1. Let's start by understanding what a fraction is. 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). 2. To add or subtract fractions, they must have the same denominator. If they don't, find the least common denominator (LCD). 3. For example, to add $\frac{1}{4} + \frac{1}{6}$, find the LCD of 4 and 6, which is 12. 4. Convert each fraction to an equivalent fraction with denominator 12: $$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$$ $$\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$$ 5. Now add the numerators: $$\frac{3}{12} + \frac{2}{12} = \frac{3+2}{12} = \frac{5}{12}$$ 6. To multiply fractions, multiply the numerators and denominators directly: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 7. For example, $\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$. 8. To divide fractions, multiply the first fraction by the reciprocal of the second: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$$ 9. For example, $\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8}$. 10. Always simplify fractions by dividing numerator and denominator by their greatest common divisor (GCD).