1. Understanding Negative Numbers
The adding, subtraction, multiplying and dividing by negative numbers is a difficult idea for many students
This presentation attempts to solve that.

2. A new invention
The idea of negative numbers is a ‘new’ idea, less than 2,000 years old.
There are several ways to think of negative numbers

3. Number lines The number line is one way to think of negative numbers2+ =4 2 -3 1 2 3 4 5 10 -1 -2 -3 -4 -5
-10
2 plus another 2 is 4 (or = 4)
2 minus 5 is NEGATIVE 3 (or = -3)

4. Vertical Number line But a number line can be vertical if you want1 2 3 4 5 10 -1 -2 -3 -4 -5
-10
But a number line can be vertical if you want
You can think of these numbers relative to the ground. Or maybe like a well
The black positive numbers are an amount above the ground, the red negative numbers are below the ground.
One might bury a hamster at ‘–3’ from the surface of the ground

5. Money and Negative Numbers
We all understand money!
We can think of a negative amount of money as a ‘bill’, or something owing. So even after you get a positive amount of money the debt will cancel it out.
Where is that $10 you owe me??
I have $10 = +
10 and negative 10
is 0 +
+10
-10

6. A Negative is an Opposite
A negative number is an ‘opposite’ number of a positive number
When a number and its ‘opposite’ are added together we get zero
Sometimes an ‘opposite’ is also called “an additive inverse”
The opposite of 5 is –5
5 plus –5 is 0
The opposite of 8 is –8
8+ (-8) = 0
The opposite of 3 is -3
The opposite of –7 is +7
= 0

7. Adding a Negative Number is Subtracting1 2 3 4 5 10 -1 -2 -3 -4 -5
-10
Adding a negative is no different than subtracting!
If I have $10 and I have to add in the fact I have a debt of $10, I really have 0 dollars.
10 plus (-10) is zero OR (-10) = 0
If I have $20 dollars, but I have to add in the fact that I owe 5 dollars, then I really have $15.
20+ (-5) = 15
If I bury my hamster at –2 feet from the surface, and the frost pushes it up 1 foot, my hamster is at –1 foot from the surface.
= -1
I hope the hamster was dead before it was buried!

8. Practice Adding Positive and Negative Numbers1 2 3 4 5 10 -1 -2 -3 -4 -5
-10
Practice Adding Positive and Negative Numbers
You try these, click the left mouse button for the answers
3 – 1=
1 – 3=
4 + (-1)=
-1 + (-1)=
-1 + (-2)=
-4 + 2=
-1+ 1=
0 + (-1)= 2 -2 3 -2 -3 -2 1 2 3 4 5 10 -1 -2 -3 -4 -5
-10 -1

9. Another way to look at Adding and Subtracting
Instead of number lines and rules, sometimes it helps to think of markers
Sort of like the way we thing of money + + + + + + + + + + + +
= 6
= 4
Six take away two

10. Adding and subtracting with markers
What if we made red markers Opposites? That is negative. And each red marker (negative) cancelled a green marker (Positive)? + + - - -
See why we say that adding a negative is the same as subtracting - - + - -
3 + (-2) = 1
(-2) = -5
Which is the same as
Which is the same as
3 – 2 = 1
-3 – 2 = -5

11. Subtracting a Negative number
Subtracting a negative number is hard to imagine
You can imagine a number line and going to the left (or down) a negative amount, which really means you are going to the right (or up)
But the markers are best
–5 take away –2
Or: – 5 – (– 2) - - - - -
–5 –(– 2)= –3
The same as –5 +2 = – 3

12. See that again! - - - - - –5 take away –2 Or: – 5 – (– 2)
–5 –(– 2)= –3
The same as –5 +2 = – 3
So taking away a negative is the same as adding

13. More to Follow
More to follow!
Come back for more