Sharing a Chocolate — Fractional Distribution to Friends A chocolate bar has 12 equal pieces. Manju gives 1/4 of it to Anju, 1/3 of it to Raj, and 1/6 of it to Fiza. How many pieces remain with Manju afterward?

Introduction / Context:
This problem applies fraction addition to a concrete sharing scenario. You translate fractional portions of a whole into actual piece counts, ensuring the fractions sum correctly before subtracting from the total pieces.

Given Data / Assumptions:

• Total pieces = 12.
• Given to Anju: 1/4 of the bar.
• Given to Raj: 1/3 of the bar.
• Given to Fiza: 1/6 of the bar.

Concept / Approach:
Compute the total fraction given away by adding 1/4 + 1/3 + 1/6. Use the common denominator 12. Multiply the resulting fraction by 12 to find the number of pieces given. Subtract from 12 to get the remainder with Manju.

Step-by-Step Solution:
Common denominator 12: 1/4 = 3/12; 1/3 = 4/12; 1/6 = 2/12.Sum of given fractions: 3/12 + 4/12 + 2/12 = 9/12 = 3/4.Pieces given: (3/4)*12 = 9 pieces.Pieces remaining: 12 − 9 = 3 pieces.

Verification / Alternative check:
Compute piece counts separately: 1/4 of 12 = 3; 1/3 of 12 = 4; 1/6 of 12 = 2; total given = 3 + 4 + 2 = 9; remaining = 3.

Why Other Options Are Wrong:
1, 2, 4, and 5 are not consistent with the total given pieces equaling 9.

Common Pitfalls:
Adding denominators directly; failing to convert all fractions to the same denominator; arithmetic slips when converting fractions to piece counts.

Final Answer:
3