Putting these understandings together we find that 

• Subtracting a negative number is the same as adding a positive number.
• Subtracting a positive number is the same as adding a negative number. 

Here are two examples showing that each subtraction problem has a related addition problem that gives the exact same answer.

5 – (-8) = 13
5 + 8 = 13

 

5 – 2 = 3
5 + (-2) = 3

 

Let's practice a little:

Change the subtraction expression into an addition expression. Then simplify.
(-4) – (+6)	(-4) – (+6) will result in the same answer as (-4) + (-6). (-4) – (+6) = (-4) + (-6) = -10
(-7) – (-9)	(-7) – (-9) will result in the same answer as (-7) + (+9) (-7) – (-9) = (-7) + (+9) = +2
(+3) – (+5)	(+3) – (+5) will result in the same answer as (+3) + (-5) (+3) – (+5) = (+3) + (-5) = -2
(+8) – (-2)	(+8) – (-2) will result in the same answer as (+8) + (+2) (+8) – (-2) = (+8) + (+2) = +10

 

By looking at the four examples above, we can see a pattern that occurs in each of the examples:

• The first integer stays the same;
• The subtraction sign turns into an addition sign;
• The second integer turns into its opposite.

In fact, the rule for subtracting positives and negatives is:

To subtract two integers: The first integer stays the same and add the opposite of the second integer