Numbers › Integers

Integers

Integers are the whole numbers, plus their negatives, plus zero. No fractions, no decimals.

Integer jumper

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Where you've been

What counts as an integer?

The set of integers is …, −3, −2, −1, 0, 1, 2, 3, …. It runs forever in both directions. 2.5, 1/3 and π are not integers — they live between the integers.

Adding and subtracting

Adding a positive — jump right on the number line.
Adding a negative — jump left. 5 + (−3) = 2.
Subtracting is the same as adding the opposite. 5 − 3 = 5 + (−3).
Two negatives in a row flip back. 5 − (−3) = 5 + 3 = 8.

Mental picture

Think of −3 as "owing 3." Owing 3 and then earning 7 leaves you with −3 + 7 = 4. The number line keeps the bookkeeping honest.

Multiplying signs

positive × positive = positive (3 × 4 = 12)
positive × negative = negative (3 × −4 = −12)
negative × negative = positive (−3 × −4 = 12)

Same idea with division — count the negatives. An odd number of negatives gives a negative answer; an even number gives a positive.

Quick check

What is −7 + 4?
What is 3 − 9?
What is (−5) × (−2)?

Answers: −3, −6, and 10.