1. **Stating the problem:** We will learn how to add, subtract, multiply, and divide fractions, which are common operations in grade 7 math. 2. **Important rules and formulas:** - To add or subtract fractions, they must have the same denominator. Use the formula: $$\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}$$ - To multiply fractions, multiply the numerators and denominators: $$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$$ - To divide fractions, multiply by the reciprocal of the divisor: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}$$ 3. **Example: Add $$\frac{2}{3}$$ and $$\frac{1}{4}$$** - Find common denominator: $$3 \times 4 = 12$$ - Convert fractions: $$\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$$ $$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$$ - Add numerators: $$\frac{8}{12} + \frac{3}{12} = \frac{8+3}{12} = \frac{11}{12}$$ 4. **Example: Multiply $$\frac{2}{3}$$ by $$\frac{4}{5}$$** - Multiply numerators and denominators: $$\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$$ 5. **Example: Divide $$\frac{3}{4}$$ by $$\frac{2}{5}$$** - Multiply by reciprocal: $$\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{3 \times 5}{4 \times 2} = \frac{15}{8}$$ 6. **Simplify fractions if possible:** - For example, $$\frac{15}{8}$$ is already in simplest form. This covers the basic operations with fractions for grade 7.