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 12 48 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 _ 1 48 1 * 2 * 2 * 2 * 2 * 3 1 * 2 * 2 4 = = = =

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 = = = = = =

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 = = = = = = = = = = = = = = =