1. Let's start by understanding fractions and the operations you mentioned: addition, subtraction, multiplication, and division. 2. **Addition and Subtraction of Fractions:** - To add or subtract fractions, you need a common denominator (the bottom number). - The common denominator is usually the least common multiple (LCM) of the denominators. - For example, to add $\frac{1}{4} + \frac{1}{6}$, find the LCM of 4 and 6, which is 12. - Convert each fraction to have denominator 12: $\frac{1}{4} = \frac{3}{12}$ and $\frac{1}{6} = \frac{2}{12}$. - Now add: $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$. 3. **Multiplication of Fractions:** - Multiply the numerators (top numbers) together and the denominators together. - No need for a common denominator. - Example: $\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$. 4. **Division of Fractions:** - To divide by a fraction, multiply by its reciprocal (flip the second fraction). - Example: $\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12}$. - Simplify $\frac{10}{12}$ by canceling common factors: $\frac{\cancel{10}^{5}}{\cancel{12}^{6}} = \frac{5}{6}$. 5. Summary: - Addition/Subtraction: find common denominator (LCM), convert, then add/subtract. - Multiplication: multiply straight across. - Division: multiply by reciprocal. Understanding which operation requires a common denominator is key: only addition and subtraction do. If you want, I can help with specific examples!