When you simplify or reduce a fraction you are making the fraction as simple as possible. For instance, when 8/16 is reduced it becomes 1/2. Think of it this way,1/2 is easier, or more simple to work with, compared to 8/16

For example:

Ex. 1 Reduce15/18

- Factor each term:

- The factors of 15 are 1, 3, 5,

- The factors of 18 are 1, 2, 3, 6, 9

- Notice that 15 and 18 have only one factor in common other than one.

- Divide the fraction by the lowest common factor, 3.

- 15 ÷ 3/18 ÷ 3 = 5/6

Is the fraction simplified? Let’s see

- The factors of 5 are 1, 5, (prime)

- The factors of 6 are 1, 2, 3, 6

They do not have any common factors other than one, therefore the fraction is simplified

- The factors of 18 are 1, 2, 3, 6, 9

- The factors of 24 are 1, 2, 3, 4, 6, 8.12

- Notice that 18 and 24 have the lowest common factor, 2. Divide the numerator and denominator by 2.

18÷2/24÷2 = 9/12

- The factors of 9 are 1, 3, 9

- The factors of 12 are 1, 3, 4, 6, 12

- The lowest common factor is 3.

9÷3/12÷3 = ¾

There are no more common factors therefore the fraction is reduced

- The factors of 18 are 1, 2, 3, 6, 9, 18

- The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

- The Greatest Common Factor is 6

- Divide the fraction by the greatest common factor

18 ÷ 6/24 ÷ 6 = 3/4

- The prime factors of 15 are 3 x 5.

- The prime factors of 18 are 2 x 3 x 3

- Remove 3 because it is common in the numerator and denominator