Multiplying Fractions Worksheet - Free Printable

Problem: Multiplying Fractions by Whole Numbers

The worksheet provided involves multiplying fractions by whole numbers and finding fractions of whole numbers. Below is a step-by-step solution for each problem, along with explanations.

---

#### 1. \( 1 \times \frac{1}{6} \)
- Explanation: Multiplying any number by 1 leaves the number unchanged.
- Solution:
\[
1 \times \frac{1}{6} = \frac{1}{6}
\]

#### 2. \( 9 \times \frac{7}{10} \)
- Explanation: Multiply the whole number (9) by the numerator (7) and keep the denominator (10) the same.
- Solution:
\[
9 \times \frac{7}{10} = \frac{9 \times 7}{10} = \frac{63}{10}
\]

#### 3. \( 7 \times \frac{4}{8} \)
- Explanation: First, simplify the fraction \(\frac{4}{8}\) to \(\frac{1}{2}\). Then multiply 7 by \(\frac{1}{2}\).
- Solution:
\[
7 \times \frac{4}{8} = 7 \times \frac{1}{2} = \frac{7 \times 1}{2} = \frac{7}{2}
\]

#### 4. \( \frac{4}{5} \text{ of } 2 \)
- Explanation: "Of" means multiplication. So, \(\frac{4}{5} \text{ of } 2\) is \(\frac{4}{5} \times 2\).
- Solution:
\[
\frac{4}{5} \times 2 = \frac{4 \times 2}{5} = \frac{8}{5}
\]

#### 5. \( \frac{1}{12} \text{ of } 1 \)
- Explanation: Multiplying any number by 1 leaves the number unchanged.
- Solution:
\[
\frac{1}{12} \times 1 = \frac{1}{12}
\]

#### 6. \( \frac{2}{6} \text{ of } 2 \)
- Explanation: Simplify \(\frac{2}{6}\) to \(\frac{1}{3}\). Then multiply \(\frac{1}{3}\) by 2.
- Solution:
\[
\frac{2}{6} \times 2 = \frac{1}{3} \times 2 = \frac{1 \times 2}{3} = \frac{2}{3}
\]

#### 7. \( \frac{1}{3} \text{ of } 5 \)
- Explanation: Multiply \(\frac{1}{3}\) by 5.
- Solution:
\[
\frac{1}{3} \times 5 = \frac{1 \times 5}{3} = \frac{5}{3}
\]

#### 8. \( \frac{3}{10} \text{ of } 8 \)
- Explanation: Multiply \(\frac{3}{10}\) by 8.
- Solution:
\[
\frac{3}{10} \times 8 = \frac{3 \times 8}{10} = \frac{24}{10} = \frac{12}{5} \quad (\text{simplify by dividing numerator and denominator by 2})
\]

#### 9. \( \frac{1}{5} \text{ of } 5 \)
- Explanation: Multiply \(\frac{1}{5}\) by 5.
- Solution:
\[
\frac{1}{5} \times 5 = \frac{1 \times 5}{5} = 1
\]

#### 10. \( \frac{2}{9} \text{ of } 9 \)
- Explanation: Multiply \(\frac{2}{9}\) by 9.
- Solution:
\[
\frac{2}{9} \times 9 = \frac{2 \times 9}{9} = 2
\]

#### 11. \( 8 \times \frac{1}{8} \)
- Explanation: Multiply 8 by \(\frac{1}{8}\).
- Solution:
\[
8 \times \frac{1}{8} = \frac{8 \times 1}{8} = 1
\]

#### 12. \( 9 \times \frac{4}{6} \)
- Explanation: Simplify \(\frac{4}{6}\) to \(\frac{2}{3}\). Then multiply 9 by \(\frac{2}{3}\).
- Solution:
\[
9 \times \frac{4}{6} = 9 \times \frac{2}{3} = \frac{9 \times 2}{3} = \frac{18}{3} = 6
\]

#### 13. \( \frac{4}{5} \text{ of } 5 \)
- Explanation: Multiply \(\frac{4}{5}\) by 5.
- Solution:
\[
\frac{4}{5} \times 5 = \frac{4 \times 5}{5} = 4
\]

#### 14. \( 7 \times \frac{5}{10} \)
- Explanation: Simplify \(\frac{5}{10}\) to \(\frac{1}{2}\). Then multiply 7 by \(\frac{1}{2}\).
- Solution:
\[
7 \times \frac{5}{10} = 7 \times \frac{1}{2} = \frac{7 \times 1}{2} = \frac{7}{2}
\]

#### 15. \( \frac{2}{12} \text{ of } 9 \)
- Explanation: Simplify \(\frac{2}{12}\) to \(\frac{1}{6}\). Then multiply \(\frac{1}{6}\) by 9.
- Solution:
\[
\frac{2}{12} \times 9 = \frac{1}{6} \times 9 = \frac{1 \times 9}{6} = \frac{9}{6} = \frac{3}{2} \quad (\text{simplify by dividing numerator and denominator by 3})
\]

#### 16. \( \frac{1}{2} \text{ of } 9 \)
- Explanation: Multiply \(\frac{1}{2}\) by 9.
- Solution:
\[
\frac{1}{2} \times 9 = \frac{1 \times 9}{2} = \frac{9}{2}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \frac{1}{6} \\
2. & \frac{63}{10} \\
3. & \frac{7}{2} \\
4. & \frac{8}{5} \\
5. & \frac{1}{12} \\
6. & \frac{2}{3} \\
7. & \frac{5}{3} \\
8. & \frac{12}{5} \\
9. & 1 \\
10. & 2 \\
11. & 1 \\
12. & 6 \\
13. & 4 \\
14. & \frac{7}{2} \\
15. & \frac{3}{2} \\
16. & \frac{9}{2} \\
\end{array}
}
\]