Multiplying Fractions by Whole Numbers Worksheet

The task involves multiplying fractions by whole numbers. Let's solve each problem step by step.

General Approach:

1. Multiply the numerator of the fraction by the whole number.
2. Keep the denominator the same.
3. Simplify the resulting fraction if possible.

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Problem 1: $\frac{1}{15} \times 4$

- Multiply the numerator $1$ by $4$: $1 \times 4 = 4$.
- The denominator remains $15$.
- Result: $\frac{4}{15}$.

Answer: $\frac{4}{15}$

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Problem 2: $\frac{3}{13} \times 3$

- Multiply the numerator $3$ by $3$: $3 \times 3 = 9$.
- The denominator remains $13$.
- Result: $\frac{9}{13}$.

Answer: $\frac{9}{13}$

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Problem 3: $\frac{4}{11} \times 2$

- Multiply the numerator $4$ by $2$: $4 \times 2 = 8$.
- The denominator remains $11$.
- Result: $\frac{8}{11}$.

Answer: $\frac{8}{11}$

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Problem 4: $\frac{2}{23} \times 4$

- Multiply the numerator $2$ by $4$: $2 \times 4 = 8$.
- The denominator remains $23$.
- Result: $\frac{8}{23}$.

Answer: $\frac{8}{23}$

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Problem 5: $\frac{4}{21} \times 2$

- Multiply the numerator $4$ by $2$: $4 \times 2 = 8$.
- The denominator remains $21$.
- Result: $\frac{8}{21}$.

Answer: $\frac{8}{21}$

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Problem 6: $\frac{2}{8} \times 2$

- Multiply the numerator $2$ by $2$: $2 \times 2 = 4$.
- The denominator remains $8$.
- Simplify $\frac{4}{8}$: Divide both numerator and denominator by their greatest common divisor (GCD), which is $4$: $\frac{4 \div 4}{8 \div 4} = \frac{1}{2}$.
- Result: $\frac{1}{2}$.

Answer: $\frac{1}{2}$

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Problem 7: $\frac{5}{12} \times 1$

- Multiply the numerator $5$ by $1$: $5 \times 1 = 5$.
- The denominator remains $12$.
- Result: $\frac{5}{12}$.

Answer: $\frac{5}{12}$

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Problem 8: $3 \times \frac{2}{17}$

- Multiply the whole number $3$ by the numerator $2$: $3 \times 2 = 6$.
- The denominator remains $17$.
- Result: $\frac{6}{17}$.

Answer: $\frac{6}{17}$

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Problem 9: $5 \times \frac{3}{19}$

- Multiply the whole number $5$ by the numerator $3$: $5 \times 3 = 15$.
- The denominator remains $19$.
- Result: $\frac{15}{19}$.

Answer: $\frac{15}{19}$

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Problem 10: $6 \times \frac{2}{13}$

- Multiply the whole number $6$ by the numerator $2$: $6 \times 2 = 12$.
- The denominator remains $13$.
- Result: $\frac{12}{13}$.

Answer: $\frac{12}{13}$

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Final Answers:

1. $\frac{4}{15}$
2. $\frac{9}{13}$
3. $\frac{8}{11}$
4. $\frac{8}{23}$
5. $\frac{8}{21}$
6. $\frac{1}{2}$
7. $\frac{5}{12}$
8. $\frac{6}{17}$
9. $\frac{15}{19}$
10. $\frac{12}{13}$

Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
1) & \frac{4}{15} \\
2) & \frac{9}{13} \\
3) & \frac{8}{11} \\
4) & \frac{8}{23} \\
5) & \frac{8}{21} \\
6) & \frac{1}{2} \\
7) & \frac{5}{12} \\
8) & \frac{6}{17} \\
9) & \frac{15}{19} \\
10) & \frac{12}{13} \\
\end{array}
}
\]