Common Denominator in Fraction Addition and Subtraction

Elementary Math (K-6th) Tutorial

Common Denominator in Fraction Addition and Subtraction


In this tutorial, we will use a simple example to illustrate the concept of common denominator in fraction addition/subtraction.

Sample Problem

I ate 1/2 of a pizza. My friend ate 1/4 of it. How much did we eat altogether?


First, let’s write the solution to the problem in words. I ate 1/2 of a pizza. In word, I ate 1-half. Similarly, my friend ate 1-quarter. Altogether, we ate

1-half + 1-quarter

We can treat the size of the pizza that we ate as a unit. A half of a pizza and a quarter of a pizza are different in size and hence in different unit. In order to add, we have to make sure that units are the same, i.e. we are talking about the same size.

A half of a pizza can be cut into two equal pieces. Each piece is a quarter in size. Therefore,

1-half + 1-quarter
= 2-quarters + 1-quarter (now we can add because units are the same)
= 3-quarters
= 3/4

Now, we can write the mathematic sentence of fraction addition.

1/2 + 1/4 (different size, we cannot add numerators)
= 2/4 + 1/4 (common denominator, we are talking about the same size so that we can add numerators)
= 3/4

Remember, addition and subtraction require that numbers have the same unit. In fraction addition and subtraction, common denominator ensures that we are talking about the same size so that we can perform addition and subtraction on numerators.

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