1. **Stating the problem:** We want to review all the important knowledge about fractions. 2. **Definition:** 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 $b \neq 0$. 3. **Types of fractions:** - Proper fractions: numerator $<$ denominator (e.g., $\frac{3}{4}$) - Improper fractions: numerator $\geq$ denominator (e.g., $\frac{7}{4}$) - Mixed numbers: a whole number and a proper fraction combined (e.g., $1 \frac{3}{4}$) 4. **Equivalent fractions:** Fractions that represent the same value, e.g., $\frac{1}{2} = \frac{2}{4} = \frac{3}{6}$. To find equivalent fractions, multiply or divide numerator and denominator by the same nonzero number. 5. **Simplifying fractions:** Divide numerator and denominator by their greatest common divisor (GCD) to get the fraction in simplest form. 6. **Adding and subtracting fractions:** - Find a common denominator (usually the least common denominator, LCD). - Convert fractions to equivalent fractions with the LCD. - Add or subtract the numerators and keep the denominator. - Simplify the result if possible. Example: $\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$. 7. **Multiplying fractions:** Multiply numerators together and denominators together. Example: $\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$. 8. **Dividing fractions:** Multiply the first fraction by the reciprocal of the second. Example: $\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$. 9. **Converting between mixed numbers and improper fractions:** - To improper: $\text{whole} \times \text{denominator} + \text{numerator}$ over denominator. - To mixed: divide numerator by denominator to get whole number and remainder. 10. **Important rules:** - Denominator can never be zero. - Always simplify your answer. - When adding/subtracting, denominators must be the same. This covers the essential knowledge about fractions.