Question

Select the correct reason for statement number 1: 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 for the statement is the Property of reciprocals.

Step-by-step explanation:

The correct reason for the statement "if a/c = b/c and c ≠ 0, then a = b" is 2) Property of reciprocals.

To understand why, we can cross-multiply the equation a/c = b/c. This gives us ac = bc. Since c ≠ 0, we can divide both sides of the equation by c to get a = b. This shows that if the fractions a/c and b/c are equal, then the original numbers a and b will also be equal.