1. Multiplication Properties
Shirley Garrett

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

3. Why Should you Learn about the Properties of Multiplication?
It helps you solve problems without working them out.
It helps with mental math.
It makes understanding math easier.

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

5. Commutative Property 9 X 3 = 3 X w 56 X p = 11 X 56 q X 8 = 8 X 4
5 X 9 = r X 5
The answers are on the next slide.

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

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

8. Associative Property 3 X (4 X 2) = (n X 4) X 2
4 X (p X 7) = (4 X 1) X 7
5 X (7 X 2) = (5 X 7) X n
(2 X z) X 5 = 2 X (8 X 5)
Is this Associative?
5 X (n X 2) = (2 X 5) X 5 Watch out!
Answers are on the next slide.

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

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

11. Identity Property 234 X 1 = z q X 2,567 = 2,567 98,765 X d = 98,765
Answers are on the next slide.

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

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

14. Zero Property
7,547,598,375 X c = 0
758,375,937 X 0 = b
z X 75,879,705 = 0

15. 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)

16. Distributive Property
4 X 509 = (4 X 500) + (4 X m)
6 X 310 = (6 X n) + (6 X 10)
s X 205 = (5 X 200) + (5 X 5)
195 X 5 = (200 X 5) – (5 X t)
The answers are on the next slide.

17. 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)

18. Test Yourself Rewrite each equation with the correct answer, and
write the name of the property.
9 X 3 = 3 X w
3 X (4 X 2 ) = (n X 4) X 2
234 X 1 = z
56 X p = 11 X 56
7,547,598,375 X c = 0
q X 8 = 8 X 4
5 X (7 X 2) = (5 X 7) X n
4 X 509 = (4 X 500) + (4 X m)
6 X 310 = (6 X n) + (6 X 10)
(2 X z) X 5 = 2 X (8 X 5)
q X 2,567 = 2,567
X 5 = (200 X 5) – (5 X t)
z X 75,879,705 = 0
98,765 X d = 98,765
5 X 9 = r X 5
s X 205 = (5 X 200) + (5 X 5)
4 X (p X 7) = (4 X 1) X 7
758,375,937 X 0 = b

19. Test Yourself Answers 9 X 3 = 3 X 9 Commutative
3 X (4 X 2) = (3 X 4) X 2 Associative
234 X 1 = 234 Identity
56 X 11 = 11 X 56 Commutative
7,547,598,375 X 0 = 0 Zero
4 X 8 = 8 X 4 Commutative
5 X (7 X 2) = (5 X 7) X 2 Associative
4 X 509 = (4 X 500) + (4 X 9) Distributive
6 X 310 = (6 X 300) + (6 X 10) Distributive
(2 X 8) X 5 = 2 X (8 X 5) Associative
1 X 2,567 = 2,567 Identity
195 X 5 = (200 X 5) – (5 X 5) Distributive
0 X 75,879,705 = 0 Zero
98,765 X 1 = 98,765 Identity
5 X 9 = 9 X 5 Commutative
5 X 205 = (5 X 200) + (5 X 5) Distributive
4 X (1 X 7) = (4 X 1) X 7 Associative
758,375,937 X 0 = 0 Zero

20. How did you do? 18 correct Excellent 17 correct Very Good
correct Good
correct Passing
12 – 0 correct You need more practice.