Examples of Fraction Multiplication and Division
Date: 05/14/98 at 20:24:10 From: Allison Subject: Fractions I know how to add and subtract fractions, but I always get confused on how to multiply and divide them. I know how to reduce, so you don't need to teach me that part. But I have a big test soon and am in dire need. This test is for a job, so I would appreciate an answer as soon as possible. Thank you, Allison
Date: 05/16/98 at 16:47:38 From: Doctor Santu Subject: Re: Fractions Multiplying and dividing fractions can actually be easier than adding and subtracting them because multiplying and dividing do not require finding common denominators. To multiply: write the fractions side-by-side, multiply the tops to get the new top ("numerator"), multiply the two bottoms to get the new bottom ("denominator"). Then simplify. Example: multiply (12/25) and (40/81) 12 40 480 96 32 -- * -- = ---- = --- = --- 25 81 2025 405 135 You can make it a bit easier by reducing first. Just like reducing a fraction by cancelling common factors of the top and the bottom, you are allowed, just before multiplying the tops together and the bottoms together, to cancel common factors of the top of one fraction and the bottom of the OTHER fraction. You can reduce the usual way, too. Remember: always cancel top against bottom. For the same problem as before: 12 40 -- * -- 25 81 4 40 = -- * -- I cancelled a 3 from the 12 (top) and the 81 (bottom) 25 27 4 8 = -- * -- I cancelled a 5 from 40 (top) against 25 (bottom) 5 27 32 = --- 135 The answer has to be the same. The only reason for doing it this way is to avoid huge numbers. Smaller numbers usually make for more accurate mental arithmetic! To divide, simply multiply by the reciprocal. For instance: (2/3) divided by (5/6) is the same as (2/3) MULTIPLIED by (6/5) You flip the number that's DOING THE DIVIDING, not the one that's being divided. In this case, the answer will be: (2/3) / (5/6) = (2/3)*(6/5) = (2/1)*(2/5) I cancelled a 3 from 3 (top) and 6 (bottom) = (4/5) Hope this helps, and hope you feel more comfortable with math as you go along. :-) -Doctor Santu, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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