Adding and Subtracting Fractions

Same Denominators (Easy!)

When denominators match, just add/subtract the numerators:

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

$\frac{5}{8} - \frac{2}{8} = \frac{5-2}{8} = \frac{3}{8}$

Different Denominators

You need a common denominator first!

Step 1: Find the Least Common Denominator (LCD)

The LCD is the smallest number both denominators divide into evenly.

Example: $\frac{1}{3} + \frac{1}{4}$

Multiples of 3: 3, 6, 9, 12, 15... Multiples of 4: 4, 8, 12, 16...

LCD = 12

Step 2: Convert to Equivalent Fractions

$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$

$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

Step 3: Add or Subtract

$\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$

Simplifying Fractions

Always reduce to lowest terms by dividing by the GCF (Greatest Common Factor):

$\frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4}$

Adding Mixed Numbers

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

1. Find LCD: 6
2. Convert: $2\frac{2}{6} + 1\frac{3}{6}$
3. Add wholes: $2 + 1 = 3$
4. Add fractions: $\frac{2}{6} + \frac{3}{6} = \frac{5}{6}$
5. Combine: $3\frac{5}{6}$