Dividing Fractions: Why Invert?Date: 01/24/2001 at 10:15:44 From: MOHD. ZULASYRAF B. MOHD. ZAKI Subject: Dividing fractions Why do we have to invert the fraction in dividing fractions? Date: 01/24/2001 at 11:41:09 From: Doctor Greenie Subject: Re: Dividing fractions Hi, Mohd - Let's first think about the division operation. When I see the division problem 24 ---- = ? 4 I can think of it as asking "how many 4's are there in 24?" So if I have the division problem 6 ------- 1 --- 2 I can think of it as asking "how many halves are there in 6?" The way I answer that question is to say that it takes 2 halves to make a whole, so in 6 wholes there must be 6*2 = 12 halves. In this case I have multiplied 6 by the reciprocal of (1/2), which is (2/1) = 2. The preceding example was easy to understand, because 1/2 is a very simple fraction. When the fractions are more complicated, like 3 --- 4 ------- 2 --- 7 it is very hard to see what is going on. So let's look at the mathematical reason for inverting when dividing fractions. In any fraction a --- b where a and b are both non-zero, it is true that a b --- * --- = 1 b a So if I need to perform the division problem 3 --- 4 ------- 2 --- 7 I simplify the expression by multiplying both numerator and denominator by 7/2, so that the denominator becomes 1: 3 7 3 7 3 7 --- --- --- * --- --- * --- 4 2 4 2 4 2 ------- * ------- = ----------- = 2 7 1 --- --- 7 2 So you can see that the original problem, 3/4 divided by 2/7, is the same as the multiplication problem 3/4 times 7/2. - Doctor Greenie, The Math Forum http://mathforum.org/dr.math/ |
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