Let's solve each of the fraction multiplication problems step by step.
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Rule for Multiplying Fractions:
To multiply two fractions:
$$
\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
$$
Then simplify the result if possible.
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Now, let's go through each problem:
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1. $\frac{1}{3} \times \frac{1}{6} = \frac{1 \times 1}{3 \times 6} = \frac{1}{18}$
✔ Answer: $\boxed{\frac{1}{18}}$
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2. $\frac{4}{5} \times \frac{5}{7} = \frac{4 \times 5}{5 \times 7} = \frac{20}{35}$
Simplify: divide numerator and denominator by 5 → $\frac{4}{7}$
✔ Answer: $\boxed{\frac{4}{7}}$
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3. $\frac{5}{6} \times \frac{2}{7} = \frac{5 \times 2}{6 \times 7} = \frac{10}{42}$
Simplify: divide by 2 → $\frac{5}{21}$
✔ Answer: $\boxed{\frac{5}{21}}$
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4. $\frac{5}{9} \times \frac{3}{10} = \frac{5 \times 3}{9 \times 10} = \frac{15}{90}$
Simplify: divide by 15 → $\frac{1}{6}$
✔ Answer: $\boxed{\frac{1}{6}}$
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5. $\frac{2}{21} \times \frac{7}{10} = \frac{2 \times 7}{21 \times 10} = \frac{14}{210}$
Simplify: divide by 14 → $\frac{1}{15}$
✔ Answer: $\boxed{\frac{1}{15}}$
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6. $\frac{6}{11} \times \frac{1}{3} = \frac{6 \times 1}{11 \times 3} = \frac{6}{33}$
Simplify: divide by 3 → $\frac{2}{11}$
✔ Answer: $\boxed{\frac{2}{11}}$
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7. $\frac{1}{8} \times \frac{2}{5} = \frac{1 \times 2}{8 \times 5} = \frac{2}{40}$
Simplify: divide by 2 → $\frac{1}{20}$
✔ Answer: $\boxed{\frac{1}{20}}$
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8. $\frac{4}{15} \times \frac{3}{22} = \frac{4 \times 3}{15 \times 22} = \frac{12}{330}$
Simplify: divide by 6 → $\frac{2}{55}$
✔ Answer: $\boxed{\frac{2}{55}}$
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9. $\frac{7}{18} \times \frac{9}{14} = \frac{7 \times 9}{18 \times 14} = \frac{63}{252}$
Simplify: divide numerator and denominator by 63 → $\frac{1}{4}$
(Or: notice $7/14 = 1/2$, $9/18 = 1/2$, so $(1/2) \times (1/2) = 1/4$)
✔ Answer: $\boxed{\frac{1}{4}}$
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10. $\frac{1}{10} \times \frac{4}{5} = \frac{1 \times 4}{10 \times 5} = \frac{4}{50}$
Simplify: divide by 2 → $\frac{2}{25}$
✔ Answer: $\boxed{\frac{2}{25}}$
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11. $\frac{5}{12} \times \frac{6}{7} = \frac{5 \times 6}{12 \times 7} = \frac{30}{84}$
Simplify: divide by 6 → $\frac{5}{14}$
✔ Answer: $\boxed{\frac{5}{14}}$
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12. $\frac{3}{14} \times \frac{7}{9} = \frac{3 \times 7}{14 \times 9} = \frac{21}{126}$
Simplify: divide by 21 → $\frac{1}{6}$
✔ Answer: $\boxed{\frac{1}{6}}$
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✔ Final Answers:
1. $\frac{1}{18}$
2. $\frac{4}{7}$
3. $\frac{5}{21}$
4. $\frac{1}{6}$
5. $\frac{1}{15}$
6. $\frac{2}{11}$
7. $\frac{1}{20}$
8. $\frac{2}{55}$
9. $\frac{1}{4}$
10. $\frac{2}{25}$
11. $\frac{5}{14}$
12. $\frac{1}{6}$
Let me know if you'd like a printable version or explanations in simpler terms!
Parent Tip: Review the logic above to help your child master the concept of multiplying fractions problems.
