1. Rewrite as an addition sentence
2. Apply addition rules (details below)


1. Rewrite as an addition sentence
a) Change subtraction operand to an addition operand or a plus sign
b) Change the sign of the following number to its opposite

This process is referred to as "addition of the opposite".


Example 1
5 – 9 = would become 5 + (-9)

Example 2
-9 - 4 =
-9 + (-4) =
Notice the first number, -9, was not changed.

Example 3
-4 – (-8) =
-4 + 8 =

Example 4
7 – (-5) =
7 + 5 =

2. Follow the Addition Rules

ADDING TWO ALIKE SIGNS – two positive numbers or two negative numbers
First Method:
1. Add absolute values
2. Attach same sign to the answer

Example:
Adding two positives integers
4 + 5 = 9

Adding two negative integers
(-4) + (-5) = (-9)

Second Method: (+) positive (-) negative
Draw (+) and (-) to represent the number sentence.

Note: A pair of (+) and (-) cancels each other or equals zero. (See end of page for more an illustration.)

4 + 5 = 9
+ + + + and + + + + +

OR
(-4) + (-5) = (-9)

(-) (-) (-) (-) and
(-) (-) (-) (-) (-)
Parentheses are used for clarity only.
Are there any zero pairs to cancel? No. So, count the signs to get a total.

Memory tip for adding two integers with same signs: Alike Signs – Add

ADDING TWO UNLIKE SIGNS
- 6 + 4 = ?
First Method:
1. Subtract absolute values
2. Use the sign of the number with the larger absolute value
| - 6| = 6 | 4 | = 4
Remember to put the larger number first when subtracting two numbers. -- > 6 - 4 = 2
Six is larger. So, the answer will have a negative sign.
- 6 + 4 = - 2

Second Method:
Parentheses are used for clarity only.

(-) (-) (-) (-) (-) (-)
+ + + +
Are there any zero pairs to cancel? Yes. Four pairs cancel each other. So, count the remaining signs to get a total. Two negatives are left. Thus, - 6 + 4 = - 2

Memory tip for adding two integers with unlike signs: Different Signs – Find the Difference

Here is proof that a positive and negative cancel each other.
( -3) + 3 = ?

(-) (-) (-)
+ + +
Three negative / positive pairs cancel each other. Thus, the answer is zero.