Help with Fractions in Simplest Form

How to Reduce Fractions

Putting a fraction in its simplest form is also called reducing it. This means expressing the fraction using the smallest numerator and denominator possible, while maintaining its equivalence to the original fraction.

Equivalent Fractions

In order to reduce fractions, you need to understand the concept of equivalent fractions. Two fractions can be equivalent even if their numerators and denominators are different. This is possible because fractions express a relationship between the top and bottom numbers. For instance, in the fraction 1/2, one is half of two, and in the equivalent fraction 2/4, two is half of four.

If you multiply both the numerator and the denominator of any fraction by the same number, you'll get an equivalent fraction because the relationship between the top and bottom numbers will still be the same. For instance, 1/2 = 2/4 because 1 x 2 = 2 and 2 x 2 = 4. Below are some other fractions that are equivalent to 1/2. Notice that, in each example, the numerator is half of the denominator.

3/6

5/10

6/12

You can also generate equivalent fractions by dividing the numerator and the denominator by the same number. For example, imagine that you're asked to find equivalent fractions for 6/12. You could multiply both the numerator and the denominator by two to get 12/24, or you could divide them both by two to get 3/6 (6 ÷ 2 = 3 and 12 ÷ 2 = 6). Since 6 ÷ 3 = 2 and 12 ÷ 3 = 4, the fraction 2/4 is also equivalent to 6/12.

Simplest Form

To put a fraction in its simplest form, you'll find the equivalent fraction that's expressed with the lowest numbers. Here's how to do this:

1. Find the largest number that both the numerator and the denominator are divisible by. For example, if the fraction is 4/8, this number is four.

2. Divide the numerator and denominator both by this number to generate an equivalent fraction. For instance, 4/8 = 1/2 because 4 ÷ 4 = 1 and 8 ÷ 4 = 2.

3. The fraction should be fully simplified now. However, you should still check your work by looking to see if there are any other numbers that both the numerator and denominator are divisible by.