Operations on integers

Multiplying integers: the product of two numbers with the same sign is positive, and with different signs is negative. Why is (−2) × (−2) positive? Look at the pattern: 2 × (−2) = −4, 1 × (−2) = −2, 0 × (−2) = 0, and each time the answer goes up by 2, so the next answers are 2 and then 4. Dividing follows the same signs: −12 ÷ 4 = −3 and −12 ÷ (−3) = 4. Zero divided by any number except 0 is 0, but dividing by 0 is undefined. With three or more factors, count the negatives: an odd number gives a negative product. Integers are closed under +, − and ×, but not ÷, since 1 ÷ 2 is not an integer. The order and grouping of a product do not change it.