Fractions Fundamentals: Simplifying Fractions

We will use what we just learned about greatest common factor to reduce a fraction into its simplest form. Our first example will be 2/4:

1) Find the greatest common factor of the number 2 and the number 4.

The factors of 2 are 1 and 2:
2 ÷ 1 = 2
2 ÷ 2 = 1

The factors of 4 are 1, 2, and 4:

4 ÷ 1 = 4
4 ÷ 2 = 2
4 ÷ 4 = 1

The greatest number in common between
1, 2
and
1, 2, 4
is 2.

2) Divide the numerator (top) by 2:
2 ÷ 2 = 1

3) Divide the denominator (bottom) by 2:
4 ÷ 2 = 2

4) 2/4 in its simplest form is 1 / 2.

Our next example will be 12 / 18:

1) Find the greatest common factor of the number 12 and the number 18.

The factors of 12 are 1, 2, 3, 4, 6, and 12:
12 ÷ 1 = 12
12 ÷ 2 = 6
12 ÷ 3 = 4
12 ÷ 4 = 3
12 ÷ 6 = 2
12 ÷ 12 = 1

The factors of 18 are 1, 2, 3, 6, 9, and 18:
18 ÷ 1 = 18
18 ÷ 2 = 9
18 ÷ 3 = 6
18 ÷ 6 = 3
18 ÷ 9 = 2
18 ÷ 18 = 1

The greatest number in common between
1, 2, 3, 4, 6, 12
and
1, 2, 3, 6, 9, 18
is 6

2) Divide the numerator (top) by 6:
12 ÷ 6 = 2

3) Divide the denominator (bottom) by 6:
18 ÷ 6 = 3

4) 12/18 in its simplest form is 2 / 3.

Sometimes, you will see a fraction that's already in its simplest form. An example is 4/7:

1) Find the greatest common factor of the number 4 and the number 7.

The factors of 4 are 1, 2, and 4:
4 ÷ 1 = 4
4 ÷ 2 = 2
4 ÷ 4 = 1

The factors of 7 are 1 and 7:
7 ÷ 1 = 7
7 ÷ 7 = 1

The greatest number in common between
1, 2, 4
and
1, 7
is 1

Because the greatest number in common between the numerator (top) 4 and the denominator (bottom) 7 is 1, 4 / 7 is in its simplest form.