Rule for adding and subtracting Integers

Adding Integers

1) When adding integers of the same sign, keep the sign and add.

Examples:

2 + 5 = 7
(-7) + (-2) = -9
(-80) + (-34) = -114

2) When adding integers of the opposite signs, we take their absolute values, subtract the smaller from the larger, and give the result the sign of the integer with the larger absolute value.

Example:

8 + (-3) = ?
The absolute values of 8 and -3 are 8 and 3. Subtracting the smaller from the larger gives 8 - 3 = 5, and since the larger absolute value was 8, we give the result the same sign as 8, so 8 + (-3) = 5.

Subtracting Integers

Subtracting an integer is the same as adding its opposite. You KEEP, CHANGE, CHANGE!

Examples:

In the following examples, we convert the subtracted integer to its opposite, and add the two integers.
7 - 4 = 7 + (-4) = 3
12 - (-5) = 12 + (5) = 17
-8 - 7 = -8 + (-7) = -15
-22 - (-40) = -22 + (40) = 18