Simplify Ratio Calculator

Created by Krishna Nelaturu
Reviewed by Anna Szczepanek, PhD
Last updated: Jun 05, 2023


Our simplify ratio calculator is here to help you reduce a ratio to its simplest form. It can handle ratios between up to three numbers! In the following article, we shall briefly discuss how to calculate simplified ratios. In addition, we shall also look at calculating reduced ratios to convert a given ratio A : B into forms like 1 : m and n : 1.

Calculating simplest ratio form of two numbers

A ratio between two numbers A : B is a way to express a quantitative relationship between two parameters. For instance, while cooking rice, the water-to-rice ratio is 2:1, which tells you that you need two portions of water to cook one portion of rice.

We say a ratio is in its simplest form if there are no non-trivial common factors between the two sides of the ratio. By non-trivial we mean here factors different from 1. For example, the ratio 4:8 is not in its simplest form since the common factors of 4 and 8 are 1, 2, and 4.

To calculate the simplest form of a ratio, we must divide both sides by the greatest common factor (GCF) of the two numbers. Coming back to our example above, the GCF of 4 and 8 is 4. Hence, the simplest form of the ratio 4:8 is:

4:8=44:84=1:24:8 = \frac{4}{4} : \frac{8}{4} = 1:2

Our GCF calculator will aid you to find out the greatest common factor of a given set of numbers.

Calculating reduced ratio of 1:m or n:1 form

We can also express a ratio A : B in 1 : m or n : 1 form. This helps us understand how many parts of a substance are related to one part of the other substance.

This conversion is very simple - To convert A : B into 1 : m, divide both sides by A. Similarly, to convert A : B into n : 1, divide both sides by B.

Say there are ten boys and twelve girls in a class. The ratio of boys to girls is 10 : 12. We can reduce this ratio to:

  • 1 : 1.2, or
  • 0.833 : 1.

Calculating ratios of 3 numbers

Simplifying ratios of three numbers is similar to that of two numbers. For example, consider a chemical reaction in which two moles of nitrogen (N2)(\rm{N_2}) and six moles of hydrogen (H2)(\rm{H_2}) mix to produce four moles of ammonia (NH3)(\rm{NH_3}).

The ratio of moles of (N2):(H2):(NH3)(\rm{N_2}) : (\rm{H_2}) : (\rm{NH_3}) is 2:6:42 : 6 : 4. Similar to 2-number ratios, we can simplify this 3-number ratio A : B : C into various forms:

  1. Simplified ratio by dividing all sides with their GCF (2):
2:6:4=22:62:42=1:3:2\quad \footnotesize 2 : 6 : 4 = \frac{2}{2}\! : \!\frac{6}{2}\! :\! \frac{4}{2} = 1 : 3 : 2
  1. 1 : n : m form by dividing all sides by A (i.e., by 2):
2:6:4=22:62:42=1:3:2\quad \footnotesize 2 : 6 : 4 = \frac{2}{2}\! :\! \frac{6}{2}\! : \!\frac{4}{2} = 1 : 3 : 2
  1. n : 1 : m form by dividing all sides by B (i.e., by 6):
2:6:4=26:66:46=0.33:1:0.66\quad \footnotesize 2 : 6 : 4 = \frac{2}{6} \!:\! \frac{6}{6} \!:\! \frac{4}{6} = 0.33\! : \!1\! :\! 0.66
  1. n : m: 1 form by dividing all sides by C (i.e., by 4):
2:6:4=24:64:44=0.5:1.5:1\quad \footnotesize 2 : 6 : 4 = \frac{2}{4}\! :\! \frac{6}{4}\! :\! \frac{4}{4} = 0.5\! :\! 1.5\! :\! 1

How to use this simplify ratio calculator?

Our simplify ratio calculator is a robust tool capable of simplifying two-number and three-number ratios:

  1. Select whether the ratio contains two or three-numbers
  2. Choose which simplified form you wish to reduce the ratio to.
  3. Enter the ratio.
  4. The simplify ratio calculator will give you the ratio in your desired simplified form.

You can also use this calculator to simplify fractions since ratios and fractions work similarly.

FAQ

How do you simplify a ratio?

Follow these steps to simplify the ratio A : B to its simplest form:

  1. Find the greatest common factor (GCF) of A and B.
  2. Divide both sides of the ratio by the GCF A/GCF : B/GCF.
  3. You've got the simplest form of your ratio!
  4. You can verify your result with and an online simplify ratio calculator.

What is the simplest form of the ratio 25 : 10?

The simplest form of the ratio 25 : 10 is 5 : 2. To verify this result, follow these steps:

  1. Find the greatest common factor (GCF) of 25 and 10, which is 5.
  2. Divide both sides of the ratio by the GCF to get 25/5 : 10/5 = 5 : 2.
  3. Omni's simplify ratio calculator can help you verify this without any manual calculations.
Krishna Nelaturu
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