The document explains the concept of negative numbers using temperatures as a relatable example and illustrates how to calculate differences between positive and negative values. It emphasizes that adding a negative value equates to going down and that subtracting a negative value results in a positive outcome. The text also briefly mentions the rules of multiplying and dividing negative numbers.

1. NEGATIVE NUMBERS
For those who find
Number lines or the thought of…
‘minus times minus’ BAFFLING!

2. What is negative?
Any amount less than nothing in the bank!
Anything below ground level!
Any temperature below 0 degrees Centigrade.
(The ‘freezing point’ of pure water)

3. Think of negative numbers as being …
Temperatures on a Thermometer!

4. What if?
The temperature at 7am is minus 3 degrees
centigrade (-3⁰C)
At noon, it is 6 ⁰C
By how much has the temperature risen?

5. A way of looking at the question
6
5
4
3
2
1
0
-1
-2
-3
Treat 0 as a baseline
START
FINISH
Gap of 6
Gap of 3
Answer = 9

6. A case of two gaps…
The gap between -3 and 0 was 3
The gap between 0 and 6 was 6
We added the gaps
You always ADD the gaps (numbers) when:
1. One number is positive
2. The other is negative

7. What have we found?
The gap (difference) between -3 and +6 is 9
Put another way, 6 take away -3 = 9
6 – (-3) = 9
I agree that it is easier to add gaps than think
hard about that lot.
But we have found that…
Taking away a negative gives a positive

8. Add UP and Take DOWN
Here is a way of how to turn + and - sums
with negative numbers into moves on a
thermometer.
Adding (+) means going UP
Taking away (-) means going DOWN

9. Adding means going UP (1)
You know that 3 + 6 = 9
You go UP 6 from 3, so:
-6 + 3
Go UP 3 from -6
One by one, we have -5, -4, -3
-6 + 3 = -3

10. Taking away means going DOWN
How about :
-6 - 3
We are taking away a POSITIVE number, so
Start at -6 and go DOWN 3
-7, -8, -9
-6 +- 3 = -9

11. Can you see the pattern?
Look at the last two slides!
With one positive (+) number and one negative (-)
You find the difference:-
(3 in both sides)
Then choose the sign of the bigger number
How’s that for simple!

12. Take Care!!
Do not confuse these with ‘minus times minus’!
6 - 2 = 4
You go DOWN 2 from 4.
In the same way:
-6 – 2 = -8
Two DOWN from -6
In both cases, we are taking away a positive from
another number.

13. So what about ‘minus times minus’
We are coming to that!
First some things to think about:
1. If you owe the bank $5 and reverse your
debt, you added $5 your account!
- (-$5) = +$5
2. If a diver goes down and then reverses his
dive, he goes up!

14. And so, …
Minus times Minus = Plus
OR
Using the UP DOWN idea…
Taking away a negative number
Results in going UP

15. We have to finish with dividing
Sorry!
But this is easy!
Signs the same - answer plus
Signs different – answer minus