Which of the following, Option 1 or Option 2, is a proportion?

Option 1: 7/8=20/22


Option 2: 7/8=21/24


(1 point)
Option (blank) is a proportion.

1 answer

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.