This worksheet helps students master equivalent fractions through a mix of multiple-choice identification and creative writing exercises.

Problem Analysis:

The worksheet focuses on equivalent fractions. Equivalent fractions are fractions that represent the same value but are expressed with different numerators and denominators. To solve these problems, we need to simplify or scale the given fractions to match the options provided.

---

Part A: Choose the correct equivalent fraction in each problem

#### Question 1:
$$
\frac{2}{16} = ?
$$

- Simplify $\frac{2}{16}$ by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2:
$$
\frac{2 \div 2}{16 \div 2} = \frac{1}{8}
$$

- Check the options:
a) $\frac{1}{4}$
b) $\frac{1}{8}$
c) $\frac{4}{20}$
d) $\frac{3}{18}$

- The correct answer is b) $\frac{1}{8}$.

#### Question 2:
$$
\frac{1}{3} = ?
$$

- The fraction $\frac{1}{3}$ is already in its simplest form. We need to find an equivalent fraction by multiplying both the numerator and denominator by the same number.

- Check the options:
a) $\frac{3}{15}$ (simplify: $\frac{3 \div 3}{15 \div 3} = \frac{1}{5}$)
b) $\frac{2}{14}$ (simplify: $\frac{2 \div 2}{14 \div 2} = \frac{1}{7}$)
c) $\frac{8}{24}$ (simplify: $\frac{8 \div 8}{24 \div 8} = \frac{1}{3}$)
d) $\frac{5}{10}$ (simplify: $\frac{5 \div 5}{10 \div 5} = \frac{1}{2}$)

- The correct answer is c) $\frac{8}{24}$.

#### Question 3:
$$
\frac{25}{10} = ?
$$

- Simplify $\frac{25}{10}$ by dividing both the numerator and denominator by their GCD, which is 5:
$$
\frac{25 \div 5}{10 \div 5} = \frac{5}{2}
$$

- Check the options:
a) $\frac{5}{2}$
b) $\frac{10}{16}$ (simplify: $\frac{10 \div 2}{16 \div 2} = \frac{5}{8}$)
c) $\frac{1}{5}$
d) $\frac{30}{20}$ (simplify: $\frac{30 \div 10}{20 \div 10} = \frac{3}{2}$)

- The correct answer is a) $\frac{5}{2}$.

#### Question 4:
$$
\frac{4}{12} = ?
$$

- Simplify $\frac{4}{12}$ by dividing both the numerator and denominator by their GCD, which is 4:
$$
\frac{4 \div 4}{12 \div 4} = \frac{1}{3}
$$

- Check the options:
a) $\frac{14}{6}$ (simplify: $\frac{14 \div 2}{6 \div 2} = \frac{7}{3}$)
b) $\frac{3}{18}$ (simplify: $\frac{3 \div 3}{18 \div 3} = \frac{1}{6}$)
c) $\frac{1}{2}$
d) $\frac{6}{18}$ (simplify: $\frac{6 \div 6}{18 \div 6} = \frac{1}{3}$)

- The correct answer is d) $\frac{6}{18}$.

#### Question 5:
$$
\frac{36}{45} = ?
$$

- Simplify $\frac{36}{45}$ by dividing both the numerator and denominator by their GCD, which is 9:
$$
\frac{36 \div 9}{45 \div 9} = \frac{4}{5}
$$

- Check the options:
a) $\frac{9}{5}$
b) $\frac{4}{5}$
c) $\frac{15}{25}$ (simplify: $\frac{15 \div 5}{25 \div 5} = \frac{3}{5}$)
d) $\frac{2}{18}$ (simplify: $\frac{2 \div 2}{18 \div 2} = \frac{1}{9}$)

- The correct answer is b) $\frac{4}{5}$.

#### Question 6:
$$
\frac{3}{18} = ?
$$

- Simplify $\frac{3}{18}$ by dividing both the numerator and denominator by their GCD, which is 3:
$$
\frac{3 \div 3}{18 \div 3} = \frac{1}{6}
$$

- Check the options:
a) $\frac{5}{30}$ (simplify: $\frac{5 \div 5}{30 \div 5} = \frac{1}{6}$)
b) $\frac{1}{9}$
c) $\frac{4}{16}$ (simplify: $\frac{4 \div 4}{16 \div 4} = \frac{1}{4}$)
d) $\frac{1}{2}$

- The correct answer is a) $\frac{5}{30}$.

---

Part B: Write any 3 equivalent fractions

#### Question 1:
$$
\frac{7}{4} = ?
$$

- To find equivalent fractions, multiply both the numerator and denominator by the same number:
- Multiply by 2: $\frac{7 \times 2}{4 \times 2} = \frac{14}{8}$
- Multiply by 3: $\frac{7 \times 3}{4 \times 3} = \frac{21}{12}$
- Multiply by 4: $\frac{7 \times 4}{4 \times 4} = \frac{28}{16}$

- Answers: $\frac{14}{8}, \frac{21}{12}, \frac{28}{16}$

#### Question 2:
$$
\frac{1}{6} = ?
$$

- To find equivalent fractions:
- Multiply by 2: $\frac{1 \times 2}{6 \times 2} = \frac{2}{12}$
- Multiply by 3: $\frac{1 \times 3}{6 \times 3} = \frac{3}{18}$
- Multiply by 4: $\frac{1 \times 4}{6 \times 4} = \frac{4}{24}$

- Answers: $\frac{2}{12}, \frac{3}{18}, \frac{4}{24}$

#### Question 3:
$$
\frac{2}{5} = ?
$$

- To find equivalent fractions:
- Multiply by 2: $\frac{2 \times 2}{5 \times 2} = \frac{4}{10}$
- Multiply by 3: $\frac{2 \times 3}{5 \times 3} = \frac{6}{15}$
- Multiply by 4: $\frac{2 \times 4}{5 \times 4} = \frac{8}{20}$

- Answers: $\frac{4}{10}, \frac{6}{15}, \frac{8}{20}$

---

Final Answers:

#### Part A:
1. b) $\frac{1}{8}$
2. c) $\frac{8}{24}$
3. a) $\frac{5}{2}$
4. d) $\frac{6}{18}$
5. b) $\frac{4}{5}$
6. a) $\frac{5}{30}$

#### Part B:
1. $\frac{14}{8}, \frac{21}{12}, \frac{28}{16}$
2. $\frac{2}{12}, \frac{3}{18}, \frac{4}{24}$
3. $\frac{4}{10}, \frac{6}{15}, \frac{8}{20}$

Boxed Final Answer:
$$
\boxed{
\text{Part A: b, c, a, d, b, a; Part B: } \frac{14}{8}, \frac{21}{12}, \frac{28}{16}; \frac{2}{12}, \frac{3}{18}, \frac{4}{24}; \frac{4}{10}, \frac{6}{15}, \frac{8}{20}
}
$$