Properties

1. Multiplication Properties
Shirley Garrett
5th Grade

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
5 X 9 = 9 X 5

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
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

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
1. 9 X 3 = 3 X w
2. 3 X (4 X 2 ) = (n X 4) X 2
3. 234 X 1 = z
4. 56 X p = 11 X 56
5. 7,547,598,375 X c = 0
6. q X 8 = 8 X 4
7. 5 X (7 X 2) = (5 X 7) X n
8. 4 X 509 = (4 X 500) + (4 X m)
9. 6 X 310 = (6 X n) + (6 X 10)
10. (2 X z) X 5 = 2 X (8 X 5)
11. q X 2,567 = 2,567
12. 12. 195 X 5 = (200 X 5) – (5 X t)
13. z X 75,879,705 = 0
14. 98,765 X d = 98,765
15. 5 X 9 = r X 5
16. s X 205 = (5 X 200) + (5 X 5)
17. 4 X (p X 7) = (4 X 1) X 7
18. 758,375,937 X 0 = b
Rewrite each equation with the correct answer, and
write the name of the property.

19. Test Yourself Answers
1. 9 X 3 = 3 X 9 Commutative
2. 3 X (4 X 2) = (3 X 4) X 2
Associative
3. 234 X 1 = 234 Identity
4. 56 X 11 = 11 X 56 Commutative
5. 7,547,598,375 X 0 = 0 Zero
6. 4 X 8 = 8 X 4 Commutative
7. 5 X (7 X 2) = (5 X 7) X 2
Associative
8. 4 X 509 = (4 X 500) + (4 X 9)
Distributive
9. 6 X 310 = (6 X 300) + (6 X 10)
Distributive
10. (2 X 8) X 5 = 2 X (8 X 5)
Associative
11. 1 X 2,567 = 2,567 Identity
12. 195 X 5 = (200 X 5) – (5 X 5)
Distributive
13. 0 X 75,879,705 = 0 Zero
14. 98,765 X 1 = 98,765 Identity
15. 5 X 9 = 9 X 5 Commutative
16. 5 X 205 = (5 X 200) + (5 X 5)
Distributive
17. 4 X (1 X 7) = (4 X 1) X 7
Associative
18. 758,375,937 X 0 = 0 Zero

20. How did you do?
18 correct Excellent
17 correct Very Good
16 - 15 correct Good
14 - 13 correct Passing
12 – 0 correct You need more practice.