Question

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

Option 1: 5/6=15/18


Option 2: 5/6=20/18


(1 point)

Answer 1

To determine which option is a proportion, we need to check if the two fractions are equivalent. A proportion states that two ratios are equal.

**Option 1:**
\( \frac{5}{6} = \frac{15}{18} \)

To check if these fractions are equal, we can simplify \( \frac{15}{18} \):
- The greatest common divisor of 15 and 18 is 3.
- \( \frac{15 \div 3}{18 \div 3} = \frac{5}{6} \)

Thus, \( \frac{5}{6} = \frac{15}{18} \) is true.

**Option 2:**
\( \frac{5}{6} = \frac{20}{18} \)

To check if these fractions are equal, we can simplify \( \frac{20}{18} \):
- The greatest common divisor of 20 and 18 is 2.
- \( \frac{20 \div 2}{18 \div 2} = \frac{10}{9} \)

Thus, \( \frac{5}{6} \neq \frac{20}{18} \).

**Conclusion:**
Option 1 is a proportion because \( \frac{5}{6} = \frac{15}{18} \). Option 2 is not a proportion because \( \frac{5}{6} \) does not equal \( \frac{20}{18} \).

Therefore, the answer is **Option 1**.