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How to Simplify a Fraction (Mathematics Lesson)

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).

An Example Question

Simplify the fraction below:

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 largest number that appears in both lists.

2 is the greatest common factor.
Step 2
Divide the top number (called the numerator) of the fraction (4) by the greatest common factor (2).
4 ÷ 2 = 2
Step 3
Divide the bottom number (called the denominator) of the fraction (6) by the greatest common factor (2).
6 ÷ 2 = 3
Step 4
The answer from Step 2 is the numerator of our answer. The answer from Step 3 is the denominator of our 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.

An Example Question

Simplify the fraction below:

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 largest number that appears in both lists.

6 is the greatest common factor.
Step 2
Divide the top number (called the numerator) of the fraction (24) by the greatest common factor (6).
24 ÷ 6 = 4
Step 3
Divide the bottom number (called the denominator) of the fraction (18) by the greatest common factor (6).
18 ÷ 6 = 3
Step 4
The answer from Step 2 is the numerator of our answer. The answer from Step 3 is the denominator of our answer.

Another Real Example of How to Simplify a Fraction

The slider below gives a real example of how to simplify a fraction.
Interactive Test
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Here's a second test on simplifying fractions.
Here's a third test on simplifying fractions.
Note

Equivalent Fractions and Simplest Form

Fractions can be equivalent, even if they look different.

For example:



The fractions are all equivalent. They represent the same amount.

Fractions are equivalent when both the top and bottom numbers are multiplied or divided by the same number (they are factors or multiples of each other).

In the example below, the top and bottom numbers are multiplied or divided by 2.



For all equivalent fractions, one fraction is the simplest.

Which is the simplest? The fraction where the top and bottom numbers are the smallest.

The simplest fraction of the three is:


Read more about equivalent fractions and simplest form

Visualizing Equivalent and Simplest Fractions

Fractions can be visualized as a cake cut into equal slices.

Using this method, equivalent fractions can be visualized. The three fractions below are equivalent:



The top cake shows the simplest fraction, as there are the fewest slices.

What Is a Factor?

A factor is a number or symbol which divides exactly into another number.

For example, the factors of 10 are:

What Is the Greatest Common Factor?

The greatest common factor is the largest factor that is common to two or more numbers.