Here are the solutions to the fraction multiplication problems.
1. $\frac{1}{3} \times \frac{1}{2}$
Multiply the top numbers (numerators): $1 \times 1 = 1$
Multiply the bottom numbers (denominators): $3 \times 2 = 6$
Answer:
$\frac{1}{6}$
2. $\frac{3}{4} \times \frac{2}{5}$
Multiply tops: $3 \times 2 = 6$
Multiply bottoms: $4 \times 5 = 20$
Result: $\frac{6}{20}$
Simplify by dividing both by 2:
$\frac{3}{10}$
3. $\frac{1}{3} \times 2$
Think of 2 as $\frac{2}{1}$.
Multiply tops: $1 \times 2 = 2$
Multiply bottoms: $3 \times 1 = 3$
Answer:
$\frac{2}{3}$
4. $\frac{2}{3} \times \frac{1}{4}$
Multiply tops: $2 \times 1 = 2$
Multiply bottoms: $3 \times 4 = 12$
Result: $\frac{2}{12}$
Simplify by dividing both by 2:
$\frac{1}{6}$
5. $\frac{5}{6} \times \frac{2}{6}$
Multiply tops: $5 \times 2 = 10$
Multiply bottoms: $6 \times 6 = 36$
Result: $\frac{10}{36}$
Simplify by dividing both by 2:
$\frac{5}{18}$
6. $\frac{11}{12} \times 2$
Think of 2 as $\frac{2}{1}$.
Multiply tops: $11 \times 2 = 22$
Multiply bottoms: $12 \times 1 = 12$
Result: $\frac{22}{12}$
Simplify by dividing both by 2: $\frac{11}{6}$
Change to a mixed number ($11 \div 6 = 1$ with remainder $5$):
$1 \frac{5}{6}$
7. $\frac{4}{7} \times \frac{3}{4}$
You can cancel the 4s before multiplying because one is on top and one is on the bottom.
This leaves $\frac{1}{7} \times \frac{3}{1}$.
Multiply tops: $1 \times 3 = 3$
Multiply bottoms: $7 \times 1 = 7$
Answer:
$\frac{3}{7}$
8. $\frac{6}{9} \times \frac{2}{3}$
First, simplify $\frac{6}{9}$ to $\frac{2}{3}$ (divide top and bottom by 3).
Now calculate $\frac{2}{3} \times \frac{2}{3}$.
Multiply tops: $2 \times 2 = 4$
Multiply bottoms: $3 \times 3 = 9$
Answer:
$\frac{4}{9}$
9. $\frac{4}{7} \times \frac{3}{8}$
You can simplify before multiplying. The 4 on top and 8 on the bottom can both be divided by 4.
The 4 becomes 1, and the 8 becomes 2.
New problem: $\frac{1}{7} \times \frac{3}{2}$.
Multiply tops: $1 \times 3 = 3$
Multiply bottoms: $7 \times 2 = 14$
Answer:
$\frac{3}{14}$
10. $\frac{5}{12} \times \frac{1}{2}$
Multiply tops: $5 \times 1 = 5$
Multiply bottoms: $12 \times 2 = 24$
Answer:
$\frac{5}{24}$
11. $\frac{11}{12} \times \frac{10}{11}$
Cancel the 11s (one on top, one on bottom).
New problem: $\frac{1}{12} \times \frac{10}{1}$.
Multiply tops: $1 \times 10 = 10$
Multiply bottoms: $12 \times 1 = 12$
Result: $\frac{10}{12}$
Simplify by dividing both by 2:
$\frac{5}{6}$
12. $\frac{9}{10} \times \frac{3}{4}$
Multiply tops: $9 \times 3 = 27$
Multiply bottoms: $10 \times 4 = 40$
Answer:
$\frac{27}{40}$ (Cannot be simplified further)
Extension 13: Area of rectangle
Formula: Width $\times$ Height
$\frac{4}{7} \times \frac{2}{9}$
Multiply tops: $4 \times 2 = 8$
Multiply bottoms: $7 \times 9 = 63$
Answer:
$\frac{8}{63} \text{ m}^2$
Extension 14: Area of rectangle
Formula: Width $\times$ Height
$\frac{7}{8} \times \frac{5}{12}$
Multiply tops: $7 \times 5 = 35$
Multiply bottoms: $8 \times 12 = 96$
Answer:
$\frac{35}{96} \text{ m}^2$
Final Answer:
1. $\frac{1}{6}$
2. $\frac{3}{10}$
3. $\frac{2}{3}$
4. $\frac{1}{6}$
5. $\frac{5}{18}$
6. $1 \frac{5}{6}$
7. $\frac{3}{7}$
8. $\frac{4}{9}$
9. $\frac{3}{14}$
10. $\frac{5}{24}$
11. $\frac{5}{6}$
12. $\frac{27}{40}$
13. $\frac{8}{63} \text{ m}^2$
14. $\frac{35}{96} \text{ m}^2$
Parent Tip: Review the logic above to help your child master the concept of worksheet on multiplying fractions.
