Determine if the following are in proportion.
15, 45, 40, 120

Answer

To determine if the numbers 15, 45, 40, and 120 are in proportion, we need to check if the ratio of the first pair (15 and 45) is equal to the ratio of the second pair (40 and 120).

### Step-by-Step Solution:

1. **Identify the Ratios**:
- The first ratio is \( \frac{15}{45} \).
- The second ratio is \( \frac{40}{120} \).

2. **Simplify the First Ratio**:
- To simplify \( \frac{15}{45} \), we can divide both the numerator and the denominator by 15.
- \( \frac{15 \div 15}{45 \div 15} = \frac{1}{3} \).

3. **Simplify the Second Ratio**:
- To simplify \( \frac{40}{120} \), we can divide both the numerator and the denominator by 40.
- \( \frac{40 \div 40}{120 \div 40} = \frac{1}{3} \).

4. **Compare the Ratios**:
- Now we compare the two simplified ratios: \( \frac{1}{3} \) and \( \frac{1}{3} \).
- Since both ratios are equal, we can conclude that the numbers are in proportion.

5. **Write the Proportion Statement**:
- We can express this as:
\[ 15 : 45 :: 40 : 120 \]
- This means that 15 is to 45 as 40 is to 120.

### Final Conclusion:
Yes, the numbers 15, 45, 40, and 120 are in proportion.

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