A boy is asked to subtract the sum of 1/4 and 1/5 from unity and express the answer in decimals. He gives the answer as 0.45. What is the percentage error in his answer?

Introduction / Context:
This question tests your ability to work with fractions, decimals, and percentage error. The student is supposed to subtract the sum of two fractions from 1 and convert the result into decimal form, but he mistakenly reports the intermediate sum instead. You must compute the correct value and then determine the error relative to that value.

Given Data / Assumptions:
- Required computation: 1 - (1/4 + 1/5).
- Boy's answer in decimal form: 0.45.
- We must find the correct value of the expression.
- Then we must calculate percentage error = (Absolute error / True value) * 100 percent.

Concept / Approach:
First add the fractions 1/4 and 1/5 by finding a common denominator, then subtract this sum from unity (1). Then convert the result into decimals. The boy's answer is compared with the correct answer to find the absolute difference. Finally, the percentage error is calculated by dividing the absolute error by the true value and multiplying by 100.

Step-by-Step Solution:
Step 1: Compute the sum 1/4 + 1/5.Step 2: Common denominator of 4 and 5 is 20, so 1/4 = 5/20 and 1/5 = 4/20.Step 3: Sum = 5/20 + 4/20 = 9/20.Step 4: Required expression is 1 - 9/20.Step 5: Write 1 as 20/20, so 1 - 9/20 = 20/20 - 9/20 = 11/20.Step 6: Convert 11/20 to decimal: 11 divided by 20 = 0.55.Step 7: True value of the expression is 0.55, while the boy's answer is 0.45.Step 8: Absolute error = |0.55 - 0.45| = 0.10.Step 9: Percentage error = (0.10 / 0.55) * 100 percent.Step 10: 0.10 / 0.55 = 10 / 55 = 2 / 11.Step 11: So percentage error = (2 / 11) * 100 percent = 200 / 11 percent.

Verification / Alternative check:
To confirm, approximate 200 / 11 percent as a decimal: 200 / 11 is about 18.18 percent. This is a reasonable size for an error of 0.10 when the true value is 0.55, because 10 is roughly 18 percent of 55. The approximate mental estimation matches our exact calculation, which increases confidence in the result.

Why Other Options Are Wrong:
- (100/11) percent, about 9.09 percent, would correspond to an error of about 0.05 on a true value of 0.55, not 0.10.
- 50 percent is far too large and would imply an error equal to half the true value.
- 10 percent would correspond to 0.055 error, which is much smaller than the actual 0.10 difference.

Common Pitfalls:
Many students forget that percentage error is based on the true value, not on the wrong value. Others mis-handle the fraction addition or accidentally subtract 1/4 - 1/5 instead of adding them. It is also easy to confuse 0.45 and 0.55 when converting fractions to decimals. Working methodically and checking the arithmetic helps avoid these mistakes.

Final Answer:
The percentage error in the boy's answer is 200 / 11 percent.