Ratio Addition Calculator

This ratio calculator by iCalculator allows you to add two ratios together. The mathematical process of adding two ratios or more than two ratios together is called ratio addition. This Ratio Addition Calculator will automatically calculate the sum of the two ratios, the equivalent whole number and equivalent fraction as part of the ratio calculations. Each step of the ratio calculation is displayed so you can check your own ratio addition calculations alongside the calculator.

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What are Ratios?

In mathematical terms, a ratio is a relational quantity that is expressed as two or more numbers separated by a colon, for example a two number ratio is written as 3:4 or a ratio with more than two numbers, lets use a four number ratio as an example, is written as 6:2:9:45 with each number being separated by a colon.

How do I calculate Ratios?

The following examples show how to complete math with ratios.

How to Add Ratios

The trick with adding ratios is to keep your eye on the number to the right of the colon (:), this number is called the Ratio Denominator. When the denominator of both ratios is the same, adding the ratio is simple. You just add the numbers to the left of the colon (this number is called the Ratio Numerator).

Ratio Addition Example 1: 1:3 + 1:3 = 2:3 Easy eh?

Now, adding ratios becomes a little (but only a little) more complicated when the denominators (the number on the right of the colon) of the ratios that you are adding are not the same. There is a simple rule when adding ratios, the denominations must always be the same, in mathematical terms this is called a Common Denominator as all the denominators have the same 'common' value.

So, your trying to add a ratio with different denominators and you need a Common Denominator, how do you get it? If you are working with 2 ratios, you can find a common denominator simply by multiplying the denominators:

Ratio Addition Example 2 Step 1: 2:5 + 3:4, our two denominators are 5 and 4.

Ratio Calculation Example 2 Step 2: 5 x 4 = 20 We multiply them: 20 is our Common Denominator.

Got it so far? Great. Now, in order to make our original ratios Equivalent Ratios. Note: you can learn more about Equivalent ratios and how to calculate equivalent ratios here.

An Equivalent Ratio is a ratio of the same value, written in a different format, for example 1:2 is the same as 2:4 and 5:10.

In order to make our ratios equivalent, we must complete the same action to the top number (the numerator) as we did to the bottom number (the denominator)

Ratio Calculation Example 2 Step 3: 5 x 3 = 15 We multiply 3 by 5 as we previously multiplied 4 by 5.

Ratio Calculation Example 2 Step 4: 15:20 is the equivalent ratio of 3:4.

We then repeat the exercise for our other ratio

Ratio Calculation Example 2 Step 5: 4 x 2 = 8 We multiply 2 by 4 as we previously multiplied 5 by 4.

Ratio Calculation Example 2 Step 6: 8:20 is the equivalent ratio of 2:5.

Excellent, we now have two ratios to add that have common denominators as we made them into equivalent ratios that are easier to add together.

Ratio Calculation Example 2 Step 7: 8:20 + 15:20 = 23:20.

Our ratio in this case is greater than one (23 parts of a 20 piece puzzle) so we can write the ratio as 23:20