1. Let's start by understanding what fractions are. A fraction represents a part of a whole and is written as $\frac{a}{b}$ where $a$ is the numerator (top number) and $b$ is the denominator (bottom number), with $b \neq 0$. 2. Important rules for fractions: - To add or subtract fractions, they must have a common denominator. - To multiply fractions, multiply the numerators and multiply the denominators. - To divide fractions, multiply by the reciprocal of the divisor. 3. Example: Add $\frac{2}{3}$ and $\frac{1}{4}$. - Find common denominator: $3 \times 4 = 12$. - Convert fractions: $\frac{2}{3} = \frac{8}{12}$ and $\frac{1}{4} = \frac{3}{12}$. - Add numerators: $8 + 3 = 11$. - Result: $\frac{11}{12}$. 4. Example: Multiply $\frac{2}{3}$ by $\frac{4}{5}$. - Multiply numerators: $2 \times 4 = 8$. - Multiply denominators: $3 \times 5 = 15$. - Result: $\frac{8}{15}$. 5. Example: Divide $\frac{2}{3}$ by $\frac{4}{5}$. - Multiply $\frac{2}{3}$ by reciprocal of $\frac{4}{5}$ which is $\frac{5}{4}$. - Multiply numerators: $2 \times 5 = 10$. - Multiply denominators: $3 \times 4 = 12$. - Result: $\frac{10}{12}$ which simplifies to $\frac{5}{6}$. Fractions are fundamental in math and mastering these operations helps in many areas.