1. What do you think....
What is the answer to: 2 x -4 = ? What about: -2 x 4 = ? Finally: -2 x -4 = ?

2. Multiplication is repeated addition Multiplication is commutative
What is 2 x 4?
Read this question using normal words:
“2 for 4 times” 2
+ 2
+ 2
+ 2
= 8
4 x 2 = 8
2 x 4 = 8
Multiplication is commutative
Multiplication is repeated addition
Multiplication is commutative

3. -2 -2 -2 -2 = -8 What is -2 x 4? -2 x 4 = -8 4 x -2 = -8
Read this question using normal words:
“ minus 2 for 4 times ” -2 -2 -2 -2
= -8
-2 x 4 = -8
4 x -2 = -8

4. “minus 2 for minus 4 times?”
What is -5 x 3 ?
“minus 5 for 3 times”
= -15
What is -2 x -4?
“minus 2 for minus 4 times?”
There is a complicated mathematical proof for this but we do not have time for that – it will be difficult to understand – maybe later in life – but for now we are going to continue patterns which will help us convince ourselves for now

5. Continue these two patterns:
Positive x Positive = Positive
Positive x Negative = Negative
2 x 3 2 x 2 2 x 1 2 x 0 2 x -1 2 x -2 2 x -3 2 x -4
= 6
= -9
3 x -3 2 x -3 1 x -3 0 x x x x x -3
- 2
+ 3
= 4
= -6
- 2
+ 3
= 2
= -3
- 2
+ 3
= 0
= 0
- 2
= -2
+ 3
= 3
- 2
= -4
+ 3
= 6
- 2
= -6
= 9
+ 3
= -8
- 2
= 12
+ 3
Positive x Negative = Negative
Negative x Negative = Positive

6. Multiplication means GROUPS OF
If we have 2 x 3, that means I have 2 bags of 3 things so in all I have 6 things If we consider money 2 x 3 means that I will give 2 bags of €3 so in all I will give €6 If we have -2 x 3 this means that I am going to take away 2 groups of €3 so I will take away €6 If we have -2 x -3 this means that I am going to take away 2 groups of €3 debt so I will give €6
2 x 3 = 6
-2 x 3 = -6
-2 x -3 = 6

7. SUMMARY: For Multiplication
Same Signs  Positive Answer
Different Signs  Negative Answer

8. Add  + Subtract  - Earnings  + Debt  -   +   -
Groups of
Earnings/Debt
Happy/Sad + x
 + -
 -
 -

9. SUMMARY: For Multiplication
Same Signs  Positive Answer
Different Signs  Negative Answer
What about for Division?
Do the same rules apply?

10. What do you think....
What is the answer to: 10 ÷ -2 = ? What about: -10 ÷ 2 = ? Finally: -10 ÷ -2 = ?

11. Division is the inverse of multiplication
We know that:
-2 x 4 = -8
If we change this around we get:
-2 = -8 ÷ 4
Therefore
-8 ÷ 4 = -2

12. Division is the inverse of multiplication
We know that:
-2 x 4 = -8
If we change this around we get:
4 = -8 ÷ -2
Therefore
-8 ÷ -2 = 4

13. SUMMARY: For Division TOO
Same Signs  Positive Answer
Different Signs  Negative Answer

14. Multiplying and Dividing
SAME SIGNS
DIFFERENT SIGNS
POSITIVE ANSWER
8 x 2 = 16
-8 x -2 = 16
24 ÷ 6 = 4
-24 ÷ -6 = 4
NEGATIVE ANSWER
-8 x 2 = -16
-2 x 8 = -16
-24 ÷ 6 = - 4
24 ÷ -6 = - 4

15. -9 x -4 = -36 -2 x 3 x -1 = -6 10 ÷ -2 = 5 -4 x 6 = 24 -8 ÷ 2 = -4
True or False?
Who?
-2 x 3 x -1 = -6
10 ÷ -2 = 5
-4 x 6 = 24
-8 ÷ 2 = -4
-7 x -5 = 35
-9 x -4 = -36
-10 x -10 = 100
-3 x 4 = -12
6 x -3 = 18
What about division?

17. L.O. To be able to multiply and divide negative numbers
By the end of the lesson we will be able to:
understand that a positive x positive = positive
understand that a positive x negative = negative
understand that a negative x negative = positive
understand that these same rules apply to dividing negative numbers

18. Choose a statement that matches your ability on this topic so far
I’m comfortable with any negative sum you throw at me
I understand negative multiplication 1 2
As long as I concentrate, I can do these questions
I made a few mistakes, but I know where I went wrong 1 2
Copy the statement, and add a sentence detailing the easiest/hardest thing you have found
I don’t understand the rules of multiplication and division
I don’t understand anything we’ve covered in this topic 1 2