Let's solve each of the multiplication problems involving fractions and whole numbers. I'll go step by step, showing the work and simplifying each answer to its
simplest form.
---
1.
$$
\frac{1}{6} \times \frac{5}{9}
$$
Multiply numerators: $1 \times 5 = 5$
Multiply denominators: $6 \times 9 = 54$
$$
= \frac{5}{54}
$$
✔ Already in simplest form.
Answer: $\boxed{\frac{5}{54}}$
---
2.
$$
\frac{2}{5} \times \frac{7}{8}
$$
Numerator: $2 \times 7 = 14$
Denominator: $5 \times 8 = 40$
$$
= \frac{14}{40}
$$
Simplify: Divide numerator and denominator by 2 → $\frac{7}{20}$
Answer: $\boxed{\frac{7}{20}}$
---
3.
$$
\frac{6}{7} \text{ of } \frac{2}{9}
$$
"Of" means multiplication:
$$
\frac{6}{7} \times \frac{2}{9} = \frac{12}{63}
$$
Simplify: Divide numerator and denominator by 3 → $\frac{4}{21}$
Answer: $\boxed{\frac{4}{21}}$
---
4.
$$
18 \times \frac{5}{6}
$$
Write 18 as a fraction: $\frac{18}{1}$
$$
\frac{18}{1} \times \frac{5}{6} = \frac{90}{6} = 15
$$
Answer: $\boxed{15}$
---
5.
$$
5 \times \frac{8}{15}
$$
$$
\frac{5}{1} \times \frac{8}{15} = \frac{40}{15}
$$
Simplify: Divide numerator and denominator by 5 → $\frac{8}{3}$
Convert to mixed number: $8 \div 3 = 2$ remainder 2 → $2\frac{2}{3}$
Answer: $\boxed{2\frac{2}{3}}$
---
6.
$$
\frac{2}{9} \text{ of } 7
$$
"Of" means multiply:
$$
\frac{2}{9} \times 7 = \frac{2}{9} \times \frac{7}{1} = \frac{14}{9}
$$
Convert to mixed number: $14 \div 9 = 1$ remainder 5 → $1\frac{5}{9}$
Answer: $\boxed{1\frac{5}{9}}$
---
7.
$$
1\frac{1}{12} \times \frac{2}{5}
$$
Convert mixed number to improper fraction:
$1\frac{1}{12} = \frac{13}{12}$
Now multiply:
$$
\frac{13}{12} \times \frac{2}{5} = \frac{26}{60}
$$
Simplify: Divide numerator and denominator by 2 → $\frac{13}{30}$
Answer: $\boxed{\frac{13}{30}}$
---
8.
$$
\frac{3}{4} \times \frac{20}{21}
$$
Multiply:
$$
\frac{3 \times 20}{4 \times 21} = \frac{60}{84}
$$
Simplify: Divide numerator and denominator by 12 → $\frac{5}{7}$
(Or divide by 6 first: $\frac{10}{14}$, then by 2 → $\frac{5}{7}$)
Answer: $\boxed{\frac{5}{7}}$
---
9.
$$
4\frac{9}{10} \times 1\frac{1}{7}
$$
Convert both to improper fractions:
- $4\frac{9}{10} = \frac{49}{10}$
- $1\frac{1}{7} = \frac{8}{7}$
Now multiply:
$$
\frac{49}{10} \times \frac{8}{7} = \frac{392}{70}
$$
Simplify: Divide numerator and denominator by 14 → $\frac{28}{5}$
Convert to mixed number: $28 \div 5 = 5$ remainder 3 → $5\frac{3}{5}$
Answer: $\boxed{5\frac{3}{5}}$
---
10.
$$
2\frac{1}{3} \text{ of } 3\frac{1}{2}
$$
"Of" means multiply.
Convert both to improper fractions:
- $2\frac{1}{3} = \frac{7}{3}$
- $3\frac{1}{2} = \frac{7}{2}$
Now multiply:
$$
\frac{7}{3} \times \frac{7}{2} = \frac{49}{6}
$$
Convert to mixed number: $49 \div 6 = 8$ remainder 1 → $8\frac{1}{6}$
Answer: $\boxed{8\frac{1}{6}}$
---
✔ Final Answers (in order):
1. $\frac{5}{54}$
2. $\frac{7}{20}$
3. $\frac{4}{21}$
4. $15$
5. $2\frac{2}{3}$
6. $1\frac{5}{9}$
7. $\frac{13}{30}$
8. $\frac{5}{7}$
9. $5\frac{3}{5}$
10. $8\frac{1}{6}$
Let me know if you'd like this formatted for printing or with steps shown on paper!
Parent Tip: Review the logic above to help your child master the concept of multiplication fraction worksheet.
