From a rope 30 m long, a person cuts as many equal pieces as possible, each being 3 1/4 m in length. What fraction of the original rope remains uncut?

Introduction / Context:
This question involves division with mixed numbers to determine how many full pieces can be cut and what leftover fraction remains. It checks careful handling of mixed fractions and remainders relative to the original total length.

Given Data / Assumptions:

• Total length = 30 m.
• Piece length = 3 1/4 m = 3.25 m.
• Cut as many full pieces as possible; leftover is less than one full piece.

Concept / Approach:
Compute the integer part of 30 / 3.25 to get the number of pieces. Then compute the leftover length and divide by the total length to get the remaining fraction.

Step-by-Step Solution:

Verification / Alternative check:
Convert 3.25 to 13/4; 30 ÷ (13/4) = 30 × (4/13) = 120/13 = 9 remainder 3/13 of a piece. Remainder length = (3/13) × 13/4 = 3/4 m; fraction of whole = (3/4)/30 = 1/40. Confirms result.

Why Other Options Are Wrong:

• 3/4, 8/13, 7/13, 1/13: These represent either piece ratios or misinterpreted remainders, not the leftover fraction of the whole 30 m rope.

Common Pitfalls:

• Rounding 3.25 to 3 or 3.5.
• Forgetting to express the leftover as a fraction of the original 30 m.

Final Answer:
1/40