Multiplication of Fractions - Multiplication of Fractions I...

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Multiplication of Fractions I. Multiplying Two Fractions Suppose that you are making lemonade and have found a recipe that requires three-quarters of a cup of sugar to make one pitcher of lemonade. You want to make a half pitcher of lemonade. How much sugar do you need? Solution The operation of arithmetic needed here is multiplication, that is, what is 3 1 x 4 2 The pictures below show how to proceed. We draw three shaded regions of four possible and than cut the shaded regions in half. The result is that there are still three shaded regions, but their are 4 x 2 total pieces. We conclude that 3 1 3 x 1 3 x = = 4 2 4 x 2 8 In general, to multiply two fractions, multiply the numerators and multiply the denominators. Example A. 2 4 2 x 4 8 x = = 3 5 3 x 5 15 B. 4 15 4 x 15 x = 9 28 9 x 28
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2 x 2 x 3 x 5 5 = = We have canceled common factors 3 x 3 x 2 x 2 x 7 21 C. 8 3 8 x 3 x = Improper fractions multiply similarly 3 16 3 x 16 2 x 2 x 2 x 3 1 = = If all factors factors, we are left with a one 3 x 2 x 2 x 2 x 2 2 D. 2 5 2 5 x = A whole number can always be put over 1.
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