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Find the product in simplest form. Cancel the common factors in the numerator and denominator.

17. [tex] \frac{1}{2} \times \frac{4}{5} = \qquad[/tex]

18. [tex] \frac{8}{12} \times \frac{4}{6} = \qquad[/tex]

19. [tex] \frac{9}{15} \times \frac{5}{6} = \qquad[/tex]

20. [tex] \frac{10}{32} \times \frac{16}{20} = \qquad[/tex]

21. [tex] 12 \times \frac{9}{36} = \qquad[/tex]

22. [tex] 18 \times \frac{18}{54} = \qquad[/tex]

23. [tex] 21 \times \frac{5}{7} \times \frac{9}{35} = \qquad[/tex]

24. [tex] \frac{18}{27} \times \frac{18}{20} \times \frac{10}{6} = \qquad[/tex]

Answer :

Sure, let's go through each question step-by-step:

### Question 17:
[tex]\[ \frac{1}{2} \times \frac{4}{5} \][/tex]

1. Multiply the numerators: [tex]\( 1 \times 4 = 4 \)[/tex]
2. Multiply the denominators: [tex]\( 2 \times 5 = 10 \)[/tex]
3. The fraction is [tex]\( \frac{4}{10} \)[/tex]
4. Simplify [tex]\( \frac{4}{10} \)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 2: [tex]\( \frac{4 \div 2}{10 \div 2} = \frac{2}{5} \)[/tex]

So, the answer is [tex]\( \frac{2}{5} \)[/tex].

### Question 21:
[tex]\[ 12 \times \frac{9}{36} \][/tex]

1. Simplify [tex]\( \frac{9}{36} \)[/tex]:
- The greatest common divisor of 9 and 36 is 9.
- [tex]\( \frac{9 \div 9}{36 \div 9} = \frac{1}{4} \)[/tex]
2. Now multiply: [tex]\( 12 \times \frac{1}{4} \)[/tex]
3. [tex]\( 12 \div 4 = 3 \)[/tex]

So, the answer is [tex]\( 3 \)[/tex].

### Question 18:
[tex]\[ \frac{8}{12} \times \frac{4}{6} \][/tex]

1. Simplify each fraction:
- [tex]\( \frac{8}{12} = \frac{2}{3} \)[/tex] (Divide both by 4)
- [tex]\( \frac{4}{6} = \frac{2}{3} \)[/tex] (Divide both by 2)
2. Now multiply: [tex]\( \frac{2}{3} \times \frac{2}{3} = \frac{2 \times 2}{3 \times 3} = \frac{4}{9} \)[/tex]

So, the answer is [tex]\( \frac{4}{9} \)[/tex].

### Question 22:
[tex]\[ 18 \times \frac{18}{54} \][/tex]

1. Simplify [tex]\( \frac{18}{54} \)[/tex]:
- The greatest common divisor of 18 and 54 is 18.
- [tex]\( \frac{18 \div 18}{54 \div 18} = \frac{1}{3} \)[/tex]
2. Now multiply: [tex]\( 18 \times \frac{1}{3} \)[/tex]
3. [tex]\( 18 \div 3 = 6 \)[/tex]

So, the answer is [tex]\( 6 \)[/tex].

### Question 19:
[tex]\[ \frac{9}{15} \times \frac{5}{6} \][/tex]

1. Simplify each fraction:
- [tex]\( \frac{9}{15} = \frac{3}{5} \)[/tex] (Divide both by 3)
- [tex]\( \frac{5}{6} \)[/tex] (already in simplest form)
2. Now multiply: [tex]\( \frac{3}{5} \times \frac{5}{6} = \frac{3 \times 5}{5 \times 6} = \frac{15}{30} \)[/tex]
3. Simplify [tex]\( \frac{15}{30} = \frac{1}{2} \)[/tex] (Divide both by 15)

So, the answer is [tex]\( \frac{1}{2} \)[/tex].

### Question 23:
[tex]\[ 21 \times \frac{5}{7} \times \frac{9}{35} \][/tex]

1. Simplify [tex]\( \frac{5}{7} \)[/tex] and [tex]\( \frac{9}{35} \)[/tex]:
- [tex]\( \frac{5}{7} \)[/tex] (already in simplest form)
- [tex]\( \frac{9}{35} \)[/tex] (already in simplest form)
2. Multiply: [tex]\( 21 \times \frac{5}{7} \times \frac{9}{35} \)[/tex]
- First: [tex]\( 21 \times \frac{5}{7} = 3 \times 5 = 15 \)[/tex] (since [tex]\( 21 \div 7 = 3 \)[/tex])
- Then: [tex]\( 15 \times \frac{9}{35} = 15 \times \frac{9}{5\times7} = \frac{15 \times 9}{35} = \frac{135}{35} = \frac{27}{7} \)[/tex]

So, the answer is [tex]\( \frac{27}{7} \)[/tex] (or approximately [tex]\( 3.86 \)[/tex]).

### Question 20:
[tex]\[ \frac{10}{32} \times \frac{16}{20} \][/tex]

1. Simplify each fraction:
- [tex]\( \frac{10}{32} = \frac{5}{16} \)[/tex] (Divide both by 2)
- [tex]\( \frac{16}{20} = \frac{4}{5} \)[/tex] (Divide both by 4)
2. Now multiply: [tex]\( \frac{5}{16} \times \frac{4}{5} = \frac{5 \times 4}{16 \times 5} = \frac{20}{80} = \frac{1}{4} \)[/tex] (Divide both by 20)

So, the answer is [tex]\( \frac{1}{4} \)[/tex].

### Question 24:
[tex]\[ \frac{18}{27} \times \frac{18}{20} \times \frac{10}{6} \][/tex]

1. Simplify each fraction:
- [tex]\( \frac{18}{27} = \frac{2}{3} \)[/tex] (Divide both by 9)
- [tex]\( \frac{18}{20} = \frac{9}{10} \)[/tex] (Divide both by 2)
- [tex]\( \frac{10}{6} = \frac{5}{3} \)[/tex] (Divide both by 2)
2. Now multiply: [tex]\( \frac{2}{3} \times \frac{9}{10} \times \frac{5}{3} \)[/tex]
- [tex]\( \frac{2 \times 9 \times 5}{3 \times 10 \times 3} = \frac{90}{90} = 1\)[/tex]

So, the answer is [tex]\( 1 \)[/tex].

These are the simplified products for each given question.

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