4-65. (from Lesson 4.1 .11 complete parts (a) through (c). a. Write two fractions that are equivalent to \( \frac{1}{2} \). b. Write two fractions that are equivalent to \( \frac{3}{5} \). c. Write two fractions that are equivalent to \( \frac{4}{7} \).

Sure, let's work through each part step by step to find equivalent fractions. Equivalent fractions are different fractions that represent the same value. To find equivalent fractions, you can multiply or divide both the numerator (the top number) and the denominator (the bottom number) by the same non-zero number. ### Part (a): Equivalent Fractions to \( \frac{1}{2} \) **Method:** Multiply both the numerator and the denominator by the same number. 1. **Multiply by 2:** \[ \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \] 2. **Multiply by 3:** \[ \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \] **Equivalent Fractions:** \[ \frac{2}{4} \quad \text{and} \quad \frac{3}{6} \] ### Part (b): Equivalent Fractions to \( \frac{3}{5} \) **Method:** Multiply both the numerator and the denominator by the same number. 1. **Multiply by 2:** \[ \frac{3 \times 2}{5 \times 2} = \frac{6}{10} \] 2. **Multiply by 3:** \[ \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \] **Equivalent Fractions:** \[ \frac{6}{10} \quad \text{and} \quad \frac{9}{15} \] ### Part (c): Equivalent Fractions to \( \frac{4}{7} \) **Method:** Multiply both the numerator and the denominator by the same number. 1. **Multiply by 2:** \[ \frac{4 \times 2}{7 \times 2} = \frac{8}{14} \] 2. **Multiply by 3:** \[ \frac{4 \times 3}{7 \times 3} = \frac{12}{21} \] **Equivalent Fractions:** \[ \frac{8}{14} \quad \text{and} \quad \frac{12}{21} \] ### Summary - **(a)** \( \frac{2}{4} \) and \( \frac{3}{6} \) - **(b)** \( \frac{6}{10} \) and \( \frac{9}{15} \) - **(c)** \( \frac{8}{14} \) and \( \frac{12}{21} \) All these fractions are equivalent to their respective original fractions.