Which of the following fractions, when added to 5/8, gives a total sum equal to 1?

Introduction / Context:
This question checks your understanding of fraction addition and complementary fractions that add up to 1. Many aptitude problems involve finding how much more is needed to complete a whole, a task, or a full unit. Here, you must find which fraction, when added to 5/8, results in exactly 1.

Given Data / Assumptions:

• Known fraction: 5/8.
• Target sum: 1.
• We must find a fraction from the options so that 5/8 plus that fraction equals 1.

Concept / Approach:
If a/b + c/d = 1, then c/d is the complement of a/b to 1. The easiest way is to compute 1 - 5/8 and then match this result to one of the options. To subtract fractions, we use a common denominator. We may also express each option with denominator 8 to see if it matches the required complement.

Step-by-Step Solution:
Step 1: Compute the complement of 5/8 to 1: 1 - 5/8. Step 2: Write 1 as 8/8 to have the same denominator: 1 = 8/8. Step 3: Now subtract: 8/8 - 5/8 = (8 - 5) / 8 = 3/8. Step 4: So the required fraction is 3/8. Step 5: Check options to see which one is equal to 3/8. Step 6: Option A is 6/16. Simplify 6/16 by dividing numerator and denominator by 2: 6/16 = 3/8. Step 7: Therefore, 6/16 is equivalent to 3/8 and is the correct choice.

Verification / Alternative Check:
Add 5/8 and 6/16 directly. First, simplify 6/16 to 3/8. Then compute 5/8 + 3/8 = (5 + 3)/8 = 8/8 = 1. This confirms that adding 6/16 to 5/8 indeed gives a total of 1.

Why Other Options Are Wrong:
5/2 is equal to 2.5, so 5/8 + 5/2 is much greater than 1.
6/24 simplifies to 1/4. Then 5/8 + 1/4 = 5/8 + 2/8 = 7/8, not 1.
6/3 is equal to 2, so 5/8 + 2 is greater than 2. Therefore none of these options give a sum of 1 when added to 5/8.

Common Pitfalls:
A common mistake is to mis-simplify fractions like 6/16 or 6/24. Always divide numerator and denominator by their greatest common divisor. Another error is to ignore simplification and compare fractions with different denominators directly, which is not reliable. Using a common denominator makes comparison and addition straightforward.

Final Answer:
The fraction that completes the sum to 1 is 6/16 (which is equal to 3/8).