Simplifying of Fractions Calculator

Published on: March 24, 2024
Final Answer: Free • Full Steps: Free

This Simplifying of Fractions Calculator helps you write a fraction with the smallest numbers possible and shows the working clearly at every step. List the numbers that divide the numerator, then the numbers that divide the denominator, and look for the biggest one on both lists. Divide the numerator and the denominator by that number and the fraction is as small as it goes. Following the same pattern every time is what makes simplifying easy to picture, check, and repeat on your own with any fraction.

Step-by-step method

  1. Set up the problem.
  2. List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
  3. Divide the numerator and the denominator by that number.
See Example 1 Hide Example 1

Problem

\(\frac{8}{12}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
  3. Divide the numerator and the denominator by that number.

Step 1

Step 1 - Set up the problem.

In this problem: We are simplifying \(\frac{8}{12}\).

\(\frac{8}{12}\)

Step 2

Step 2 - List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.

In this problem: Listing what divides each one, both lists contain \(1, 2, 4\). The biggest of those is \(4\), so \(4\) is the number to divide by.

\(8\)1248
\(12\)1234612

Step 3

Step 3 - Divide the numerator and the denominator by that number.

In this problem: Divide both by \(4\): \(8 \div 4 = 2\) and \(12 \div 4 = 3\).

\(\frac{8}{12} = \frac{2}{3}\)

Final Answer

\(\frac{8}{12} = \frac{2}{3}\)
See Example 2 Hide Example 2

Problem

\(\frac{45}{60}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
  3. Divide the numerator and the denominator by that number.

Step 1

Step 1 - Set up the problem.

In this problem: We are simplifying \(\frac{45}{60}\).

\(\frac{45}{60}\)

Step 2

Step 2 - List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.

In this problem: Listing what divides each one, both lists contain \(1, 3, 5, 15\). The biggest of those is \(15\), so \(15\) is the number to divide by.

\(45\)13591545
\(60\)123456101215203060

Step 3

Step 3 - Divide the numerator and the denominator by that number.

In this problem: Divide both by \(15\): \(45 \div 15 = 3\) and \(60 \div 15 = 4\).

\(\frac{45}{60} = \frac{3}{4}\)

Final Answer

\(\frac{45}{60} = \frac{3}{4}\)

Example Problems

Click one to load it into the box and solve it.