Write fractions in lowest terms

Key Notes :

What is the simplest form?

A fraction is in simplest form if the top and bottom have no common factors other than 1. In other words, you cannot divide the top and bottom any further and have them still be whole numbers.

You might also hear simplest form called “lowest terms”.

For example, the fraction 4/5 is in simplest form. There’s no number that divides both 4 and 5, other than 1.

The fraction 3/6 is not in simplest form. You can divide both the numerator and denominator by 3.

Since you cannot divide 1 and 2 any further, you know that 1/2 is the simplest form of 3/6.

How do you simplify a fraction?

To find the simplest form of a fraction, you can divide the numerator and denominator by their greatest common factor, or GCF.

Let’s try it with 12/18.

First, find the GCF of 12 and 18. List out all the factors of each number. Find the biggest factor they share.

  • Factors of 12: 1, 2, 3, 4, 6, 12
  • Factors of 18: 1, 2, 3, 6, 9, 18

The GCF of 12 and 18 is 6.

Next, simplify the fraction. Divide the numerator and the denominator by their GCF.

So, the simplest form of 12/18 is 2/3!

💡 Tip A fraction and its simplest form are equivalent fractions. They represent the same amount.

The equation twelve eighteenths equals two thirds, with models for each fraction underneath. The model for twelve eighteenths shows a rectangle divided into six rows and three columns, with two of the columns shaded in. The model for two thirds shows a rectangle divided into three columns, with two of the columns shaded in.

Learn with an example

😮 Write 2/8 in lowest terms.

Find the largest number that divides both the numerator and the denominator. The largest number that divides both 2 and 8 is 2. Divide the numerator and denominator by 2.

2 ÷ 2 = 1

8 ÷ 2 = 4

2/8  written in lowest terms is  1/4 .

😮 Write 2/4 in lowest terms.

Find the largest number that divides both the numerator and the denominator. The largest number that divides both 2 and 4 is 2. Divide the numerator and denominator by 2.

2 ÷ 2 = 1

4 ÷ 2 = 2

2/4  written in lowest terms is  1/2 .

😮 Write 6/9 in lowest terms.

Find the largest number that divides both the numerator and the denominator. The largest number that divides both 6 and 9 is 3. Divide the numerator and denominator by 3.

6 ÷ 3 = 2

9 ÷ 3 = 3

6/9  written in lowest terms is  2/3

Try some practice problems!