Question

exercise 1 (answers on page 40)
multiply these fractions. cancel and simplify if possible.

1. (\frac{1}{8} \times \frac{2}{3} =)
2. (\frac{1}{2} \times \frac{4}{5} =)
3. (\frac{3}{5} \times \frac{10}{11} =)
4. (\frac{8}{9} \times \frac{3}{4} =)
5. (\frac{7}{10} \times \frac{2}{21} =)
6. (\frac{3}{4} \times \frac{5}{7} =)
7. (\frac{5}{9} \times \frac{7}{8} =)
8. (6 \times \frac{1}{3} =)
9. (\frac{5}{9} \times 9 =)
10. (10 \times \frac{1}{2} =)
11. (\frac{1}{3} \times 12 =)
12. (\frac{15}{16} \times \frac{8}{10} =)
13. (\frac{7}{8} \times \frac{12}{13} =)
14. (\frac{6}{9} \times \frac{1}{3} =)
15. (\frac{5}{10} \times \frac{3}{4} =)
16. (\frac{16}{17} \times \frac{23}{24} =)
17. (\frac{5}{16} \times \frac{20}{30} =)
18. (\frac{9}{10} \times \frac{50}{100} =)

Explanation:

Problem 1: $\boldsymbol{\frac{1}{8} \times \frac{2}{3}}$

Step 1: Multiply numerators and denominators

Multiply the numerators ($1 \times 2$) and the denominators ($8 \times 3$).
$\frac{1 \times 2}{8 \times 3} = \frac{2}{24}$

Step 2: Simplify the fraction

Divide numerator and denominator by their greatest common divisor (2).
$\frac{2 \div 2}{24 \div 2} = \frac{1}{12}$

Step 1: Multiply numerators and denominators

Multiply the numerators ($1 \times 4$) and the denominators ($2 \times 5$).
$\frac{1 \times 4}{2 \times 5} = \frac{4}{10}$

Step 2: Simplify the fraction

Divide numerator and denominator by their greatest common divisor (2).
$\frac{4 \div 2}{10 \div 2} = \frac{2}{5}$

Step 1: Cancel common factors (optional)

The numerator 10 and denominator 5 have a common factor of 5. Simplify before multiplying:
$\frac{3}{\cancel{5}} \times \frac{\cancel{10}^2}{11} = \frac{3 \times 2}{1 \times 11}$

Step 2: Multiply numerators and denominators

Multiply the simplified numerators and denominators.
$\frac{3 \times 2}{1 \times 11} = \frac{6}{11}$

Answer:

$\boldsymbol{\frac{1}{12}}$

Problem 2: $\boldsymbol{\frac{1}{2} \times \frac{4}{5}}$