Multiplying FractionsDate: 01/20/97 at 10:31:59 From: Jen Subject: Multiplication Since we have defined multiplication as repeated addition, how is it possible that when you multiply two fractions, the product is smaller than either of the fractions? Date: 01/20/97 at 13:34:58 From: Doctor Ken Subject: Re: Multiplication Hi there - Perhaps a more useful way to think of multiplication is to use the words "groups of." For instance, when you have 4 x 5, think of it as "4 groups of 5". We can write that out as 5 + 5 + 5 + 5, and add it up to get 20. If we have 1/2 x 2, then we think of it as "half a group of twos", so our total is 1. If we have 1/3 x 1/4, then that's one-third of a group of 1/4ths, and maybe this will make more sense to you. One-third of a positive number is always smaller than the original number was. That's one way to make sense of the equation 1/3 x 1/4 = 1/12. -Doctor Ken, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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