Is (x+y)/z equal to x/z + y/z for nonzero z?

• A. True
• B. False
• C. Sometimes true
• D. Only when x or y is zero

Answer: (A)

Dividing a sum by a nonzero number distributes across the addends. Specifically, (x + y)/z = (1/z)(x + y) = (1/z)x + (1/z)y = x/z + y/z, as long as z ≠ 0. This works because multiplication by 1/z distributes over addition. For example, with x = 4, y = 6, z = 2, both sides give 10/2 = 5 and 4/2 + 6/2 = 2 + 3 = 5. The property relies on z being nonzero; if z = 0, division is undefined, so the identity doesn’t apply.