Lesson 24: Adding and Subtracting Fractions That Have Common Denominators

New Concept

To add fractions with the same denominator, add their numerators. To subtract, subtract their numerators. The denominator of the answer remains the same.

What’s next

This is the foundation for all fraction arithmetic. Next, we will walk through worked examples to solidify your understanding of this core principle.

Property

When adding fractions that have the same denominator, we add the numerators. The denominator does not change. This rule can be written as $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$.

Examples

$\frac{1}{4} + \frac{1}{4} = \frac{2}{4}$
$\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$
$\frac{1}{8} + \frac{1}{8} + \frac{1}{8} = \frac{3}{8}$

Explanation

Imagine you have a pizza cut into 8 giant slices. The denominator '8' is your slice size. If you have 3 slices and your friend gives you 2 more, you now have 5 slices! You simply added the number of slices (the numerators) together. The size of the slices (the denominator) stayed the same. Easy peasy!

Property

When subtracting fractions that have the same denominator, we subtract the numerators. The denominator does not change. This rule can be written as $\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$.

Examples

$\frac{5}{8} - \frac{2}{8} = \frac{3}{8}$
$\frac{7}{8} - \frac{2}{8} = \frac{5}{8}$
$\frac{3}{4} - \frac{2}{4} = \frac{1}{4}$

Explanation

Picture a chocolate bar with 8 squares. If you start with 7 squares and eat 2, you're left with 5. You only subtracted the number of squares you had (the numerators), not the total number of squares the bar was broken into (the denominator). So, keep the bottom number the same and just subtract the top numbers!