Simplify Fractions

About simplifying fractions

Enter a fraction and click the "Calculate" button to calculate and simplify the fraction you entered and convert it to a simple fraction.

The numerator and denominator of a fraction can be entered as decimals.

You can enter up to 10 digits for the numerator and denominator.

The calculation method is also displayed along with the calculation.

What is simplify fractions?

Simplifying a fraction means dividing the numerator and denominator by the same number to make a simpler fraction.

Multiplying the numerator and denominator of a fraction by the same non-zero number, or dividing the numerator and denominator by the same non-zero number, does not change the size of the fraction.

Therefore, by dividing by the same number, you can convert it into a simple fraction, which is an equal fraction with the same magnitude.

For example, 12 multiplied by 2 to get 24 and 36 multiplied by 3 both yield the same fraction.

12 = 1 × 22 × 2 = 24

12 = 1 × 32 × 3 = 36

Therefore, by taking advantage of this property, we can turn a number into a simple fraction by dividing the numerator and denominator by the same number.

How to simplify fractions

Dividing by a common factor

To simplify a fraction, first find a number that divides both the numerator and denominator (a common factor), and then divide the numerator and denominator by that number.

You can simplify by repeating this process until there are no more common factors.

  • 1. Find the common factor of the numerator and denominator and divide the numerator by the denominator.
  • 2. Repeat this until there are no more divisible numbers.

Calculation example

Example: Simplify 618.

Divide the numerator and denominator by 2.

618 = 6 ÷ 218 ÷ 2

= 39

Divide the numerator and denominator by 3.

= 3 ÷ 39 ÷ 2

= 13

Since there are no further divisible numbers, 618 = 13.

How to divide by the greatest common denominator

When simplifying by dividing the numerator and denominator by a common factor, you will need to divide multiple times if there are many common factors.

Alternatively, you can reduce it in one go by dividing by the greatest common factor of the numerator and denominator.

  • 1. Calculates the greatest common divisor of the numerator and denominator.
  • 2. Divide the numerator and denominator by the greatest common factor found in step 1.

Calculation example

Example: Simplify 2436.

The greatest common factor between 24 and 36 is 12.

Divide the numerator and denominator by 12.

2436 = 24 ÷ 1236 ÷ 12

= 23

Therefore, 2436 = 23.