Multiplying Fractions and Mixed NumbersMultiplying FractionsIf your friend has onequarter of a pie, and she gives you half, how much of the pie do you have? Or, to put it another way, what's half of onequarter? Or, to put it into mathematical notation: ^{1}/2 x ^{1}/4 = ? To get the answer, multiply the numerators (the top parts) and denominators (the bottom parts) separately. In this case, first we multiply the numerators: 1 x 1 = 1 Next we multiply the denominators: 2 x 4 = 8 The answer has a numerator of 1 and a denominator of 8. In other words: ^{1}/2 x ^{1}/4 = ^{1 x 1}/2 x 4 = ^{1}/8 You have oneeighth of the pie. Another ExampleLet's try another. ^{2}/9 x ^{3}/4 = ? First we multiply the numerators: 2 x 3 = 6 Next we multiply the denominators: 9 x 4 = 36 The answer has a numerator of 6 and a denominator of 36. In other words: ^{2}/9 x ^{3}/4 = ^{2 x 3}/9 x 4 = ^{6}/36 This can be further reduced: ^{6 ÷ 6}/36 ÷ 6 = ^{1}/6 (See Reducing Fractions.) Multiplying Mixed NumbersTo multiply two mixed numbers, or a mixed number and a fraction, first convert each mixed number to a fraction. Then multiply the fractions. What is 2^{1}/3 x ^{1}/4 = ? First we write 2^{1}/3 as a fraction: 2^{1}/3 = ^{7}/3 Then we multiply the fractions. ^{7}/3 x ^{1}/4 = ? First we multiply the numerators: 7 x 1 = 7 Next we multiply the denominators: 3 x 4 = 12 The answer has a numerator of 7 and a denominator of 12. In other words: 2^{1}/3 x ^{1}/4 = ^{7 x 1}/3 x 4 = ^{7}/12
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