1. Let's solve an example involving fractions: Simplify the expression $$\frac{3}{4} + \frac{2}{5}$$. 2. To add fractions, we need a common denominator. The denominators here are 4 and 5. 3. The least common denominator (LCD) of 4 and 5 is 20. 4. Convert each fraction to an equivalent fraction with denominator 20: $$\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$$ $$\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}$$ 5. Now add the fractions: $$\frac{15}{20} + \frac{8}{20} = \frac{15 + 8}{20} = \frac{23}{20}$$ 6. The fraction $$\frac{23}{20}$$ is an improper fraction and can be expressed as a mixed number: $$23 \div 20 = 1 \text{ remainder } 3$$ So, $$\frac{23}{20} = 1 \frac{3}{20}$$ 7. Final answer: $$\frac{3}{4} + \frac{2}{5} = 1 \frac{3}{20}$$.