Operations with Fractions

Adding and Subtracting Fractions

Same denominator: Add or subtract numerators, keep denominator $\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$

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: $\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$