Math Help: Simplifying Fractions

How to Simplify Fractions

If someone asks you to simplify or reduce a fraction, they're asking you to write it using the smallest whole numbers possible. You know that a fraction is simplified when there is no number that you can evenly divide both its numerator and denominator by. The fraction 3/6 is not simplified, because three and six are both divisible by three. The fraction 3/4 is simplified because there is no whole number that three and four are both divisible by.

Using Factors

Now that you can tell whether or not a fraction is simplified, the next step is learning how to simplify fractions. This number that you can divide both the numerator and its denominator by is called a common factor. To simplify the fraction, divide both parts by that common factor.

For example, we mentioned earlier that 3/6 isn't simplified, because three and six are both divisible by three. To simplify 3/6, divide three by three to get one (3 ÷ 3 = 1), and divide six by three to get two (6 ÷ 3 = 2). The simplified version of 3/6 is 1/2. You know for sure that 1/2 is simplified because there are no whole numbers that you can evenly divide both one and two by.

Practice Simplifying Fractions

Simplify these fractions, and then check your answers. Watch out for fractions that are already simplified!

1. 4/12

2. 8/10

3. 6/7

4. 7/14

5. 3/9

Answer Key

1. First, ask yourself whether four and 12 have a common factor. If you said, 'Yes,' you're right! Their common factor is four. When you divide both parts of 4/12 by four, you get the simplified fraction 1/3.

2. Two is the common factor for eight and ten. Since 8 ÷ 2 = 4, and 10 ÷ 2 = 5, the simplified version of 8/10 is 4/5.

3. Since six and seven have no common factor, 6/7 is already simplified.

4. The common factor of seven and 14 is seven. If you divide seven and 14 both by seven, you get one and two, which means your simplified fraction is 1/2.

5. The common factor of three and nine is three. Since 3 ÷ 3 = 1, and 9 ÷ 3 = 3, the fraction 3/9 simplifies to 1/3.