Tell whether the ratios form a proportion. Explain your answer. \( \begin{array}{ll}\text { 7. } \frac{56}{20}, \frac{24}{10} & 8 . \frac{5}{8}, \frac{42.5}{68}\end{array} \)

To determine whether the given pairs of ratios form a proportion, we need to check if the two ratios in each pair are equivalent. Two ratios \( \frac{a}{b} \) and \( \frac{c}{d} \) form a proportion if \( a \times d = b \times c \) or if they simplify to the same value. Let's analyze each pair: --- ### **Problem 7** **Ratios:** \( \frac{56}{20} \) and \( \frac{24}{10} \) **Simplification:** 1. **Simplify each ratio:** - \( \frac{56}{20} = \frac{56 \div 4}{20 \div 4} = \frac{14}{5} = 2.8 \) - \( \frac{24}{10} = \frac{24 \div 2}{10 \div 2} = \frac{12}{5} = 2.4 \) 2. **Compare the simplified values:** - \( 2.8 \) vs. \( 2.4 \) → **Not equal** 3. **Alternatively, cross-multiply to verify:** - \( 56 \times 10 = 560 \) - \( 20 \times 24 = 480 \) - Since \( 560 \neq 480 \), the ratios are **not equivalent**. **Conclusion:** The ratios \( \frac{56}{20} \) and \( \frac{24}{10} \) **do not form a proportion** because they are not equivalent. --- ### **Problem 8** **Ratios:** \( \frac{5}{8} \) and \( \frac{42.5}{68} \) **Simplification:** 1. **Simplify each ratio:** - \( \frac{5}{8} = 0.625 \) - \( \frac{42.5}{68} \) 2. **Simplify \( \frac{42.5}{68} \):** - Recognize that \( 42.5 = 5 \times 8.5 \) and \( 68 = 8 \times 8.5 \) - So, \( \frac{42.5}{68} = \frac{5 \times 8.5}{8 \times 8.5} = \frac{5}{8} = 0.625 \) 3. **Compare the simplified values:** - \( 0.625 \) vs. \( 0.625 \) → **Equal** 4. **Alternatively, cross-multiply to verify:** - \( 5 \times 68 = 340 \) - \( 8 \times 42.5 = 340 \) - Since \( 340 = 340 \), the ratios are **equivalent**. **Conclusion:** The ratios \( \frac{5}{8} \) and \( \frac{42.5}{68} \) **form a proportion** because they are equivalent. --- **Summary:** - **Problem 7:** The ratios do **not** form a proportion. - **Problem 8:** The ratios **do** form a proportion.