Simplify Ratio Calculator

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.

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:

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

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.

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

The ratio of moles of $(\rm{N_2}) : (\rm{H_2}) : (\rm{NH_3})$ is $2 : 6 : 4$. 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. 1 : n : m form by dividing all sides by A (i.e., by 2):

3. n : 1 : m form by dividing all sides by B (i.e., by 6):

4. n : m: 1 form by dividing all sides by C (i.e., by 4):

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.

Take a look at other relevant ratio calculators:

• Ratio calculator;
• Ratio of 2 Numbers Calculator;
• Ratio of 3 Numbers Calculator; and
• Equivalent Ratio Calculator.