Sharing an Estate — Sum of Fractions Given Away A man gives 1/4 of his property to his daughter, 1/2 to his sons, and 1/5 to charity. What fraction of his property has he given away in total?

Introduction / Context:This problem evaluates fluency with adding fractions that have different denominators. The setup mimics practical distributions (family and charity), making it a good test of fraction arithmetic in everyday contexts.

Given Data / Assumptions:

• Daughter's share: 1/4 of the property.
• Sons' share: 1/2 of the property.
• Charity: 1/5 of the property.
• Goal: total fraction given away.

Concept / Approach:Add the fractions using a common denominator. The least common multiple of 4, 2, and 5 is 20. Convert each fraction to twentieths and sum. The result can be simplified if needed, but here it will already be in simplest terms.

Step-by-Step Solution:Convert to twentieths: 1/4 = 5/20; 1/2 = 10/20; 1/5 = 4/20.Add: 5/20 + 10/20 + 4/20 = 19/20.Therefore, 19/20 of the property has been given away.Remaining portion = 1 − 19/20 = 1/20 (for completeness).

Verification / Alternative check:Use decimal equivalents: 0.25 + 0.5 + 0.2 = 0.95 = 19/20. This matches the fraction sum.

Why Other Options Are Wrong:1/20 is the remainder, not the given amount; 1/10 and 9/10 miscompute the sum; 17/20 omits part of a share.

Common Pitfalls:Adding numerators and denominators directly (invalid); forgetting to use a common denominator; mixing up “given away” with “leftover.”

Final Answer:19/20