Adding and Subtracting Positive and Negative Integers
Adding and Subtracting Positive and Negative Integers
The best way to learn how to add and subtract positive and negative numbers is to look at a lot of examples.
Here is an explanation of how to do it, though.
First of all, a positive number can be written with a plus sign in front of it, like a negative number is written with a minus sign in front. But for a positive number, the plus sign can be left off.
The absolute number of a negative number is that number without the minus sign, which is positive. The absolute value of a positive number is the same positive number.
So the absolute values of are .
{…,-4,-3,-2,-1,0,1,2,3,4,…}
{…,4,3,2,1,0,1,2,3,4,…}
You add and subtract positive and negative numbers using three basic ideas:
(1) Subtracting a negative number is the same as adding its absolute value.
For example, .
12-(-4)=12+4=16
(2) If the two numbers have the same sign, add their absolute values and keep the sign.
For example, and .
12+4=16
(-12)+(-4)=-16
(3) If the two number have different signs, either add or subtract their absolute values, keeping track of the signs using (1).
For example, .
(-12)+4=(-12)+(-4)=-(12-4)=-8
Another example: .
4-12=(-12)+4=(-12)-(-4)=-(12-4)=-8