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:

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) = ?

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

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 – 0 – 150 = 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

To see the solution look at the video in the next page.

We want to solve the following simple arithmetic problem using this basic number line. So the problem simply reads; -3 + (-6). So we want to see what that equals but we want to use our number line here to really understand what’s happening. So we begin at -3. So -1, 2 ,3. We begin here and we want to see what happens when we add -6 to that. So if we added a positive number we would go to the right but when we add a negative number it’s the same as subtracting so when we add a negative number so we go to the left. So instead of going to the right six, we go to the left six. So from -3, 6 more. 1,2,3,4,5,6. Where does that leave us? That leaves us at -9. So there’s our answer right there. So from here we can see from the number line that -3 + -6 is the same as -9.

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