Simplifying Fractions

Simplifying Fractions (Reducing Fractions)

Simplifying (or reducing) fractions means to make the fraction as simple as possible.

There are three ways to simplify a fraction:

Method 1

• Find the Greatest Common Factor (GCF) of the numerator and denominator
• Divide the numerator and the denominator by the GCF

for example

Method 2

• Try dividing both the top and bottom of the fraction until you can't go any further (try dividing by 2,3,5,7,... etc)

for example

Method 3

- Factor the numerator.
- Factor the denominator.
- Find the fraction mix that equals 1.

for example

Reduce the fraction 120 / 160

Answer: Factor the numerator and factor the denominator and look for the fractions in the mix that have a value of 1.

The fraction 120 / 160 has been reduced into the equivalent fraction 3 / 4.

Now prove to yourself with your calculator that both fractions are equivalent. When you divide 120 by 160, you will get the same answer as when you divide 3 by 4.

Question: Reduce the fraction 150 / 650

Answer: Rewrite the fraction with the numerator factored and the denominator factored. The fraction 150 / 650 can be written as

Although we have reduced the fraction, we have not reduced it completely. So repeat the above steps.

The fraction 15 / 65 can be written as

The fraction 150 / 650 is equivalent to the fraction 3 / 13.

You can check the answer with your calculator. When you divide 150 by 650, you will get the same answer as when you divide 3 by 13.