1. **Stating the problem:** We will learn about fractions, how to add, subtract, multiply, and divide them. 2. **What is a fraction?** 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. **Adding and subtracting fractions:** - To add or subtract fractions, they must have the same denominator. - If denominators are different, find the least common denominator (LCD). - Formula: $$\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}$$ 4. **Example of addition:** $$\frac{2}{3} + \frac{1}{4} = \frac{2 \times 4}{3 \times 4} + \frac{1 \times 3}{4 \times 3} = \frac{8}{12} + \frac{3}{12} = \frac{8+3}{12} = \frac{11}{12}$$ 5. **Multiplying fractions:** - Multiply numerators and denominators directly. - Formula: $$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$$ 6. **Example of multiplication:** $$\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$$ 7. **Dividing fractions:** - Multiply the first fraction by the reciprocal of the second. - Formula: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}$$ 8. **Example of division:** $$\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12}$$ 9. **Simplifying fractions:** - Find the greatest common divisor (GCD) of numerator and denominator. - Divide numerator and denominator by the GCD. - Example: $$\frac{10}{12} = \frac{\cancel{2} \times 5}{\cancel{2} \times 6} = \frac{5}{6}$$ 10. **Important rules:** - Denominator cannot be zero. - Always simplify your answer. - When adding/subtracting, find common denominators first. This covers the basics of fractions including addition, subtraction, multiplication, division, and simplification.