Math worksheets • Teacha! - Free Printable

Problem: Solving the given equivalent fractions problems

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

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#### 1. Multiplication Problems

Problem 1:
\[
\frac{2}{3} \times \frac{2}{2}
\]

- Simplify \(\frac{2}{2}\) to \(1\).
- Multiply:
\[
\frac{2}{3} \times 1 = \frac{2}{3}
\]

Answer: \(\frac{2}{3}\)

---

Problem 2:
\[
\frac{6}{7} \times \frac{3}{3}
\]

- Simplify \(\frac{3}{3}\) to \(1\).
- Multiply:
\[
\frac{6}{7} \times 1 = \frac{6}{7}
\]

Answer: \(\frac{6}{7}\)

---

Problem 3:
\[
\frac{4}{9} \times \frac{5}{5}
\]

- Simplify \(\frac{5}{5}\) to \(1\).
- Multiply:
\[
\frac{4}{9} \times 1 = \frac{4}{9}
\]

Answer: \(\frac{4}{9}\)

---

Problem 4:
\[
\frac{3}{5} \times \frac{4}{4}
\]

- Simplify \(\frac{4}{4}\) to \(1\).
- Multiply:
\[
\frac{3}{5} \times 1 = \frac{3}{5}
\]

Answer: \(\frac{3}{5}\)

---

Problem 5:
\[
\frac{6}{7} \times \frac{2}{2}
\]

- Simplify \(\frac{2}{2}\) to \(1\).
- Multiply:
\[
\frac{6}{7} \times 1 = \frac{6}{7}
\]

Answer: \(\frac{6}{7}\)

---

#### 2. Division Problems

Problem 6:
\[
\frac{14}{22} \div \frac{2}{2}
\]

- Simplify \(\frac{2}{2}\) to \(1\).
- 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: \(\frac{7}{11}\)

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Problem 7:
\[
\frac{12}{20} \div \frac{4}{4}
\]

- Simplify \(\frac{4}{4}\) to \(1\).
- 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: \(\frac{3}{5}\)

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Problem 8:
\[
\frac{21}{24} \div \frac{3}{3}
\]

- Simplify \(\frac{3}{3}\) to \(1\).
- 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: \(\frac{7}{8}\)

---

Problem 9:
\[
\frac{24}{36} \div \frac{6}{6}
\]

- Simplify \(\frac{6}{6}\) to \(1\).
- 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: \(\frac{2}{3}\)

---

Problem 10:
\[
\frac{15}{20} \div \frac{5}{5}
\]

- Simplify \(\frac{5}{5}\) to \(1\).
- 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: \(\frac{3}{4}\)

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Final Answers:

\[
\boxed{
\begin{array}{cc}
\frac{2}{3} & \frac{7}{11} \\
\frac{6}{7} & \frac{3}{5} \\
\frac{4}{9} & \frac{7}{8} \\
\frac{3}{5} & \frac{2}{3} \\
\frac{6}{7} & \frac{3}{4}
\end{array}
}
\]