1. The problem is to understand how to solve fractions, which means simplifying or performing operations like addition, subtraction, multiplication, or division with fractions. 2. Let's start with an example: Add $\frac{2}{3}$ and $\frac{1}{4}$. 3. The formula for adding fractions is: $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a$, $b$, $c$, and $d$ are integers and $b, d \neq 0$. 4. Important rule: To add fractions, they must have a common denominator. If they don't, find the least common denominator (LCD). 5. For $\frac{2}{3} + \frac{1}{4}$, the denominators are 3 and 4. The LCD is 12. 6. Convert each fraction to an equivalent fraction with denominator 12: $$\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$$ $$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$$ 7. Now add the numerators: $$\frac{8}{12} + \frac{3}{12} = \frac{8 + 3}{12} = \frac{11}{12}$$ 8. The fraction $\frac{11}{12}$ is already in simplest form because 11 and 12 have no common factors other than 1. 9. Therefore, the final answer is $\frac{11}{12}$. This method applies to other operations with fractions as well, with specific formulas for subtraction, multiplication, and division.