Which of these expressions has NO value at all?

Class 7Integers (Extended)Integers

A $0 \div (- 9)$
B $(- 9) \div (- 9)$
C $(- 9) \times 0$
D $(- 9) \div (7 - 7)$

Step-by-Step Solution

Simplify the bracket: 7 − 7 = 0, so the last expression is (−9) ÷ 0 — division by zero, which is undefined. The other three all have values: 0 ÷ (−9) = 0, (−9) ÷ (−9) = 1 and (−9) × 0 = 0. Dividing zero BY a number is perfectly legal; dividing a number by zero is not, and the answer is not 0 either.

Answer: D)

(- 9) \div (7 - 7)

Key idea: Dividing integers

The sign rule for division is **the same as for multiplication**: same signs → positive, different signs → negative.

12 ÷ 4 = 3
(−12) ÷ (−4) = 3
12 ÷ (−4) = −3
(−12) ÷ 4 = −3

Also: integer ÷ 1 = the integer; integer ÷ itself = 1; **never divide by 0** — division by zero is undefined.

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