Multiplication Properties
Shirley Garrett
5th Grade
Multiplication Properties
Commutative Property
Associative Property
Identity Property
Zero Property
Distributive Property
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.
Commutative Property
The order of the numbers doesn’t
change the result (answer to the
problem)
pXq=qXp
Commutative Property
9X3=3Xw
56 X p = 11 X 56
qX8=8X4
5X9=rX5
The answers are on the next slide.
Commutative Property
9X3=3X9
56 X 11 = 11 X 56
4X8=8X4
5X9=9X5
Associative Property
The grouping of the factors doesn’t
change the answer.
(p X q) X r = p X (q X r)
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.
Associative Property
3 X (4 X 2)
4 X (1 X 7)
5 X (7 X 2)
(2 X 8) X 5
=
=
=
=
(3 X 4) X 2
(4 X 1) X 7
(5 X 7) X 2
2 X (8 X 5)
Is this Associative? No, it’s commutative.
5 X (5 X 2) = (2 X 5) X 5
Identity Property
Any number multiplied by 1 will give
you the original number.
23,487 X 1 = 23,487
Identity Property
234 X 1 = z
q X 2,567 = 2,567
98,765 X d = 98,765
Answers are on the next slide.
Identity Property
234 X 1 = 234
1 X 2,567 = 2,567
98,765 X 1 = 98,765
Zero Property
When any number is multiplied with
zero, the answer is zero.
98,756,432 X 0 = 0
Zero Property
7,547,598,375 X c = 0
758,375,937 X 0 = b
z X 75,879,705 = 0
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)
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.
Distributive Property
4 X 509
6 X 310
5 X 205
195 X 5
=
=
=
=
(4 X 500)
(6 X 300)
(5 X 200)
(200 X 5)
+ (4 X 9)
+ (6 X 10)
+ (5 X 5)
– (5 X 5)
Test Yourself
Rewrite each equation with the correct answer, and
write the name of the property.
1.
2.
3.
4.
5.
6.
7.
8.
9.
9X3=3Xw
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
qX8=8X4
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)
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
Test Yourself Answers
1. 9 X 3 = 3 X 9 Commutative
2. 3 X (4 X 2) = (3 X 4) X 2
3.
4.
5.
6.
7.
8.
9.
10. (2 X 8) X 5 = 2 X (8 X 5)
Associative
Associative
11. 1 X 2,567 = 2,567 Identity
234 X 1 = 234 Identity
12. 195 X 5 = (200 X 5) – (5 X 5)
Distributive
56 X 11 = 11 X 56 Commutative
13. 0 X 75,879,705 = 0 Zero
7,547,598,375 X 0 = 0 Zero
14. 98,765 X 1 = 98,765 Identity
4 X 8 = 8 X 4 Commutative
15. 5 X 9 = 9 X 5 Commutative
5 X (7 X 2) = (5 X 7) X 2
Associative
16. 5 X 205 = (5 X 200) + (5 X 5)
Distributive
4 X 509 = (4 X 500) + (4 X 9)
Distributive
17. 4 X (1 X 7) = (4 X 1) X 7
Associative
6 X 310 = (6 X 300) + (6 X 10)
Distributive
18. 758,375,937 X 0 = 0 Zero
How did you do?
18
17
16
14
12
correct
correct
- 15 correct
- 13 correct
– 0 correct
Excellent
Very Good
Good
Passing
You need more practice.