1. Multiplication and Division Properties

2. Multiplication Properties Commutative Property Associative Property Identity Property Zero Property Distributive Property

3. Commutative Property The order of the numbers doesn’t change the result (answer to the problem) p X q = q X p

4. Commutative Property 9 X 3 = 3 X 9 56 X 11 = 11 X 56 4 X 8 = 8 X 4 5 X 9 = 9 X 5

5. Associative Property The grouping of the factors doesn’t change the answer. (p X q) X r = p X (q X r)

6. Associative Property 3 X (4 X 2) = (3 X 4) X 2 4 X (1 X 7) = (4 X 1) X 7 5 X (7 X 2) = (5 X 7) X 2 (2 X 8) X 5 = 2 X (8 X 5) Is this Associative? No, it’s commutative. 5 X (5 X 2) = (2 X 5) X 5

7. Identity Property Any number multiplied by 1 will give you the original number. 23,487 X 1 = 23,487

8. Identity Property 234 X 1 = 234 1 X 2,567 = 2,567 98,765 X 1 = 98,765

9. Zero Property When any number is multiplied with zero, the answer is zero. 98,756,432 X 0 = 0

10. Zero Property 7,547,598,375 X 0 = 0 758,375,937 X 0 = 0 0 X 75,879,705 = 0

11. Distributive Property Multiplying the sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the product. 9 X (20 - 3) = (9 X 20) – (9 X 3) 8 X (40 + 5) = (8 X 40) + (8 X 5) 8 X 45 = (8 X 40) + (8 X 5)

12. Distributive Property 4 X 509 = (4 X 500) + (4 X 9) 6 X 310 = (6 X 300) + (6 X 10) 5 X 205 = (5 X 200) + (5 X 5) 195 X 5 = (200 X 5) – (5 X 5)

13. Properties of Division Identity Property of Division Zero Property of Division Equality Property of Division

14. Identity Property of Division Any number divided by 1 is the original number. 3/1=3

15. Identity Property of Division 567/1=567 70,935/1=70,935 67/1=67

16. Zero Property of Division Zero divided by any number is zero. 0/3=0

17. Zero Property of Division 0/134,643=0 0/453=0 0/32=0

18. Equality Property of Division If you take a non-zero number on both sides of the equation and divide it by another non-zero number the answer is the same. 10/5=10/5 2=2

19. Equality property of Division 54/9=54/9 6=6 100/10=100/10 10=10