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 answer

To determine which of the two options is a proportion, we need to check if the cross products are equal for each option.

A proportion states that two ratios are equal, meaning that if we have the ratio \( \frac{a}{b} = \frac{c}{d} \), then the cross products \( a \cdot d \) should equal \( b \cdot c \).

Let's evaluate both options:

Option 1: \( \frac{7}{8} = \frac{20}{22} \)

Cross products:

  • \( 7 \times 22 = 154 \)
  • \( 8 \times 20 = 160 \)

Since \( 154 \neq 160 \), Option 1 is not a proportion.

Option 2: \( \frac{7}{8} = \frac{21}{24} \)

Cross products:

  • \( 7 \times 24 = 168 \)
  • \( 8 \times 21 = 168 \)

Since \( 168 = 168 \), Option 2 is a proportion.

So, the answer is: Option 2 is a proportion.