For each of the following, write throe fractions equal to the given fraction. \( \begin{array}{ll}\text { a. } \frac{1}{3} & \text { b. } \frac{6}{7} \\ \text { c. } \frac{-9}{10} & \text { d. } \frac{a}{8} \\ \frac{a}{8}=\frac{\square}{16} & \text { (Simplify your answer.) } \\ \text { Enter the correct numerator to match the new denominator. } \\ \frac{a}{8}=\frac{\square}{48} & \text { (Simplify your answer.) } \\ \text { Enter the correct numerator to match the new denominator. } \\ \frac{a}{8}=\frac{\square}{160} \text { (Simplify your answer.) }\end{array} \)

**a. Fractions equivalent to \( \frac{1}{3} \):** - Multiply numerator and denominator by 2: \( \frac{1}{3} = \frac{2}{6} \) - Multiply numerator and denominator by 3: \( \frac{1}{3} = \frac{3}{9} \) - Multiply numerator and denominator by 4: \( \frac{1}{3} = \frac{4}{12} \) **b. Fractions equivalent to \( \frac{6}{7} \):** - Multiply numerator and denominator by 2: \( \frac{6}{7} = \frac{12}{14} \) - Multiply numerator and denominator by 3: \( \frac{6}{7} = \frac{18}{21} \) - Multiply numerator and denominator by 4: \( \frac{6}{7} = \frac{24}{28} \) **c. Fractions equivalent to \( \frac{-9}{10} \):** - Multiply numerator and denominator by 2: \( \frac{-9}{10} = \frac{-18}{20} \) - Multiply numerator and denominator by 3: \( \frac{-9}{10} = \frac{-27}{30} \) - Multiply numerator and denominator by 4: \( \frac{-9}{10} = \frac{-36}{40} \) **d. Equivalent fractions for \( \frac{a}{8} \):** 1. To express \( \frac{a}{8} \) with a denominator of 16, multiply numerator and denominator by 2: \[ \frac{a}{8} = \frac{2a}{16} \] Thus, the correct numerator is \( 2a \). 2. To express \( \frac{a}{8} \) with a denominator of 48, multiply numerator and denominator by 6: \[ \frac{a}{8} = \frac{6a}{48} \] Thus, the correct numerator is \( 6a \). 3. To express \( \frac{a}{8} \) with a denominator of 160, multiply numerator and denominator by 20: \[ \frac{a}{8} = \frac{20a}{160} \] Thus, the correct numerator is \( 20a \).