I see you've uploaded a math problem sheet. I'll transcribe and solve each problem step-by-step below:

Problems:

3a) $\frac{6}{7} - \frac{5}{7}$

Subtract the numerators (since the denominators are the same): $\frac{6 - 5}{7} = \frac{1}{7}$ Answer: $\frac{1}{7}$

3b) $\frac{2}{3} + \frac{1}{4}$

Find the least common denominator (LCD) of 3 and 4, which is 12. Rewrite the fractions: $\frac{2}{3} = \frac{8}{12}, \quad \frac{1}{4} = \frac{3}{12}$ Add the fractions: $\frac{8}{12} + \frac{3}{12} = \frac{11}{12}$ Answer: $\frac{11}{12}$

3c) $\frac{3}{7} \times \frac{10}{7}$

Multiply the numerators and denominators: $\frac{3 \cdot 10}{7 \cdot 7} = \frac{30}{49}$ Answer: $\frac{30}{49}$

3d) $\frac{8}{15} \div 9$

Rewrite the division as multiplication by the reciprocal of $9$: $\frac{8}{15} \div 9 = \frac{8}{15} \times \frac{1}{9} = \frac{8}{135}$ Answer: $\frac{8}{135}$

3e) $\frac{3}{4} \times 5$

Rewrite $5$ as $\frac{5}{1}$ and multiply: $\frac{3}{4} \times \frac{5}{1} = \frac{3 \cdot 5}{4 \cdot 1} = \frac{15}{4}$ Convert to a mixed number if needed: $\frac{15}{4} = 3 \frac{3}{4}$ Answer: $3 \frac{3}{4}$ or $\frac{15}{4}$

3f) $\frac{9}{5} \div \frac{11}{5}$

Rewrite the division as multiplication by the reciprocal of $\frac{11}{5}$: $\frac{9}{5} \div \frac{11}{5} = \frac{9}{5} \times \frac{5}{11} = \frac{9 \cdot 5}{5 \cdot 11}$ Cancel the $5$ in the numerator and denominator: $\frac{9}{11}$ Answer: $\frac{9}{11}$

3g) $\frac{5}{9} \div \frac{4}{3}$

Rewrite the division as multiplication by the reciprocal of $\frac{4}{3}$: $\frac{5}{9} \div \frac{4}{3} = \frac{5}{9} \times \frac{3}{4} = \frac{5 \cdot 3}{9 \cdot 4} = \frac{15}{36}$ Simplify: $\frac{15}{36} = \frac{5}{12}$ Answer: $\frac{5}{12}$

Summary of Answers:

• a) $\frac{1}{7}$
• b) $\frac{11}{12}$
• c) $\frac{30}{49}$
• d) $\frac{8}{135}$
• e) $3 \frac{3}{4}$ or $\frac{15}{4}$
• f) $\frac{9}{11}$
• g) $\frac{5}{12}$

Would you like me to explain any of these steps further?

Here are 5 related questions to deepen your understanding:

1. How can you find the least common denominator for fractions?
2. What is the rule for dividing fractions?
3. How do you convert an improper fraction to a mixed number?
4. What are the steps to simplify fractions?
5. How do you solve a fraction with a whole number (like $\frac{3}{4} \times 5$)?

Tip: When dividing fractions, always multiply by the reciprocal of the second fraction!