Fractions
Add and Subtract Fractions with the Same Denominator
When two fractions have the same denominator, we call them like fractions. Like fractions express the fraction in terms of equivalent-sized parts of the whole. In order to add or subtract fractions we must express them as like fractions. That is, they must have the same denominator. The example illustrates the situation in which two fractions are expressed in terms of the same denominator.
The figures above show two larger squares each divided into four equal parts. The three shaded regions on the left and the one on the right are of equal size. Therefore, the fractions expressed are like fractions.
Steps to Adding and Subtracting Like Fractions
- Add or subtract the numerators.
- Write this sum or difference over the common denominator.
- Simplify, if possible.
Examples:
| Adding Fractions | Subtracting Fractions |
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| Both denominators are three (3), so we add the numerators (2+1=3). |
Both denominators are three (3), so we subtract the numerators (2-1=1). |
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| The denominator in both fractions is 3 so our answer has a denominator of 3 as well.
Three over three simplifies to 1. |
The denominator in the fractions is 3 so our answer has a denominator of 3 as well. |
Practice:
Find the following sums and differences. Write your answer in lowest terms.
