The Best Free 7th Grade Math Resources: Complete List! — Mashup Math - Free Printable

Problem: Solving Equivalent Fractions

The task involves solving multiplication and division problems with fractions. Let's solve each problem step by step.

---

#### 1. Multiplication Problems

Problem 1:
$$
\frac{2}{3} \times \frac{2}{2}
$$

- Simplify the second fraction: $\frac{2}{2} = 1$.
- Multiply:
$$
\frac{2}{3} \times 1 = \frac{2}{3}
$$

Answer:
$$
\boxed{\frac{2}{3}}
$$

---

Problem 2:
$$
\frac{6}{7} \times \frac{3}{3}
$$

- Simplify the second fraction: $\frac{3}{3} = 1$.
- Multiply:
$$
\frac{6}{7} \times 1 = \frac{6}{7}
$$

Answer:
$$
\boxed{\frac{6}{7}}
$$

---

Problem 3:
$$
\frac{4}{9} \times \frac{5}{5}
$$

- Simplify the second fraction: $\frac{5}{5} = 1$.
- Multiply:
$$
\frac{4}{9} \times 1 = \frac{4}{9}
$$

Answer:
$$
\boxed{\frac{4}{9}}
$$

---

Problem 4:
$$
\frac{3}{5} \times \frac{4}{4}
$$

- Simplify the second fraction: $\frac{4}{4} = 1$.
- Multiply:
$$
\frac{3}{5} \times 1 = \frac{3}{5}
$$

Answer:
$$
\boxed{\frac{3}{5}}
$$

---

Problem 5:
$$
\frac{6}{7} \times \frac{2}{2}
$$

- Simplify the second fraction: $\frac{2}{2} = 1$.
- Multiply:
$$
\frac{6}{7} \times 1 = \frac{6}{7}
$$

Answer:
$$
\boxed{\frac{6}{7}}
$$

---

#### 2. Division Problems

Problem 6:
$$
\frac{14}{22} \div \frac{2}{2}
$$

- Simplify the second fraction: $\frac{2}{2} = 1$.
- Dividing by 1 leaves the fraction unchanged:
$$
\frac{14}{22}
$$
- Simplify $\frac{14}{22}$ by dividing both numerator and denominator by their greatest common divisor (GCD), which is 2:
$$
\frac{14 \div 2}{22 \div 2} = \frac{7}{11}
$$

Answer:
$$
\boxed{\frac{7}{11}}
$$

---

Problem 7:
$$
\frac{12}{20} \div \frac{4}{4}
$$

- Simplify the second fraction: $\frac{4}{4} = 1$.
- Dividing by 1 leaves the fraction unchanged:
$$
\frac{12}{20}
$$
- Simplify $\frac{12}{20}$ by dividing both numerator and denominator by their GCD, which is 4:
$$
\frac{12 \div 4}{20 \div 4} = \frac{3}{5}
$$

Answer:
$$
\boxed{\frac{3}{5}}
$$

---

Problem 8:
$$
\frac{21}{24} \div \frac{3}{3}
$$

- Simplify the second fraction: $\frac{3}{3} = 1$.
- Dividing by 1 leaves the fraction unchanged:
$$
\frac{21}{24}
$$
- Simplify $\frac{21}{24}$ by dividing both numerator and denominator by their GCD, which is 3:
$$
\frac{21 \div 3}{24 \div 3} = \frac{7}{8}
$$

Answer:
$$
\boxed{\frac{7}{8}}
$$

---

Problem 9:
$$
\frac{24}{36} \div \frac{6}{6}
$$

- Simplify the second fraction: $\frac{6}{6} = 1$.
- Dividing by 1 leaves the fraction unchanged:
$$
\frac{24}{36}
$$
- Simplify $\frac{24}{36}$ by dividing both numerator and denominator by their GCD, which is 12:
$$
\frac{24 \div 12}{36 \div 12} = \frac{2}{3}
$$

Answer:
$$
\boxed{\frac{2}{3}}
$$

---

Problem 10:
$$
\frac{15}{20} \div \frac{5}{5}
$$

- Simplify the second fraction: $\frac{5}{5} = 1$.
- Dividing by 1 leaves the fraction unchanged:
$$
\frac{15}{20}
$$
- Simplify $\frac{15}{20}$ by dividing both numerator and denominator by their GCD, which is 5:
$$
\frac{15 \div 5}{20 \div 5} = \frac{3}{4}
$$

Answer:
$$
\boxed{\frac{3}{4}}
$$

---

Final Answers:

1. $\frac{2}{3}$
2. $\frac{6}{7}$
3. $\frac{4}{9}$
4. $\frac{3}{5}$
5. $\frac{6}{7}$
6. $\frac{7}{11}$
7. $\frac{3}{5}$
8. $\frac{7}{8}$
9. $\frac{2}{3}$
10. $\frac{3}{4}$

$$
\boxed{\frac{2}{3}, \frac{6}{7}, \frac{4}{9}, \frac{3}{5}, \frac{6}{7}, \frac{7}{11}, \frac{3}{5}, \frac{7}{8}, \frac{2}{3}, \frac{3}{4}}
$$