Question

Select the correct reason for statement number 2: if a/c = b/c and c ≠ 0, then a = b.

1) Definition of division
2) Property of reciprocals
3) Cannot be determined
4) None of the above

Answer 1

The correct reason that a/c = b/c leads to a = b when c ≠ 0 is the Definition of division, which allows the cancellation of the common nonzero divisor on both sides. The correct answer is option: 1) Definition of division.

Step-by-step explanation:

When given that a/c = b/c and c ≠ 0, and asked to select the correct reason for statement number 2 which asserts a = b, the correct option is 1) Definition of division.

This is because division by a non-zero number can be undone by multiplication by that same number, implying that if two quantities divided by the same non-zero number are equal, then the original quantities must be equal as well.

This can be shown through multiplication: a/c × c = b/c × c, which simplifies to a = b because the c's cancel out on both sides.