Equivalent fractions worksheet featuring multiplication and division problems with fractions.

Let's solve each problem step by step. The worksheet is titled "Equivalent Fractions", but the problems involve multiplying and dividing fractions. We'll go through each one carefully.

---

🔹 Left Column: Multiplication of Fractions

#### 1. $\frac{2}{3} \times \frac{2}{2}$

- Multiply numerators: $2 \times 2 = 4$
- Multiply denominators: $3 \times 2 = 6$
- Result: $\frac{4}{6}$
- Simplify: $\frac{4}{6} = \frac{2}{3}$

✔ Answer: $\frac{2}{3}$

---

#### 2. $\frac{6}{7} \times \frac{3}{3}$

- $\frac{3}{3} = 1$, so multiplying by 1 doesn't change the value
- So, $\frac{6}{7} \times 1 = \frac{6}{7}$

✔ Answer: $\frac{6}{7}$

---

#### 3. $\frac{4}{9} \times \frac{5}{5}$

- $\frac{5}{5} = 1$, so result is just $\frac{4}{9}$

✔ Answer: $\frac{4}{9}$

---

#### 4. $\frac{3}{5} \times \frac{4}{4}$

- $\frac{4}{4} = 1$, so result is $\frac{3}{5}$

✔ Answer: $\frac{3}{5}$

---

#### 5. $\frac{6}{7} \times \frac{2}{2}$

- $\frac{2}{2} = 1$, so result is $\frac{6}{7}$

✔ Answer: $\frac{6}{7}$

---

🔹 Right Column: Division of Fractions

> Remember: To divide fractions, multiply by the reciprocal.

#### 6. $\frac{14}{22} \div \frac{2}{2}$

- $\frac{2}{2} = 1$, so dividing by 1 doesn’t change the value
- So, $\frac{14}{22} \div 1 = \frac{14}{22}$
- Simplify: $\frac{14}{22} = \frac{7}{11}$

✔ Answer: $\frac{7}{11}$

---

#### 7. $\frac{12}{20} \div \frac{4}{4}$

- $\frac{4}{4} = 1$, so $\frac{12}{20} \div 1 = \frac{12}{20}$
- Simplify: $\frac{12}{20} = \frac{3}{5}$

✔ Answer: $\frac{3}{5}$

---

#### 8. $\frac{21}{24} \div \frac{3}{3}$

- $\frac{3}{3} = 1$, so $\frac{21}{24} \div 1 = \frac{21}{24}$
- Simplify: $\frac{21}{24} = \frac{7}{8}$

✔ Answer: $\frac{7}{8}$

---

#### 9. $\frac{24}{36} \div \frac{6}{6}$

- $\frac{6}{6} = 1$, so $\frac{24}{36} \div 1 = \frac{24}{36}$
- Simplify: $\frac{24}{36} = \frac{2}{3}$

✔ Answer: $\frac{2}{3}$

---

#### 10. $\frac{15}{20} \div \frac{5}{5}$

- $\frac{5}{5} = 1$, so $\frac{15}{20} \div 1 = \frac{15}{20}$
- Simplify: $\frac{15}{20} = \frac{3}{4}$

✔ Answer: $\frac{3}{4}$

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| $\frac{2}{3} \times \frac{2}{2}$ | $\frac{2}{3}$ |
| $\frac{6}{7} \times \frac{3}{3}$ | $\frac{6}{7}$ |
| $\frac{4}{9} \times \frac{5}{5}$ | $\frac{4}{9}$ |
| $\frac{3}{5} \times \frac{4}{4}$ | $\frac{3}{5}$ |
| $\frac{6}{7} \times \frac{2}{2}$ | $\frac{6}{7}$ |
| $\frac{14}{22} \div \frac{2}{2}$ | $\frac{7}{11}$ |
| $\frac{12}{20} \div \frac{4}{4}$ | $\frac{3}{5}$ |
| $\frac{21}{24} \div \frac{3}{3}$ | $\frac{7}{8}$ |
| $\frac{24}{36} \div \frac{6}{6}$ | $\frac{2}{3}$ |
| $\frac{15}{20} \div \frac{5}{5}$ | $\frac{3}{4}$ |

---

🧠 Explanation:

- In all multiplication problems, we're multiplying by a fraction equal to 1 (like $\frac{2}{2}, \frac{3}{3}, \ldots$), which means the value doesn't change.
- In division problems, we're dividing by a fraction equal to 1, which also leaves the original fraction unchanged.
- Then we simplify the original fraction to its lowest terms.

So, in essence, these problems are testing understanding of equivalent fractions — that multiplying or dividing by 1 (in fraction form) keeps the value the same, but simplifying reveals the simplest equivalent form.

Let me know if you'd like this formatted as a printable answer sheet!