Cutting into equal pieces: A rod 192 m long is cut into small pieces, each 3.2 m in length. How many pieces are obtained?

Introduction / Context:
For uniform cutting, the number of pieces equals total length divided by piece length, provided the total length is an exact multiple. This is a straightforward unitary method with careful decimal handling (3.2 m = 32/10 m).

Given Data / Assumptions:

• Total length = 192 m.
• Each piece length = 3.2 m.
• No wastage; exact division assumed.

Concept / Approach:
Compute N = total length / piece length. Use fraction conversion to avoid decimal errors: 3.2 = 32/10. Then N = 192 / (32/10) = 192 * (10/32). Reduce to find an integer if divisible.

Step-by-Step Solution:

Verification / Alternative check:
Multiply back: 60 pieces * 3.2 m = 192 m, matching the original length with no remainder.

Why Other Options Are Wrong:
52, 62, 64, 68 are not equal to 192 / 3.2. Only 60 satisfies the exact division.

Common Pitfalls:
Dividing by 32 instead of 3.2, or moving the decimal the wrong way when converting 3.2 to a fraction.

Final Answer:
60