Example: $\frac{2}{7} + \frac{3}{7} = \frac{5}{7}$

Different denominators: Find common denominator first!

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

LCD = 12: $\frac{1}{3} = \frac{4}{12}, \quad \frac{1}{4} = \frac{3}{12}$ $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$

Multiplying Fractions

Multiply numerators, multiply denominators $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

Example: $\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$

Tip: Simplify before multiplying when possible!

Dividing Fractions

Multiply by the reciprocal $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

Example: $\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$

Memory aid: "Keep, Change, Flip"

Simplifying Fractions

Divide numerator and denominator by their GCF: $\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$

Simplify (divide by 2): $\frac{6}{20} = \frac{3}{10}$

Answer: $\frac{3}{10}$

Multiply: $\frac{3 \times 3}{4 \times 2} = \frac{9}{8}$

Convert to mixed number: $\frac{9}{8} = 1\frac{1}{8}$

Answer: $\frac{9}{8}$ or $1\frac{1}{8}$