Multiplying Fractions

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

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Step 1: Multiplying Whole Numbers

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

Step 2: Multiplying Fractions by Whole Numbers

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

Step 3: Multiplying Fractions Together

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

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)

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    6 Discussions

    cutting Matt

    10 years ago on Introduction

    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)

    1 reply

    5 years ago on Step 4

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


    7 years ago on Step 4

    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.