Which of the following fractions must be added to 5/8 to obtain a total of 1?

Introduction / Context:
This question tests simple fraction addition and understanding of equivalent fractions. You are asked to find which fraction, when added to 5/8, gives a total of 1.

Given Data / Assumptions:

• Known fraction: 5/8.
• Target sum: 1.
• Options: 6/16, 5/2, 6/24 and 6/3.

Concept / Approach:
If a/b + c/b = 1, then c/b = 1 - a/b. Here we first find the difference 1 - 5/8, then check which option is an equivalent fraction to that difference. Alternatively, we can convert each option to an equivalent fraction with denominator 8 and test directly.

Step-by-Step Solution:

Verification / Alternative check:
We can convert each option to decimal form. 5/8 is 0.625. We need 0.375 more. 6/16 simplifies to 0.375, whereas 5/2 is 2.5, 6/24 equals 0.25 and 6/3 equals 2. None of these other options add to 0.375.

Why Other Options Are Wrong:
5/2 and 6/3 are both greater than 1, so adding them to 5/8 would produce a number larger than 1. 6/24 simplifies to 1/4, which is 0.25, and 0.625 + 0.25 = 0.875, not 1.

Common Pitfalls:
Some students do not simplify fractions and may incorrectly think 6/16 and 6/24 have the same value. Others may try to add without bringing fractions to a common denominator, leading to incorrect sums.

Final Answer:
The fraction that must be added to 5/8 to make 1 is 6/16, which is equivalent to 3/8.