Working with Integers
A guide to understanding and using positive and negative whole numbers.
What are Integers?
Integers are whole numbers (not fractions) that can be positive, negative, or zero. They are used to represent quantities that can have a direction, like temperature, elevation, or debt.
... -3, -2, -1, 0, 1, 2, 3 ... Adding Integers
Same Signs
Add the numbers and keep the sign.
(+3) + (+2) = +5
(-3) + (-2) = -5
Different Signs
Subtract the smaller number from the larger number and keep the sign of the larger number.
(+5) + (-2) = +3
(-5) + (+2) = -3
Subtracting Integers
The Rule: Add the Opposite
Change the subtraction sign to an addition sign, and flip the sign of the second number. Then follow the rules for addition.
(+5) - (+2) (+5) + (-2) = +3
(+5) - (-2) (+5) + (+2) = +7
(-5) - (-2) (-5) + (+2) = -3
/ Multiplying & Dividing Integers
The rules for multiplication and division are the same.
Same Signs POSITIVE
If the signs are the same, the result is always positive.
(+3) × (+2) = +6
(-3) × (-2) = +6
(+6) ÷ (+2) = +3
(-6) ÷ (-2) = +3
Different Signs NEGATIVE
If the signs are different, the result is always negative.
(+3) × (-2) = -6
(-3) × (+2) = -6
(+6) ÷ (-2) = -3
(-6) ÷ (+2) = -3