Adding Fractions

Study Sheet

Adding Fractions

Same denominator, then different

Why Denominators Must Match

Concept
The Big Idea
2 of 8 parts shaded

You can only add pieces that are the same size. The denominator names the piece size, so it must match before you add the tops.

Example
Finding 28+38\dfrac{2}{8} + \dfrac{3}{8}

The pieces are both eighths, so add the counts: 2+3=52 + 3 = 5 eighths, or 58\dfrac{5}{8}.

In Plain Terms & More Examples

Concept
In plain terms

When the denominators already match, just add or subtract the top numbers — the piece size (the bottom) stays the same.

Example
Finding 310+410\dfrac{3}{10} + \dfrac{4}{10}

Same tenths, so add the tops: 3+4=73 + 4 = 7, giving 710\dfrac{7}{10}.

Example
Finding 56−26\dfrac{5}{6} - \dfrac{2}{6}

Same sixths, so subtract the tops: 5−2=35 - 2 = 3, giving 36=12\dfrac{3}{6} = \dfrac{1}{2}.