Fill the missing fraction to complete the sum: 3 1/4 + 4 1/6 + ? + 1/4 = 10. Determine the exact value of the missing term as a simplified fraction.

Introduction / Context:This completion problem checks comfort with mixed numbers, conversion to improper fractions, and solving a simple linear equation in one unknown fraction. Accuracy with common denominators ensures the missing term is identified exactly.

Given Data / Assumptions:

• Total required: 10.
• Known terms: 3 1/4, 4 1/6, and 1/4.
• Unknown term represented by ?.

Concept / Approach:Convert mixed numbers to improper fractions, combine known fractions, and subtract from 10 to isolate the missing fraction. Keep exact fractional arithmetic (avoid decimals) to reach a simplified result.

Step-by-Step Solution:Convert 3 1/4 = 13/4.Convert 4 1/6 = 25/6.Add known parts: 13/4 + 1/4 = 14/4 = 7/2.Now 7/2 + 25/6 = (21/6 + 25/6) = 46/6 = 23/3.We need total 10 = 30/3, so ? = 30/3 − 23/3 = 7/3.

Verification / Alternative check:Convert 7/3 to 2 1/3; adding to 3 1/4 + 4 1/6 + 1/4 indeed reaches 10 when recomputed carefully with common denominators.

Why Other Options Are Wrong:21/6 = 7/2 is too large; 41/3 and 11/3 overshoot or undershoot the needed difference; 21/3 = 7 is far from the fractional gap remaining.

Common Pitfalls:Mistreating mixed numbers; adding 1/4 incorrectly; switching to decimal approximations and rounding off, which can mask the exact value.

Final Answer:7/3