Multiplying and Dividing Fractions Worksheets with Answer Key - Free Printable

Problem: Multiplying and Dividing Fractions by Whole Numbers

We are tasked with solving the given problems involving multiplication and division of fractions by whole numbers. Let's solve each problem step by step.

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#### Problem 1: $\frac{3}{8} \times 3$

Solution:
To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number, keeping the denominator the same.

\[
\frac{3}{8} \times 3 = \frac{3 \times 3}{8} = \frac{9}{8}
\]

Answer:
\[
\boxed{\frac{9}{8}}
\]

---

#### Problem 2: $\frac{1}{5} \div 8$

Solution:
To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. The reciprocal of 8 is $\frac{1}{8}$.

\[
\frac{1}{5} \div 8 = \frac{1}{5} \times \frac{1}{8} = \frac{1 \times 1}{5 \times 8} = \frac{1}{40}
\]

Answer:
\[
\boxed{\frac{1}{40}}
\]

---

#### Problem 3: $\frac{1}{18} \times 16$

Solution:
Multiply the numerator of the fraction by the whole number, keeping the denominator the same.

\[
\frac{1}{18} \times 16 = \frac{1 \times 16}{18} = \frac{16}{18}
\]

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 2.

\[
\frac{16}{18} = \frac{16 \div 2}{18 \div 2} = \frac{8}{9}
\]

Answer:
\[
\boxed{\frac{8}{9}}
\]

---

#### Problem 4: $\frac{11}{12} \times 6$

Solution:
Multiply the numerator of the fraction by the whole number, keeping the denominator the same.

\[
\frac{11}{12} \times 6 = \frac{11 \times 6}{12} = \frac{66}{12}
\]

Simplify the fraction by dividing the numerator and denominator by their GCD, which is 6.

\[
\frac{66}{12} = \frac{66 \div 6}{12 \div 6} = \frac{11}{2}
\]

Answer:
\[
\boxed{\frac{11}{2}}
\]

---

#### Problem 5: $\frac{9}{8} \div 18$

Solution:
To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. The reciprocal of 18 is $\frac{1}{18}$.

\[
\frac{9}{8} \div 18 = \frac{9}{8} \times \frac{1}{18} = \frac{9 \times 1}{8 \times 18} = \frac{9}{144}
\]

Simplify the fraction by dividing the numerator and denominator by their GCD, which is 9.

\[
\frac{9}{144} = \frac{9 \div 9}{144 \div 9} = \frac{1}{16}
\]

Answer:
\[
\boxed{\frac{1}{16}}
\]

---

#### Problem 6: $\frac{2}{10} \div 9$

Solution:
To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. The reciprocal of 9 is $\frac{1}{9}$.

\[
\frac{2}{10} \div 9 = \frac{2}{10} \times \frac{1}{9} = \frac{2 \times 1}{10 \times 9} = \frac{2}{90}
\]

Simplify the fraction by dividing the numerator and denominator by their GCD, which is 2.

\[
\frac{2}{90} = \frac{2 \div 2}{90 \div 2} = \frac{1}{45}
\]

Answer:
\[
\boxed{\frac{1}{45}}
\]

---

#### Problem 7: $\frac{20}{26} \times 5$

Solution:
Multiply the numerator of the fraction by the whole number, keeping the denominator the same.

\[
\frac{20}{26} \times 5 = \frac{20 \times 5}{26} = \frac{100}{26}
\]

Simplify the fraction by dividing the numerator and denominator by their GCD, which is 2.

\[
\frac{100}{26} = \frac{100 \div 2}{26 \div 2} = \frac{50}{13}
\]

Answer:
\[
\boxed{\frac{50}{13}}
\]

---

#### Problem 8: $\frac{21}{24} \div 6$

Solution:
To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. The reciprocal of 6 is $\frac{1}{6}$.

\[
\frac{21}{24} \div 6 = \frac{21}{24} \times \frac{1}{6} = \frac{21 \times 1}{24 \times 6} = \frac{21}{144}
\]

Simplify the fraction by dividing the numerator and denominator by their GCD, which is 3.

\[
\frac{21}{144} = \frac{21 \div 3}{144 \div 3} = \frac{7}{48}
\]

Answer:
\[
\boxed{\frac{7}{48}}
\]

---

#### Problem 9: $\frac{9}{72} \times 8$

Solution:
Multiply the numerator of the fraction by the whole number, keeping the denominator the same.

\[
\frac{9}{72} \times 8 = \frac{9 \times 8}{72} = \frac{72}{72}
\]

Simplify the fraction.

\[
\frac{72}{72} = 1
\]

Answer:
\[
\boxed{1}
\]

---

#### Problem 10: $\frac{18}{21} \times 35$

Solution:
Multiply the numerator of the fraction by the whole number, keeping the denominator the same.

\[
\frac{18}{21} \times 35 = \frac{18 \times 35}{21} = \frac{630}{21}
\]

Simplify the fraction by dividing the numerator and denominator by their GCD, which is 21.

\[
\frac{630}{21} = \frac{630 \div 21}{21 \div 21} = \frac{30}{1} = 30
\]

Answer:
\[
\boxed{30}
\]

---

#### Problem 11: $\frac{16}{3} \div 7$

Solution:
To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. The reciprocal of 7 is $\frac{1}{7}$.

\[
\frac{16}{3} \div 7 = \frac{16}{3} \times \frac{1}{7} = \frac{16 \times 1}{3 \times 7} = \frac{16}{21}
\]

Answer:
\[
\boxed{\frac{16}{21}}
\]

---

#### Problem 12: $\frac{10}{9} \times 15$

Solution:
Multiply the numerator of the fraction by the whole number, keeping the denominator the same.

\[
\frac{10}{9} \times 15 = \frac{10 \times 15}{9} = \frac{150}{9}
\]

Simplify the fraction by dividing the numerator and denominator by their GCD, which is 3.

\[
\frac{150}{9} = \frac{150 \div 3}{9 \div 3} = \frac{50}{3}
\]

Answer:
\[
\boxed{\frac{50}{3}}
\]

---

#### Problem 13: $\frac{2}{3} \div 13$

Solution:
To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. The reciprocal of 13 is $\frac{1}{13}$.

\[
\frac{2}{3} \div 13 = \frac{2}{3} \times \frac{1}{13} = \frac{2 \times 1}{3 \times 13} = \frac{2}{39}
\]

Answer:
\[
\boxed{\frac{2}{39}}
\]

---

#### Problem 14: $\frac{3}{16} \div 9$

Solution:
To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. The reciprocal of 9 is $\frac{1}{9}$.

\[
\frac{3}{16} \div 9 = \frac{3}{16} \times \frac{1}{9} = \frac{3 \times 1}{16 \times 9} = \frac{3}{144}
\]

Simplify the fraction by dividing the numerator and denominator by their GCD, which is 3.

\[
\frac{3}{144} = \frac{3 \div 3}{144 \div 3} = \frac{1}{48}
\]

Answer:
\[
\boxed{\frac{1}{48}}
\]

---

Final Answers:

1. $\boxed{\frac{9}{8}}$
2. $\boxed{\frac{1}{40}}$
3. $\boxed{\frac{8}{9}}$
4. $\boxed{\frac{11}{2}}$
5. $\boxed{\frac{1}{16}}$
6. $\boxed{\frac{1}{45}}$
7. $\boxed{\frac{50}{13}}$
8. $\boxed{\frac{7}{48}}$
9. $\boxed{1}$
10. $\boxed{30}$
11. $\boxed{\frac{16}{21}}$
12. $\boxed{\frac{50}{3}}$
13. $\boxed{\frac{2}{39}}$
14. $\boxed{\frac{1}{48}}$