A person distributes property as follows: one-fourth to the daughter, one-half to the sons, and one-fifth to charity. What fraction of the property has been given away in total?

Introduction / Context:
This is a fraction addition problem with different denominators. It tests the ability to find a common denominator, sum the parts, and interpret the result as the total fraction distributed. Such distribution problems appear routinely in aptitude and arithmetic reasoning tests.

Given Data / Assumptions:

• Fractions to sum: 1/4, 1/2, and 1/5.
• Each fraction represents a portion of the whole property.
• We assume the whole is 1.

Concept / Approach:
Find the least common denominator (LCD) of 4, 2, and 5, which is 20. Convert each fraction to twentieths and add the numerators. The resulting fraction is the total given away. The remaining part, if needed, would be 1 minus this sum.

Step-by-Step Solution:

Verification / Alternative check:
Compute the remainder: 1 − 19/20 = 1/20. This means 1/20 is left, which is consistent and less than the whole.

Why Other Options Are Wrong:
1/20 represents the remainder, not the given total. 9/10 and 17/20 undercount the distribution. 1/10 is much too small and reflects an arithmetic error.

Common Pitfalls:
Using 10 instead of 20 as the LCD, forgetting to convert 1/5 properly, or adding denominators directly which is incorrect.

Final Answer:
19/20