ASVAB Preparation: How to Simplify Fractions

By Rod Powers

Simplifying (or reducing) fractions means to make the fraction as simple as possible. You’re usually required to simplify fractions on the ASVAB math subtests before you can select the correct answer.

For example, if you worked out a problem and the answer were 4/8 , the correct answer choice on the math subtest would probably be 1/2 , which is the simplest equivalent to 4/8.

Many methods of simplifying fractions are available. Here, you will find the two that are the easiest; you can decide which is best for you.

Method 1: Dividing by the lowest prime numbers

Try dividing the numerator and denominator by the lowest prime numbers until you can’t go any farther.

Simplify 24/108.

Both the numerator and denominator are even numbers, so they can be divided by the lowest prime number, which is 2. Then 24 ÷ 2 = 12, and 108 ÷ 2 = 54. The result is 12/54.

The numerator and denominator are both still even numbers, so divide by 2 again: 12 ÷ 2 = 6 and 54 ÷ 2 = 27. The result is 6/27.

This time the denominator is an odd number, so you know it isn’t divisible by 2. Try the next highest prime number, which is 3: 6 ÷ 3 = 2, and 27 ÷ 3 = 9. The result is 2/9.

Because no common prime numbers divide evenly into both 2 and 9, the fraction is fully simplified.

Method 2: Listing prime factors

This method of simplification is another good choice. Simply list the prime factors of both the numerator and the denominator and then see whether any cancel out (are the same).

Simplify 24/108.

The prime factors of 24 are 2 × 2 × 2 × 3.

The prime factors of 108 are 2 × 2 × 3 × 3 × 3.

You can now write the fraction as

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Two of the 2s and one of the 3s cancel out, so you can remove them from both the numerator and the denominator. What’s left is

image1.jpg

or 2/9.