1. Multiplication Properties
5th Grade

2. Multiplication Properties
Associative Property
Commutative Property
Zero Property
Identity 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. Associative Property
The grouping of the factors doesn’t change the answer (the parenthesis are moved).
(p X q) X r = p X (q X r)
(2 X 3) X 4 = 2 X (3 X 4)

5. 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.

6. 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

7. Commutative Property
The order of the numbers doesn’t change the result (answer to the problem)
p X q = q X p
4 X 5 = 5 X 4

8. 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.

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

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

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

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

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

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

15. Distributive Property
To multiply a sum by a number, you can multiply each addend by the number and then add the products.
6 X 23 = 6 X (20+3) = (6X20)+(6X3)

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)
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)

18. Test Yourself Rewrite each equation with the correct answer, and
write the name of the property.
9 X 3 = 3 X 9
3 X (4 X 2 ) = (3 X 4) X 2
234 X 1 = 234
56 X 11 = 11 X 56
7,547,598,375 X 0 = 0
4 X 8 = 8 X 4
5 X (7 X 2) = (5 X 7) X 2
4 X 509 = (4 X 500) + (4 X 9)
6 X 310 = (6 X 300) + (6X 10)
(2 X 8) X 5 = 2 X (8 X 5)
1 X 2,567 = 2,567
X 5 = (200 X 5) – (5 X 5)
0 X 75,879,705 = 0
98,765 X 1 = 98,765
5 X 9 = 9 X 5
5 X 205 = (5 X 200) + (5 X 5)
4 X (1 X 7) = (4 X 1) X 7
758,375,937 X 0 = 0

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.