The problem is to multiply fractions and simplify the results. We have 8 different multiplication problems to solve: 9. $\frac{3}{17} \times \frac{7}{15}$ 10. $\frac{14}{24} \times \frac{6}{12}$ 11. $\frac{10}{15} \times \frac{4}{8}$ 12. $\frac{3}{6} \times \frac{25}{60}$ 13. $\frac{3}{4} \times \frac{1}{8}$ 14. $\frac{9}{20} \times \frac{3}{15}$ 15. $\frac{2}{3} \times \frac{5}{16}$ 16. $\frac{3}{7} \times \frac{8}{16}$

1. Problem Description

The problem is to multiply fractions and simplify the results. We have 8 different multiplication problems to solve:

9. $\frac{3}{17} \times \frac{7}{15}$

1

0. $\frac{14}{24} \times \frac{6}{12}$

1

1. $\frac{10}{15} \times \frac{4}{8}$

1

2. $\frac{3}{6} \times \frac{25}{60}$

1

3. $\frac{3}{4} \times \frac{1}{8}$

1

4. $\frac{9}{20} \times \frac{3}{15}$

1

5. $\frac{2}{3} \times \frac{5}{16}$

1

6. $\frac{3}{7} \times \frac{8}{16}$

2. Solution Steps

To multiply fractions, we multiply the numerators and the denominators. Then, we simplify the resulting fraction to its lowest terms.

Problem 9: $\frac{3}{17} \times \frac{7}{15}$

Multiply the numerators: $3 \times 7 = 21$

Multiply the denominators: $17 \times 15 = 255$

Result: $\frac{21}{255}$

Simplify by dividing both numerator and denominator by 3:

$\frac{21 \div 3}{255 \div 3} = \frac{7}{85}$

Problem 10: $\frac{14}{24} \times \frac{6}{12}$

Multiply the numerators: $14 \times 6 = 84$

Multiply the denominators: $24 \times 12 = 288$

Result: $\frac{84}{288}$

Simplify by dividing both numerator and denominator by 12:

$\frac{84 \div 12}{288 \div 12} = \frac{7}{24}$

Problem 11: $\frac{10}{15} \times \frac{4}{8}$

Multiply the numerators: $10 \times 4 = 40$

Multiply the denominators: $15 \times 8 = 120$

Result: $\frac{40}{120}$

Simplify by dividing both numerator and denominator by 40:

$\frac{40 \div 40}{120 \div 40} = \frac{1}{3}$

Problem 12: $\frac{3}{6} \times \frac{25}{60}$

Multiply the numerators: $3 \times 25 = 75$

Multiply the denominators: $6 \times 60 = 360$

Result: $\frac{75}{360}$

Simplify by dividing both numerator and denominator by 15:

$\frac{75 \div 15}{360 \div 15} = \frac{5}{24}$

Problem 13: $\frac{3}{4} \times \frac{1}{8}$

Multiply the numerators: $3 \times 1 = 3$

Multiply the denominators: $4 \times 8 = 32$

Result: $\frac{3}{32}$

Problem 14: $\frac{9}{20} \times \frac{3}{15}$

Multiply the numerators: $9 \times 3 = 27$

Multiply the denominators: $20 \times 15 = 300$

Result: $\frac{27}{300}$

Simplify by dividing both numerator and denominator by 3:

$\frac{27 \div 3}{300 \div 3} = \frac{9}{100}$

Problem 15: $\frac{2}{3} \times \frac{5}{16}$

Multiply the numerators: $2 \times 5 = 10$

Multiply the denominators: $3 \times 16 = 48$

Result: $\frac{10}{48}$

Simplify by dividing both numerator and denominator by 2:

$\frac{10 \div 2}{48 \div 2} = \frac{5}{24}$

Problem 16: $\frac{3}{7} \times \frac{8}{16}$

Multiply the numerators: $3 \times 8 = 24$

Multiply the denominators: $7 \times 16 = 112$

Result: $\frac{24}{112}$

Simplify by dividing both numerator and denominator by 8:

$\frac{24 \div 8}{112 \div 8} = \frac{3}{14}$

3. Final Answer

9. $\frac{7}{85}$

1

0. $\frac{7}{24}$

1

1. $\frac{1}{3}$

1

2. $\frac{5}{24}$

1

3. $\frac{3}{32}$

1

4. $\frac{9}{100}$

1

5. $\frac{5}{24}$

1

6. $\frac{3}{14}$