Multiplying Improper Fractions by Whole Numbers with All ... - Free Printable

Here are the solutions for each problem on the worksheet. To solve these, you multiply the whole number by the numerator (the top number) of the fraction and keep the denominator (the bottom number) the same. Then, simplify the fraction if possible.

1. $\frac{16}{9} \times 3$
* Multiply: $\frac{16 \times 3}{9} = \frac{48}{9}$
* Simplify: Both numbers divide by 3. $48 \div 3 = 16$, $9 \div 3 = 3$.
* Result: $\frac{16}{3}$ or $5 \frac{1}{3}$

2. $2 \times \frac{5}{2}$
* Multiply: $\frac{2 \times 5}{2} = \frac{10}{2}$
* Simplify: $10 \div 2 = 5$
* Result: $5$

3. $\frac{11}{3} \times 3$
* Multiply: $\frac{11 \times 3}{3} = \frac{33}{3}$
* Simplify: $33 \div 3 = 11$
* Result: $11$

4. $3 \times \frac{10}{3}$
* Multiply: $\frac{3 \times 10}{3} = \frac{30}{3}$
* Simplify: $30 \div 3 = 10$
* Result: $10$

5. $\frac{3}{2} \times 6$
* Multiply: $\frac{3 \times 6}{2} = \frac{18}{2}$
* Simplify: $18 \div 2 = 9$
* Result: $9$

6. $\frac{23}{9} \times 9$
* Multiply: $\frac{23 \times 9}{9} = \frac{207}{9}$
* Simplify: The 9s cancel out perfectly.
* Result: $23$

7. $3 \times \frac{8}{3}$
* Multiply: $\frac{3 \times 8}{3} = \frac{24}{3}$
* Simplify: $24 \div 3 = 8$
* Result: $8$

8. $\frac{10}{3} \times 6$
* Multiply: $\frac{10 \times 6}{3} = \frac{60}{3}$
* Simplify: $60 \div 3 = 20$
* Result: $20$

9. $3 \times \frac{17}{9}$
* Multiply: $\frac{3 \times 17}{9} = \frac{51}{9}$
* Simplify: Both divide by 3. $51 \div 3 = 17$, $9 \div 3 = 3$.
* Result: $\frac{17}{3}$ or $5 \frac{2}{3}$

10. $\frac{11}{8} \times 6$
* Multiply: $\frac{11 \times 6}{8} = \frac{66}{8}$
* Simplify: Both divide by 2. $66 \div 2 = 33$, $8 \div 2 = 4$.
* Result: $\frac{33}{4}$ or $8 \frac{1}{4}$

11. $\frac{5}{4} \times 4$
* Multiply: $\frac{5 \times 4}{4} = \frac{20}{4}$
* Simplify: $20 \div 4 = 5$
* Result: $5$

12. $\frac{23}{9} \times 3$
* Multiply: $\frac{23 \times 3}{9} = \frac{69}{9}$
* Simplify: Both divide by 3. $69 \div 3 = 23$, $9 \div 3 = 3$.
* Result: $\frac{23}{3}$ or $7 \frac{2}{3}$

13. $\frac{5}{2} \times 2$
* Multiply: $\frac{5 \times 2}{2} = \frac{10}{2}$
* Simplify: $10 \div 2 = 5$
* Result: $5$

14. $\frac{5}{3} \times 6$
* Multiply: $\frac{5 \times 6}{3} = \frac{30}{3}$
* Simplify: $30 \div 3 = 10$
* Result: $10$

15. $\frac{13}{6} \times 2$
* Multiply: $\frac{13 \times 2}{6} = \frac{26}{6}$
* Simplify: Both divide by 2. $26 \div 2 = 13$, $6 \div 2 = 3$.
* Result: $\frac{13}{3}$ or $4 \frac{1}{3}$

16. $6 \times \frac{5}{4}$
* Multiply: $\frac{6 \times 5}{4} = \frac{30}{4}$
* Simplify: Both divide by 2. $30 \div 2 = 15$, $4 \div 2 = 2$.
* Result: $\frac{15}{2}$ or $7 \frac{1}{2}$

17. $\frac{14}{5} \times 5$
* Multiply: $\frac{14 \times 5}{5} = \frac{70}{5}$
* Simplify: The 5s cancel out.
* Result: $14$

18. $6 \times \frac{7}{3}$
* Multiply: $\frac{6 \times 7}{3} = \frac{42}{3}$
* Simplify: $42 \div 3 = 14$
* Result: $14$

19. $\frac{21}{8} \times 8$
* Multiply: $\frac{21 \times 8}{8} = \frac{168}{8}$
* Simplify: The 8s cancel out.
* Result: $21$

20. $\frac{3}{2} \times 4$
* Multiply: $\frac{3 \times 4}{2} = \frac{12}{2}$
* Simplify: $12 \div 2 = 6$
* Result: $6$

Final Answer:
1. $\frac{16}{3}$ (or $5 \frac{1}{3}$)
2. $5$
3. $11$
4. $10$
5. $9$
6. $23$
7. $8$
8. $20$
9. $\frac{17}{3}$ (or $5 \frac{2}{3}$)
10. $\frac{33}{4}$ (or $8 \frac{1}{4}$)
11. $5$
12. $\frac{23}{3}$ (or $7 \frac{2}{3}$)
13. $5$
14. $10$
15. $\frac{13}{3}$ (or $4 \frac{1}{3}$)
16. $\frac{15}{2}$ (or $7 \frac{1}{2}$)
17. $14$
18. $14$
19. $21$
20. $6$