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Which single integer leaves every integer unchanged when it is ADDED to it, and turns every integer into 0 when it is MULTIPLIED by it?

Class 7Integers (Extended)Integers
  • A0
  • B1
  • C−1
  • DNo integer does both.

Step-by-Step Solution

0 is the additive identity, so a + 0 = a for every integer a; it also wipes out any product, since a × 0 = 0. 1 is the multiplicative identity — it leaves an integer unchanged under multiplication, not addition — and −1 flips the sign. Only 0 does both jobs.
Answer: A) 0

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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