Fractions in the Simplest Form: Problems and Answers

How to Simplify Fractions

Your child can simplify a fraction when the numerator (the number on top) and the denominator (the number on the bottom) have a common factor. To figure this out, have you child find the factors of each number. For example, the fraction 6/10 can be rewritten like this: (2 x 3) / (2 x 5). This is known as prime factorization, which is finding the prime numbers that multiply to make the number. Because there is a common factor of 2 in both the numerator and the denominator, you can cancel both out. As a result, the simplified fraction is 3/5.

Often, teachers will want your child to answer a problem with the simplest fraction possible. Remind your child that the trickiest part of simplification is remembering to do it. He might get through a complex problem and want to move on; however, it is important that he checks over his work before turning it in because that final step of simplifying the fractions can be so easy to forget.

Problems and Answers

Ask your child to simplify these fractions on her own first, and then check her answers with the ones provided below. There are also explanations provided.

1. 9/33

The answer is 3/11. The prime factorization of this fraction is (3 x 3) / (3 x 11). After canceling the common factor (3), the final, simplified answer is 3/11.

2. 8/24

The fraction can be rewritten like this: (2 x 2 x 2) / (2 x 2 x 2 x 3). Cross out three 2s from the numerator and the denominator because they cancel each other out. The simplified form is 1/3.

3. 7/20

This problem cannot be simplified more. The numerator (7) cannot be factored further, so it is already in its simplest form.

4. 99/300

This fraction is more complicated because the numbers are larger. It can be reduced to this: (3 x 3 x 11) / (3 x 5 x 2 x 2 x 5). Only one 3 can be canceled out from both the numerator and the denominator. Multiply the remaining prime factors to find the simplest form, so the answer is 33/100.

5. 5 4/12

To simplify a mixed number, follow the same steps. Simplify 4/12, which is 1/3. The final, simplified answer is 5 1/3.

6. Peter runs for 25 minutes on Mondays and Wednesdays. How much of an hour does he run each week?

Because Peter runs for 25 minutes twice a week, he runs for 50 minutes total in one week. Using this information, you can make the fraction 50/60, which is simplified to 5/6.