Question

Which of the following, Option 1 or Option 2, is a proportion?
Option 1 : 7/8 = 20/22
Option 2: 7/8 = 21/24

Answer 1

To determine which option represents a proportion, we need to check if the fractions in each option are equivalent. A proportion states that two ratios (fractions) are equal.

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

We can simplify \( \frac{20}{22} \):
- The greatest common divisor (GCD) of 20 and 22 is 2.
- So, \( \frac{20}{22} = \frac{20 ÷ 2}{22 ÷ 2} = \frac{10}{11} \).

Now we compare \( \frac{7}{8} \) and \( \frac{10}{11} \):
- \( 7 \times 11 = 77 \)
- \( 8 \times 10 = 80 \)
- Since \( 77 \neq 80 \), \( \frac{7}{8} \) is not equal to \( \frac{10}{11} \), so Option 1 is not a proportion.

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

Let's simplify \( \frac{21}{24} \):
- The GCD of 21 and 24 is 3.
- So, \( \frac{21}{24} = \frac{21 ÷ 3}{24 ÷ 3} = \frac{7}{8} \).

Since \( \frac{7}{8} = \frac{7}{8} \), Option 2 is indeed a proportion.

In conclusion, **Option 2** is a proportion.