Example 1

(+3) – (+8) means three balloons are tied to the basket which raises the basket three feet above the clouds. Then eight balloons are removed from the basket, which lowers the basket eight feet. In all, the basket is now five feet below the clouds. Therefore, the answer to (+3) – (+8) is -5.

Example 2

What does the subtraction problem (-5) – (+7) mean?

Example 3

(-4) – (-9) =

Example 4

(+5) – (-4) =

Finding the rules of subtraction

Remember that we can use balloons and sand bags to help explain subtraction. Previously, we learned that when "subtracting +3" we imagine removing three balloons, which would lower the basket. We also learned that when "subtracting –5" we imagine removing five sand bags, which would raise the basket.

For each of the following examples we will draw the changes on number lines. Beneath the problem we will also record what changes actually occurred to the basket.

Example 1 (-7) – (+3) =		Example 2 (-7) – (-3) =
The problem	(-7)–(+3)= -10	The problem	(-7)–(-3)= -4
What actually happened	(-7)+(-3)= -10	What actually happened	(-7)+(+3)= -4
Example 3 (+7) – (-3) =		Example 4 (+7) – (+3) =
The problem	(+7)–(-3)= +10	The problem	(+7)–(+3)= +4
What actually happened	(+7)+(+3)= +10	What actually happened	(+7)+(-3)= +4

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

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

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

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