1. Multiplication Properties
7th Grade

2. Multiplication Properties
Commutative Property
Associative Property
Distributive Property
Identity Property
Zero 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 in which 2 numbers are added or multiplied does not change the answer.
p X q = q X p

5. Commutative Property What is missing? 9 X 3 = 3 X w 56 X p = 11 X 56
q X 8 = 8 X 4
5 X 9 = r X 5

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 3 numbers when they are added or multiplied does not change the answer. Parenthesis change; Order does not!!
(p X q) X r = p X (q X r)

8. Associative Property What is missing? 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 (3 X 2) = (3 X 5) X 2

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

10. Identity Property
Any number multiplied by 1 will give you the original number.
23,487 X 1 = 23,487
Any number added to zero will give you the original number.
= 456

11. Identity Property
234 X 1 = z
q X 2,567 = 2,567
98,765 X d = 98,765

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)

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.