A proportion is an equation that states that two ratios are equal. To determine which of the given options is a proportion, we can simplify each ratio and check if they are equal.
Option 1: \[ \frac{7}{8} \quad \text{and} \quad \frac{20}{22} \] First, simplify \(\frac{20}{22}\): \[ \frac{20}{22} = \frac{10}{11} \quad (\text{dividing both numerator and denominator by 2}) \] Now compare \(\frac{7}{8}\) and \(\frac{10}{11}\). Since \(7 \times 11 \neq 8 \times 10\), this means: \[ 7 \times 11 = 77 \quad \text{and} \quad 8 \times 10 = 80 \] So, \(77 \neq 80\). Thus, \(\frac{7}{8} \neq \frac{20}{22}\).
Option 2: \[ \frac{7}{8} \quad \text{and} \quad \frac{21}{24} \] Now simplify \(\frac{21}{24}\): \[ \frac{21}{24} = \frac{7}{8} \quad (\text{dividing both numerator and denominator by 3}) \] Since both sides are equal, \(\frac{7}{8} = \frac{21}{24}\) holds true.
Thus, Option 2 is a proportion.
So you can write: Option 2 is a proportion.