How to Simplify a Fraction

Simplifying a Fraction

Simplifying (or reducing) a fraction makes the fraction as simple as possible.

A fraction is as simple as possible when the top and bottom numbers are as small as possible.

Some examples of simplifying a fraction are shown below:

How to Simplify a Fraction

To simplify a fraction, divide both the top number and the bottom numbers by their greatest common factor (which is the largest number that will divide exactly into both numbers).

Question

Simplify the fraction below.

Step-by-Step:

1

Find the greatest common factor of the top and bottom numbers.

The factors of 4 are: 1, 2, 4

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

2 is the greatest common factor.

2

Divide the top number (called the numerator) of the fraction (4) by the greatest common factor (2).

4 ÷ 2 = 2

3

Divide the bottom number (called the denominator) of the fraction (6) by the greatest common factor (2).

6 ÷ 2 = 3

4

The answer from Step 2 is the numerator of our answer. The answer from Step 3 is the denominator of our answer.

Answer:

A Real Example of How to Simplify a Fraction

In the example above, a proper fraction (where the top number is smaller than the bottom) was simplified.

In this example, an improper fraction (where the top number is bigger than the bottom) will be simplified. It's exactly the same method.

Question

Simplify the fraction below.

Step-by-Step:

1

Find the greatest common factor of the top and bottom numbers.

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

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

6 is the greatest common factor.

2

Divide the top number (called the numerator) of the fraction (24) by the greatest common factor (6).

24 ÷ 6 = 4

3

Divide the bottom number (called the denominator) of the fraction (18) by the greatest common factor (6).

18 ÷ 6 = 3

4

The answer from Step 2 is the numerator of our answer. The answer from Step 3 is the denominator of our answer.

Answer:

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See Also

What is a fraction? What is a numerator? What is a denominator? Simplifying fractions What is a factor? What is the greatest common factor? What is a multiple? Equivalent fractions and simplest form