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When you multiply or divide the numerator and denominator of a fraction by the same number, you don’t change the value of the fraction. In fact, you’re basically multiplying or dividing by 1 because any time the numerator and denominator of a fraction are the same number, it equals 1.

For example, how much of a 32-ounce package are you using if your recipe calls for 12 ounces? You’re using of the package. If you divide both the 12 and the 32 by 4, you’re basically dividing by , which equals 1. The same goes for multiplying the numerator and denominator by the same number. So, you’re using of the package.

Here’s another example: Create two new versions of the fraction — one with smaller numbers and one with larger numbers.

To come up with smaller numbers, you need to find something that divides both the 16 and the 20 evenly. There are two possibilities: 2 and 4.

The fraction is said to be in “lowest possible terms” because there are no common factors available. No whole numbers can divide the two numbers evenly except for 1.

There is no end to the possibilities when creating multiples of a particular fraction:

and and , and so on. You choose the numbers that work best for you in the situation.

However, not all fractions with large numbers can be changed to smaller numbers. Certain rules have to be followed so that the fraction maintains its integrity; the fraction has to have the same value as it did originally.

Q. Find a fraction equivalent to with a denominator of 40.

A. Because 5 times 8 is 40, you multiply both the numerator and denominator by 5. In reality, you’re just multiplying by 1, which doesn’t change the real value of anything.

Q. Reduce by multiplying the numerator and denominator by . The same thing is accomplished if you divide both the numerator and denominator by 3.

A. or

7 Find an equivalent fraction with a denominator of 28 for .

8 Find an equivalent fraction with a denominator of 30 for .

9 Reduce this fraction: .

10 Reduce this fraction: .