1. The problem is to understand how to work with fractions. 2. 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). 3. Important rules: - To add or subtract fractions, they must have the same denominator. - To multiply fractions, multiply the numerators and multiply the denominators. - To divide fractions, multiply by the reciprocal of the divisor. 4. Example: Add $\frac{1}{3} + \frac{1}{4}$. 5. Find a common denominator: $3$ and $4$ have least common denominator $12$. 6. Convert fractions: $\frac{1}{3} = \frac{4}{12}$ and $\frac{1}{4} = \frac{3}{12}$. 7. Add numerators: $4 + 3 = 7$. 8. Result: $\frac{7}{12}$. 9. Example: Multiply $\frac{2}{5} \times \frac{3}{4}$. 10. Multiply numerators: $2 \times 3 = 6$. 11. Multiply denominators: $5 \times 4 = 20$. 12. Result: $\frac{6}{20}$. 13. Simplify by dividing numerator and denominator by $2$: $$\frac{\cancel{6}^{3}}{\cancel{20}^{10}} = \frac{3}{10}$$. 14. Example: Divide $\frac{3}{7} \div \frac{2}{5}$. 15. Multiply by reciprocal: $\frac{3}{7} \times \frac{5}{2}$. 16. Multiply numerators: $3 \times 5 = 15$. 17. Multiply denominators: $7 \times 2 = 14$. 18. Result: $\frac{15}{14}$ or $1 \frac{1}{14}$ as a mixed number. Fractions are parts of a whole and can be added, subtracted, multiplied, and divided using these rules.