Make the sum an integer: Add 1 3/4, 2 1/2, 5 7/12, 3 1/3, and 2 1/4. What is the smallest fraction that must be subtracted from this sum to make the final result a whole number?

Introduction / Context:
Questions of this type focus on fractional parts. To convert a total to the next lower whole number, we only need to subtract the fractional part of the sum. Efficient handling of common denominators speeds up the process.

Given Data / Assumptions:

• Numbers: 1 3/4, 2 1/2, 5 7/12, 3 1/3, 2 1/4.
• We seek the smallest fraction to subtract so the total becomes an integer.

Concept / Approach:
Extract and add only the fractional parts; the whole-number parts do not affect the needed subtraction. The fractional sum modulo 1 is the minimum fraction to remove to land exactly on an integer.

Step-by-Step Solution:
Fractional parts: 3/4, 1/2, 7/12, 1/3, 1/4.Use denominator 12: 3/4 = 9/12; 1/2 = 6/12; 7/12 = 7/12; 1/3 = 4/12; 1/4 = 3/12.Sum = (9 + 6 + 7 + 4 + 3)/12 = 29/12 = 2 + 5/12.The fractional part is 5/12, so subtracting 5/12 makes the total an integer.

Verification / Alternative check:
Any full computation of the entire mixed-number sum will have a fractional part of 5/12. Removing exactly that amount yields a whole number.

Why Other Options Are Wrong:
7/12 and 1/2 overshoot the fractional remainder; 7 is not a fraction and changes the integer part; 1/12 is too small and leaves a fractional residue.

Common Pitfalls:
Adding whole and fractional parts together and then trying to reduce; picking the complement-to-1 (7/12) instead of the actual fractional part.

Final Answer:
5/12