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

Question

Option 1: 7/8 = 20/22
Option 2: 7/8 = 21/24
Option __ is a proportion.

Answer 1

To determine which option is a proportion, we need to check if the two ratios on each side of the equation are equivalent.

Option 1: \[ \frac{7}{8} = \frac{20}{22} \] To check if these two fractions are equivalent, we cross-multiply: \[ 7 \times 22 \stackrel{?}{=} 8 \times 20 \] \[ 154 \stackrel{?}{=} 160 \] This is false, so Option 1 is not a proportion.

Option 2: \[ \frac{7}{8} = \frac{21}{24} \] We cross-multiply again: \[ 7 \times 24 \stackrel{?}{=} 8 \times 21 \] \[ 168 \stackrel{?}{=} 168 \] This is true, so Option 2 is a proportion.

Therefore, Option 2 is a proportion.