Introduction: Multiplying Fractions

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How to multiply fractions!
This instructable is an entry to the Burning Questions Round 6.5 contest.
The fraction images were generated using this site

Step 1: Multiplying Whole Numbers

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To whole numbers we simply do this: (See image)

Step 2: Multiplying Fractions by Whole Numbers

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The theory is the same for multiplying fractions by whole numbers(See image)

Step 3: Multiplying Fractions Together

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To multiply fractions together you simply multiply both of the numerators(top numbers) together and both of the denominators (bottom numbers) together.(See image)
If necessary, remember to simplify your fraction!

Step 4: Cross-Cancelling

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Cross cancelling is basically simplifying before you multiply, but, don't just simplify the fractions the normal way, instead cross-cancel. Cross-cancelling also makes it easier to multiply if using large numbers.
To cross-cancel the the multiplication 81/21 X 49/27,(See first image) try and divide the diagonals by the same number, e.g.
21 and 49 can both divide by 7, so we replace them with 3 and 7 respectively(See second image),
then we cancel the other diagonal, 81 and 27 can both be divided by 9, so we replace them with 9 and 3(See third image), then do the multiplication as in step 3. Remember that it doesn't matter if you can only cross-cancel in 1 direction.
The final answer to 81/21 X 49/27 is the improper fraction 63/9, in a mixed number that's 7/1 or just 7(See fourth image)


cutting Matt (author)2009-02-10

but i think you can cancel from the top and the bottom of the same fraction because it is just the same thing as a diagonal (it's one of the properties of multiplication)

FukBimk (author)cutting Matt2016-05-05


AlliP (author)2014-10-01

how do you multiply them if neither number can go into each other when cross reducing, would you just keep the same number?

dolphinlms (author)2012-01-19

This could have been cross cancelled two more times. The 9 & 3 (either denominator!) could be cross cancelled so you would have either 3/1 x 7/3 = 1/1 x 7/1 = 7 OR 3/3 x 7/1 = 1 x 7 = 7. I review this with 6th graders by writing a ridiculously long multiplication problem to demonstrate how much you can simplify a problem.

sciencefreak101 (author)2009-06-18

wow, education is very important !!

MROHM (author)sciencefreak1012010-12-15


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