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.
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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.
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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.