Adding and Subtracting Positive and Negative Integers

10

4

subtract

add

10 + 4 =

14

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

{…,-4,-3,-2,-1,0,1,2,3,4,…}

are

{…,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,

12+4=16

and

(-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

.