Adding any number to its opposite —also called the additive inverse—always gives zero as the result. For example:
− 999 + 999 = 0 2.5 + ( − 2.5 ) = 0 1 + ( − 1 ) = 0
Once you know this, there are several ways to think about addition.
Let yellow tiles represent positive numbers, and red tiles represent negative numbers.
The addition problem 5 + ( − 2 ) can be represented as
Group the two negative tiles with two positive tiles.
Since 2 + ( − 2 ) = 0 , these tiles disappear. We are left with 3 positive tiles.
So 5 + ( − 2 ) = 3 .
When both numbers are negative , we have only negative tiles, so the answer is also negative.
The addition problem − 3 + ( − 4 ) can be represented as
The result is simply 7 negatives tiles.
So − 3 + ( − 4 ) = − 7 .
When you add a positive number, you move to the right on the number line.
When you add a negative number, you move to the left on the number line.
Add 6 + ( − 8 ) using a number line.
Start at 6 , and move 8 units to the left.
6 + ( − 8 ) = − 2
Subtracting a number is the same as adding its opposite.
So, subtracting a positive number is like adding a negative; you move to the left on the number line.
Subtracting a negative number is like adding a positive; you move to the right on the number line.
Subtract − 4 − ( − 7 ) .
Start at − 4 , and move 7 units to the right.
− 4 − ( − 7 ) = 3 .
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