip the divisor over, and change the division sign to a multiplication sign: ^{4}/5 x ^{7}/6 = ? We multiply the numerators: 4 x 7 = 28 And we multiply the denominators: 5 x 6 = 30 The answer has a numerator of 28 and a denominator of 30. In other words: ^{4 x 7}/5 x 6 =^{28}/30 We can reduce this fraction by dividing the numerator and denominator by 2: ^{28 ÷ 2}/30 ÷ 2 = ^{14}/15 Mixed NumbersLet's try one more, this time with a mixed number: 2^{1}/4 ÷ ^{2}/3 = ? First we change the mixed number to an improper fraction: ^{9}/4 ÷ ^{2}/3 = ? Next we flip the divisor over and change the division sign to a multiplication sign: ^{9}/4 x ^{3}/2 = ? We multiply the numerators: 9 x 3 = 27 And we multiply the denominators: 4 x 2 = 8 The answer has a numerator of 27 and a denominator of 8. In other words: ^{9 x 3}/4 x 2 =^{27}/8 Finally, we turn the result—an improper fraction—into a mixed number. ^{27}/8 = 3^{3}/8 =
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