Working with integers is a major area of pain where students usually start mugging up algebra and that's the beginning of the end of logical thinking. This presentation aims at explaining graphically the multiplication of integers.

1. MultiplicationMultiplication
of Integers

2. 3 x - 2

3. 3 x - 2
means

4. 3 x - 2
means 3 times - 2

5. 3 x - 2
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
means 3 times - 2
1 time - 2

6. 3 x - 2
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
means 3 times - 2
1 time - 22 times - 2

7. 3 x - 2
0 1 2 3 4 5 6- 1- 2- 3- 4- 5- 6 + + + + + +
means 3 times - 2
1 time - 22 times - 23 times - 2
- 6

8. Another Problem

9. -4 x 2

10. -4 x 2 OR 2 x -4

11. means 2 times - 4
-4 x 2 OR 2 x -4

12. 0 1 2 3 4- 1- 2- 3- 4- 5- 6 + + + +
-4 x 2 OR 2 x -4
- 7- 8
means 2 times - 4

13. 0 1 2 3 4- 1- 2- 3- 4- 5- 6 + + + +
1 time - 4
-4 x 2 OR 2 x -4
- 7- 8
means 2 times - 4

14. 0 1 2 3 4- 1- 2- 3- 4- 5- 6 + + + +
1 time - 42 times - 4
-4 x 2 OR 2 x -4
- 7- 8
means 2 times - 4

15. 0 1 2 3 4- 1- 2- 3- 4- 5- 6 + + + +
1 time - 42 times - 4
-4 x 2 OR 2 x -4
- 7- 8
means 2 times - 4

16. 0 1 2 3 4- 1- 2- 3- 4- 5- 6 + + + +
1 time - 42 times - 4
- 8
-4 x 2 OR 2 x -4
- 7- 8
means 2 times - 4