Adding and subtracting integers

You already know how to add 3 + 4 and so on. But there are many ways to add integers. One way to add integers is by using a number line.

Example

−4+(−3)=?

figure01

We always start at zero. Our first number is negative four (-4) so we move 4 units to the left. We then have plus negative three (-3) which is the same as subtracting 3 so we move 3 more units to the left. This gives us the value of negative seven, (-7).

−4+(−3)=?

−4−3=−7

We do the same thing if we have a positive integer, but instead we move to the right.

−4+3=?

−4+3=−1

figure02

You can also add integers and variables.

Example

13x+(−2)x=?

13x−2x=

(13−2)x=11x

When subtracting something from something we wish to find out the difference between the two numbers. When you subtract a negative number from any number the difference is even bigger. The distance from the seabed at a depth of 150ft and an airplane flying at 3000ft altitude at sea level is

3000−(−150)=3000+150=3150ft.

Thus when we subtract negative numbers, we get:

4−(−3)=4+3=7

Subtracting −3 is the same as adding 3.

If we have a plus sign before the parentheses then we will not change the signs within the parentheses

If we have a minus sign before the parentheses then we the signs within the parentheses will change.

Two negatives make one positive!

Video lesson

Calculate -3 + (-6) on a number line