Which best describes the error in finding the percent increase from 18 to 26?
A. The denominator should be 18, which is the original amount.
B. The numerator should be 18, which is the original amount.
C. The numerator should be 26, which is the new amount.
D. The denominator should be 18, which is the new amount.
E. The expression was simplified incorrectly.
Correct the error. Round your answer to the nearest whole number. The percent increase from 18 to 26 is about _%.
The Correct Answer and Explanation is:
To calculate the percent increase from 18 to 26, we follow these steps:
- Identify the original amount and the new amount:
- Original amount (initial value): 18
- New amount (final value): 26
- Calculate the increase:
- Increase = New amount – Original amount
- Increase = 26 – 18 = 8
- Determine the percent increase:
- Percent Increase = (Increase / Original amount) × 100
- Percent Increase = (8 / 18) × 100
Now, to simplify the calculation:
- Perform the division:
- (8 / 18) = 0.4444 (approximately)
- Multiply by 100 to get the percentage:
- Percent Increase = 0.4444 × 100 = 44.44%
- Round to the nearest whole number:
- Percent Increase = 44%
Analysis of Errors
The answer choice that best describes the error in finding the percent increase from 18 to 26 is A: “The denominator should be 18, which is the original amount.”
Explanation:
In calculating percent change, it is crucial to use the original amount as the denominator because percent change is defined in relation to the original value. Using the original amount (18) in the denominator ensures that the calculation accurately reflects how much the value has increased relative to where it started.
If one were to mistakenly use the new amount (26) as the denominator, the calculation would be incorrect because it would suggest that the increase is being evaluated against the new total, which skews the true percentage of growth from the original value. For example, if 26 were used as the denominator, the calculation would be:
[
\text{Percent Increase} = \left( \frac{8}{26} \right) \times 100 \approx 30.77\%
]
This is not the correct representation of the growth from the original value. Therefore, correctly identifying the original value as the base for the percent increase is essential for accurate financial analysis and reporting. Thus, the correct answer for the percent increase from 18 to 26 is about 44%.