Reducing Fractions by Cancelling

To reduce fractions, we look for factors that are common to the numerator and the denominator. Then, we divide these factors out of both. Consider the fraction

1248

We can factor both the numerator and denominator. It is not always necessary to factor the numbers all the way to prime factors, but we have done so for this illustration. Working with prime factors ensures that you haven’t missed any common factors.

12 1 * 2 * 2 * 3 _48 1 * 2 * 2 * 2 * 2 * 3

Then, to reduce the fraction, we cancel out the common factors (except 1):

12 1 * 2 * 2 * 3 _ 1 _ 148 1 * 2 * 2 * 2 * 2 * 3 1 * 2 * 2 4

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Reducing Fractions by Cancelling

Note also, that we don’t really need to show 1 as a factor. We simply need to keep in mind that in cases where all factors cancel, a factor of 1 remains.

9 3 * 3 _ _1_45 3 * 3 * 5 5

Finally, we can also reduce improper fractions by cancelling. Even though the numerator is greater than the denominator, the same techniques can be applied.

18 2 * 3 * 3_ _3_12 2 * 2 * 3 2

56 2 * 2 * 2 * 7_ _7_ 8 2 * 2 * 2 1

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Reducing Fractions by Cancelling

For the three problems below, cross out the common factors, carry forward the remaining factors, and write the reduced fraction.

10 2 * 5 _ _____1______ _1__60 2 * 2 * 3 * 5 2 * 3 6

30 2 * 3 * 5 _ _____5______ _5__18 2 * 3 * 3 3 3

42 2 * 3 * 7 _ ___2 * 7______ _14_45 3 * 3 * 5 3 * 5 15

For the next two problems, factor the numerator and denominator to the point where you can reduce the fraction by cancelling.

81 _3 * 3 * 3 * 3 __ ___3 * 3_____ _9__36 2 * 2 * 3 * 3 2 * 2 4

24 _2 * 2 * 2 * 3 __ _____1______ _1__72 2 * 2 * 2 * 3 * 3 3 3

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