Dividing FractionsDate: 09/08/99 at 22:29:38 From: Olivia Baker Subject: Dividing Fractions How do you divide fractions? I love math and I am good at it. This is the only thing slowing me down. I've tried and cannot find a way. Thanks. Date: 09/09/99 at 09:29:02 From: Doctor Rick Subject: Re: Dividing Fractions Hi, Olivia. Let's think about a few simple examples. Once you understand them, you will be able to put them together to make harder problems. What is 2 divided by 1/5? Here are 2 blocks: +---------+---------+ | | | | | | | | | | | | | | | | | | | | | | | | | | | +---------+---------+ Here is 1/5 of a block (the shaded part): +---------+ |XXXXXXXXX| +.........+ | | +.........+ | | +.........+ | | +.........+ | | +---------+ To divide 2 by 1/5, we divide 2 blocks into pieces the size of the 1/5 block. +---------+---------+ | | | +.........+.........+ | | | +.........+.........+ | | | +.........+.........+ | | | +.........+.........+ | | | +---------+---------+ There are 10 pieces this size in the 2 blocks. In other words, 2 divided by 1/5 = 10 That's the same as 2 x 5 = 10 Do you see why? To make 1/5 size blocks, we had to make each whole block into 5 pieces. In other words, we multiplied the number of pieces by 5. Next problem: 2 divided by 2/5 = ? Here is 2/5 of a block (the shaded part): +---------+ |XXXXXXXXX| +.........+ |XXXXXXXXX| +.........+ | | +.........+ | | +.........+ | | +---------+ Let's divide the 2 blocks into pieces this size. +---------+---------+ | | | + + + | | | +.........+.........+ | | | + + + | | | +.........+.........+ | | +---------+---------+ The bottom block is a different shape, but it's the same size, because it's made of 2 1/5-size pieces. Since the pieces we want are twice as big, there are only 1/2 as many of them. The answer is 2 divided by 2/5 = 10/2 = 5 This is the same as 2 x 5/2 = 5 Do you see how the two equations are related? You take the fraction, 2/5, and "turn it upside down" (in math words, we say "invert the fraction," or "take its reciprocal"). Then replace the division sign by a multiplication sign. Now we can tackle harder problems. The same method always works, even if the answer isn't a whole number as in the simple examples. For instance, 5 divided by 3/8 = ? Invert the fraction 3/8; you get 8/3. Then multiply by this fraction: 5 x 8/3 = 40/3 = 13 1/3 We can even replace the whole number in the problem with a fraction, like this: 5/7 divided by 3/8 = ? 5/7 x 8/3 = ? 5 8 40 19 --- x --- = ---- = 1 ---- 7 3 21 21 If you are comfortable with multiplying fractions, then you will have no trouble dividing fractions. Just remember: invert the fraction you are dividing by (the divisor), and multiply instead of dividing. If you still have trouble, write back and tell me just what you don't understand; if you can do some problems but you have trouble with others, give some examples of the ones you have trouble with. I want to give you just the help you need, so the more you can tell me, the better. You can also read the answers to other students' questions about dividing fractions. Go to our Search Dr. Math page: http://mathforum.org/mathgrepform.html Type in "divide fractions" (no quotes), select "that exact phrase" and click on "Search." You will see half a dozen or more answers. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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