Ratio of 3 Numbers Calculator

Created by Anna Szczepanek, PhD
Reviewed by Davide Borchia
Last updated: Nov 04, 2022

With this Omni's ratio of 3 numbers calculator you'll never again struggle with finding the ratio of 3 numbers A : B : C! This tool can perform various math operations related to ratios of three numbers, for instance simplify them or determine equivalent ratios. In what follows, we briefly recall how to calculate the ratio of 3 numbers and go together through some examples.

How do I calculate the ratio of 3 numbers?

Recall that ratios represent the quantitative relationship between two or more numbers, i.e., how many times one number is bigger/smaller than other numbers. In particular, the ratio A : B : C describes the ratio between the numbers A, B and C.

For example, if to bake a cake you need 100 g of butter, 200 g of sugar and 400 g of flour, then your ingredients are in ratio 100 : 200 : 400. You need two times more flour than sugar and two times more sugar than butter. And, obviously, four times more flour than butter. That is, our ratio can be equivalently written as 1 : 2 : 4. Here, we've simplified the ratio by dividing all three numbers by 100. On the other hand, to determine the amount of ingredients for two cakes, it's best to write our ratio as 200 : 400 : 800. That is, we've multiplied each element o the initial ratio by 2.

How do I simplify a ratio of three numbers?

To simplify a ratio of three numbers A : B : C:

  1. Write down the factors of A, of B, and of C.
  2. Determine the greatest common factor (GCF) of A, B, and C.
  3. Divide the three numbers in the ratio by the number from Step 2.

🙋 To learn more about finding the greatest common factor, visit the GCF calculator.

As you can see, it's quite easy to learn how to calculate ratio of 3 numbers by hand! You can always use our tool to verify your computations.

How to use this ratio of 3 numbers calculator?

Our ratio of 3 numbers calculator features a lot of different options, but it's really easy to use!

  1. Start by deciding what math operation you want to perform:
    • Simplify a ratio. This is the option you should choose to find the ratio of 3 numbers.
    • Transform to the specific form:
      • 1 : n : m;
      • n : 1 : m; or
      • n : m : 1.
    • Multiply/divide by a given number k.
    • Determine an equivalent ratio. You need to provide one number of the new ratio.
  2. Input the initial ratio A : B : C and, if needed, provide the factor k or one of the numbers D, E or F.
  3. Our tool will immediately perform the computations and show you the results. Enjoy!

With this Omni tool, finding the ratio of 3 numbers will become a piece of cake!

If you want to dive deeper in the world of ratios, we recommend the following Omni tools:

FAQ

How do I divide $50 in ratio 2 : 3 : 5?

To find out how to divide a given amount of money based on a ratio of three numbers:

  1. Add the numbers appearing in the ratio: 2 + 3 + 5 = 10. There's ten parts in total.
  2. Divide the total amount of money by the result of Step 1: $50 / 10 = $5. One part is five dollars.
  3. The first person gets two parts, so $10. The next person gets three parts, so $15. The last person gets five parts, that is $25.

How do I simplify the ratio 4 : 6 : 10?

  1. The factors of 4 are 1, 2, 4.
  2. The factors of 6 are 1, 2, 3, 6.
  3. The factors of 10 are 1, 2, 5, 10.
  4. The greatest common factor of the three numbers under consideration is 2.
  5. Divide our numbers by 2 and write down the new ratio.
  6. We've arrived at the ratio 2 : 3 : 5.

How do I simplify the ratio 3 : 6 : 8?

  1. The factors of 3 are 1, 3.
  2. The factors of 6 are 1, 2, 3, 6.
  3. The factors of 8 are 1, 2, 4, 8.
  4. The greatest common factor of the three numbers under consideration is 1. That is, these numbers are (setwise) coprime.
  5. This means our ratio cannot be simplified! 3: 6 : 8 is the simplest form we can have.
Anna Szczepanek, PhD
Ratio of...
three numbers (A : B : C)
I would like to...
simplify the ratio.
A
B
C
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