Multiplying fractions by integers worksheet with practice problems and examples.

The task involves multiplying fractions by integers. Let's solve the problems step by step and explain the process.

General Steps for Multiplying a Fraction by an Integer:

1. Write the integer as a fraction: Any integer can be written as a fraction by placing it over 1.
2. Multiply the numerators: Multiply the numerator of the fraction by the numerator of the integer (which is the integer itself).
3. Multiply the denominators: Multiply the denominator of the fraction by the denominator of the integer (which is 1).
4. Simplify the result: Reduce the resulting fraction to its simplest form if possible.

---

Problem Set Solutions:

#### Section A: Basic Multiplication
1. $\frac{3}{7} \times 5$
- Write $5$ as $\frac{5}{1}$.
- Multiply: $\frac{3}{7} \times \frac{5}{1} = \frac{3 \times 5}{7 \times 1} = \frac{15}{7}$.
- Simplify: $\frac{15}{7}$ is already in simplest form.
- Answer: $\frac{15}{7}$

2. $\frac{2}{9} \times 6$
- Write $6$ as $\frac{6}{1}$.
- Multiply: $\frac{2}{9} \times \frac{6}{1} = \frac{2 \times 6}{9 \times 1} = \frac{12}{9}$.
- Simplify: $\frac{12}{9} = \frac{4}{3}$.
- Answer: $\frac{4}{3}$

3. $\frac{5}{8} \times 4$
- Write $4$ as $\frac{4}{1}$.
- Multiply: $\frac{5}{8} \times \frac{4}{1} = \frac{5 \times 4}{8 \times 1} = \frac{20}{8}$.
- Simplify: $\frac{20}{8} = \frac{5}{2}$.
- Answer: $\frac{5}{2}$

4. $\frac{7}{10} \times 3$
- Write $3$ as $\frac{3}{1}$.
- Multiply: $\frac{7}{10} \times \frac{3}{1} = \frac{7 \times 3}{10 \times 1} = \frac{21}{10}$.
- Simplify: $\frac{21}{10}$ is already in simplest form.
- Answer: $\frac{21}{10}$

5. $\frac{3}{5} \times 10$
- Write $10$ as $\frac{10}{1}$.
- Multiply: $\frac{3}{5} \times \frac{10}{1} = \frac{3 \times 10}{5 \times 1} = \frac{30}{5}$.
- Simplify: $\frac{30}{5} = 6$.
- Answer: $6$

---

#### Section B: Mixed Problems
6. $\frac{2}{3} \times 6$
- Write $6$ as $\frac{6}{1}$.
- Multiply: $\frac{2}{3} \times \frac{6}{1} = \frac{2 \times 6}{3 \times 1} = \frac{12}{3}$.
- Simplify: $\frac{12}{3} = 4$.
- Answer: $4$

7. $\frac{5}{6} \times 12$
- Write $12$ as $\frac{12}{1}$.
- Multiply: $\frac{5}{6} \times \frac{12}{1} = \frac{5 \times 12}{6 \times 1} = \frac{60}{6}$.
- Simplify: $\frac{60}{6} = 10$.
- Answer: $10$

8. $\frac{3}{8} \times 16$
- Write $16$ as $\frac{16}{1}$.
- Multiply: $\frac{3}{8} \times \frac{16}{1} = \frac{3 \times 16}{8 \times 1} = \frac{48}{8}$.
- Simplify: $\frac{48}{8} = 6$.
- Answer: $6$

9. $\frac{7}{12} \times 24$
- Write $24$ as $\frac{24}{1}$.
- Multiply: $\frac{7}{12} \times \frac{24}{1} = \frac{7 \times 24}{12 \times 1} = \frac{168}{12}$.
- Simplify: $\frac{168}{12} = 14$.
- Answer: $14$

10. $\frac{5}{9} \times 18$
- Write $18$ as $\frac{18}{1}$.
- Multiply: $\frac{5}{9} \times \frac{18}{1} = \frac{5 \times 18}{9 \times 1} = \frac{90}{9}$.
- Simplify: $\frac{90}{9} = 10$.
- Answer: $10$

---

#### Section C: More Complex Problems
11. $\frac{3}{4} \times 16$
- Write $16$ as $\frac{16}{1}$.
- Multiply: $\frac{3}{4} \times \frac{16}{1} = \frac{3 \times 16}{4 \times 1} = \frac{48}{4}$.
- Simplify: $\frac{48}{4} = 12$.
- Answer: $12$

12. $\frac{5}{7} \times 21$
- Write $21$ as $\frac{21}{1}$.
- Multiply: $\frac{5}{7} \times \frac{21}{1} = \frac{5 \times 21}{7 \times 1} = \frac{105}{7}$.
- Simplify: $\frac{105}{7} = 15$.
- Answer: $15$

13. $\frac{2}{5} \times 25$
- Write $25$ as $\frac{25}{1}$.
- Multiply: $\frac{2}{5} \times \frac{25}{1} = \frac{2 \times 25}{5 \times 1} = \frac{50}{5}$.
- Simplify: $\frac{50}{5} = 10$.
- Answer: $10$

14. $\frac{4}{9} \times 27$
- Write $27$ as $\frac{27}{1}$.
- Multiply: $\frac{4}{9} \times \frac{27}{1} = \frac{4 \times 27}{9 \times 1} = \frac{108}{9}$.
- Simplify: $\frac{108}{9} = 12$.
- Answer: $12$

15. $\frac{3}{8} \times 32$
- Write $32$ as $\frac{32}{1}$.
- Multiply: $\frac{3}{8} \times \frac{32}{1} = \frac{3 \times 32}{8 \times 1} = \frac{96}{8}$.
- Simplify: $\frac{96}{8} = 12$.
- Answer: $12$

---

Final Answer:

$$
\boxed{
\begin{array}{ll}
1. & \frac{15}{7} \\
2. & \frac{4}{3} \\
3. & \frac{5}{2} \\
4. & \frac{21}{10} \\
5. & 6 \\
6. & 4 \\
7. & 10 \\
8. & 6 \\
9. & 14 \\
10. & 10 \\
11. & 12 \\
12. & 15 \\
13. & 10 \\
14. & 12 \\
15. & 12 \\
\end{array}
}
$$