Handle “of”, division, and addition correctly: Evaluate 2 of 3/4 ÷ 3/4 + 1/4, treating “of” as multiplication and following left-to-right rules for multiply/divide.

Introduction / Context:
Many test-takers stumble on expressions with “of” and division. Remember that “of” indicates multiplication. Also, when only multiplication and division appear at the same precedence, evaluate strictly from left to right before doing the addition at the end.

Given Data / Assumptions:

• Expression: 2 of 3/4 ÷ 3/4 + 1/4.
• “of” means multiply; multiply/divide left to right.
• Return a simplified fraction.

Concept / Approach:
Compute the left product, then divide by 3/4, and finally add 1/4. Convert division by a fraction to multiplication by its reciprocal to simplify cancellations.

Step-by-Step Solution:
Compute product: 2 of 3/4 = 2 * 3/4 = 3/2.Divide by 3/4: (3/2) ÷ (3/4) = (3/2) * (4/3) = 2.Add 1/4: 2 + 1/4 = 9/4.

Verification / Alternative check:
Convert 2 to 8/4; 8/4 + 1/4 = 9/4, confirming consistency.

Why Other Options Are Wrong:
3/2 and 7/4 arise from stopping too early or misdividing; 5/2 and 8/3 result from mishandling the reciprocal during division.

Common Pitfalls:
Performing addition before completing multiply/divide; failing to invert 3/4 correctly during division; reducing incorrectly.

Final Answer:
9/4