The problem consists of 8 multiplication problems involving fractions. We need to calculate the result of each multiplication. The problems are: 17. $\frac{6}{18} \times \frac{3}{9}$ 18. $\frac{14}{24} \times \frac{3}{12}$ 19. $\frac{20}{30} \times \frac{6}{18}$ 20. $\frac{6}{30} \times \frac{9}{40}$ 21. $\frac{4}{14} \times \frac{9}{27}$ 22. $\frac{6}{20} \times \frac{3}{10}$ 23. $\frac{5}{10} \times \frac{7}{20}$ 24. $\frac{6}{14} \times \frac{8}{20}$

1. Problem Description

The problem consists of 8 multiplication problems involving fractions. We need to calculate the result of each multiplication. The problems are:

1

7. $\frac{6}{18} \times \frac{3}{9}$

1

8. $\frac{14}{24} \times \frac{3}{12}$

1

9. $\frac{20}{30} \times \frac{6}{18}$

2

0. $\frac{6}{30} \times \frac{9}{40}$

2

1. $\frac{4}{14} \times \frac{9}{27}$

2

2. $\frac{6}{20} \times \frac{3}{10}$

2

3. $\frac{5}{10} \times \frac{7}{20}$

2

4. $\frac{6}{14} \times \frac{8}{20}$

2. Solution Steps

We solve each multiplication problem by multiplying the numerators and denominators, then simplifying the resulting fraction.

Problem 17:

$\frac{6}{18} \times \frac{3}{9} = \frac{6 \times 3}{18 \times 9} = \frac{18}{162}$

We can simplify the fraction by dividing both numerator and denominator by

1

8. $\frac{18}{162} = \frac{18 \div 18}{162 \div 18} = \frac{1}{9}$

Problem 18:

$\frac{14}{24} \times \frac{3}{12} = \frac{14 \times 3}{24 \times 12} = \frac{42}{288}$

Both numerator and denominator are divisible by

6. $\frac{42 \div 6}{288 \div 6} = \frac{7}{48}$

Problem 19:

$\frac{20}{30} \times \frac{6}{18} = \frac{20 \times 6}{30 \times 18} = \frac{120}{540}$

Both numerator and denominator are divisible by

6

0. $\frac{120 \div 60}{540 \div 60} = \frac{2}{9}$

Problem 20:

$\frac{6}{30} \times \frac{9}{40} = \frac{6 \times 9}{30 \times 40} = \frac{54}{1200}$

Both numerator and denominator are divisible by

6. $\frac{54 \div 6}{1200 \div 6} = \frac{9}{200}$

Problem 21:

$\frac{4}{14} \times \frac{9}{27} = \frac{4 \times 9}{14 \times 27} = \frac{36}{378}$

Both numerator and denominator are divisible by

1

8. $\frac{36 \div 18}{378 \div 18} = \frac{2}{21}$

Problem 22:

$\frac{6}{20} \times \frac{3}{10} = \frac{6 \times 3}{20 \times 10} = \frac{18}{200}$

Both numerator and denominator are divisible by

2. $\frac{18 \div 2}{200 \div 2} = \frac{9}{100}$

Problem 23:

$\frac{5}{10} \times \frac{7}{20} = \frac{5 \times 7}{10 \times 20} = \frac{35}{200}$

Both numerator and denominator are divisible by

5. $\frac{35 \div 5}{200 \div 5} = \frac{7}{40}$

Problem 24:

$\frac{6}{14} \times \frac{8}{20} = \frac{6 \times 8}{14 \times 20} = \frac{48}{280}$

Both numerator and denominator are divisible by

8. This is wrong. They are divisible by

4. $\frac{48 \div 4}{280 \div 4} = \frac{12}{70}$

Now divide by 2:

$\frac{12 \div 2}{70 \div 2} = \frac{6}{35}$

3. Final Answer

1

7. $\frac{1}{9}$

1

8. $\frac{7}{48}$

1

9. $\frac{2}{9}$

2

0. $\frac{9}{200}$

2

1. $\frac{2}{21}$

2

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

2

3. $\frac{7}{40}$

2

4. $\frac{6}{35}$