Adding and Subtracting Fractions

Same Denominators

When fractions have the same denominator (like denominators), just add or subtract the numerators:

$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$

$\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}$

Examples

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

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

Always simplify your answer if possible!

Mixed Numbers

A mixed number has a whole number and a fraction: $2\frac{3}{4}$

To add mixed numbers:

1. Add the whole numbers
2. Add the fractions
3. Simplify if needed

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

When the Fraction Part Is Too Big

$2\frac{3}{4} + 1\frac{3}{4} = 3\frac{6}{4} = 3 + 1\frac{2}{4} = 4\frac{1}{2}$

Since $\frac{6}{4} = 1\frac{2}{4} = 1\frac{1}{2}$

Fractions Greater Than 1

$\frac{5}{3} = 1\frac{2}{3}$

To convert: Divide the numerator by the denominator. $5 \div 3 = 1$ remainder $2$, so $\frac{5}{3} = 1\frac{2}{3}$

Rule: You can only add or subtract fractions that have the same denominator. In Grade 5, you'll learn how to handle different denominators!