1. Let's start with a fractions problem: Suppose you want to add $\frac{3}{4}$ and $\frac{2}{5}$.\n\n2. The formula for adding fractions is to find a common denominator and then add the numerators: $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$\n\n3. For $\frac{3}{4} + \frac{2}{5}$, the common denominator is $4 \times 5 = 20$.\n\n4. Convert each fraction: $$\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$$ and $$\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}$$\n\n5. Now add the numerators: $$\frac{15}{20} + \frac{8}{20} = \frac{15 + 8}{20} = \frac{23}{20}$$\n\n6. $\frac{23}{20}$ is an improper fraction and can be written as a mixed number: $$1 \frac{3}{20}$$\n\n7. Now for a two-digit multiplication example: Multiply 23 by 15.\n\n8. Use the distributive property: $$23 \times 15 = 23 \times (10 + 5) = 23 \times 10 + 23 \times 5$$\n\n9. Calculate each part: $$23 \times 10 = 230$$ and $$23 \times 5 = 115$$\n\n10. Add the results: $$230 + 115 = 345$$\n\nSo, the answers are $\frac{23}{20}$ or $1 \frac{3}{20}$ for the fraction addition, and 345 for the two-digit multiplication.