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### Properties of Multiplication

### Now that you can identify the properties…

6.C.1.a Multiply whole numbers

3.A.1.a.Use technology tools, including software and hardware, from a range of teacher-selected options to learn a new content or reinforce skills

Definitions

- Zero Property – The product of any factor and 0 equals 0.
- 65 x 0 = 0
- 8 x 0 = 0

Zero Property

- 5 x 0 = 0 4 x 0 = 0
- a x 0 = 0 b x 0 = 0
- 6 x 0 = 0 3 x 0 = 0
- y x 0 = 0 z x 0 = 0
- 18 x 0 = 0 19 x 0 = 0

Solve these equations using the zero property

n = 0

- 7 x n = 0
- 2 x m = 0
- 3 x z = 0
- 6 x g = 0
- 4 x s = 0
- 8 x c = 0

m = 0

z = 0

g = 0

s = 0

c = 0

Definitions

- Commutative Property – The order of the factors does not change the product.
- 6 x 8 = 8 x 6
- 14 x 3 = 3 x 14

Commutative Property

- 5 x 4 = 20 4 x 5 = 20
- a x b = c b x a = c
- 6 x 3 = 18 3 x 6 = 18
- a x y = z y x a = z
- 3 x 4 x 1 = 12 1 x 3 x 4 = 12

Solve these equations using the commutative property

n = 4

- n + 7 = 7 + 4
- m + 2 = 2 + 5
- z + 3 = 3 + 9
- g + 6 = 6 + 11
- s + 4 = 4 + 20
- c + 8 = 8 + 32

m = 5

z = 9

g = 11

s = 20

c = 32

Definitions

- Associative Property – The way factors are grouped does not change a product.
- (11 x 3) x 4 = 11 x (3 x 4)
- 5 x (5 x 10) = (5 x 5) x 10

Associative Property

- 5 x (7 x 4) = (5 x 7) x 4
- a x (b x c) = (a x b) x c
- (6 x 3) x 2 = 6 x (3 x 2)
- 12 x (8 x 1) = (12 x 8) x 1
- (9 x 10) x 2 = 9 x (10 x 2)

Rewrite these equations using the associative property

- 2 x (3 x 3) =
- 4 x (9 x 8) =
- 3 x (7 x 4) =
- 5 x (6 x 3) =
- 10 x (5 x 7) =
- 11 x (2 x 2) =

(2 x 3) x 3

(4 x 9) x 8

(3 x 7) x 4

(5 x 6) x 3

(10 x 5) x 7

(11 x 2) x 2

Definitions

- Identity Property –The product of any factor and 1 equals the factor.
- 56 x 1 = 56
- 38 x 1 = 38

Identity Property

- 5 x 1 = 5 4 x 1 = 4
- a x 1 = a b x 1 = b
- 6 x 1 = 6 3 x 1 = 3
- y x 1 = y z x 1 = z
- 18 x 1 = 18 19 x 1 = 19

Solve these equations using the identity property

- n x 1 = 8
- b x 1 = 7
- 3 x 1 = m
- v x 1 = 5
- 4 x 1 = w
- r x 1 = 2

n = 8

b = 7

m = 3

v = 5

w = 4

r = 2

Definitions

- Distributive Property of Multiplication over Addition – Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
- 6 x (12 + 9) = (6 x 12) + (6 x 9)
- 4 x (15 + 6) = (4 x 15) + (4 x 6)

Distributive Property of Multiplication over Addition

- 5 x (7 + 4) = (5 x 7) + (5 x 4)
- a x (b + c) = (a x b) + (a x c)
- 6 x (3 + 2) = (6 x 3) + (6 x 2)
- 12 x (8 + 1) = (12 x 8) + (12 x 1)
- 9 x (10 + 2) = (9 x 10) + (9 x 2)

Solve these equations using the distributive property of multiplication over addition

- 10 x (5 + 2) =
- 3 x (3 + 4) =
- 8 x (9 + 2) =
- 12 x (4 + 8) =
- 15 x (10 + 11) =
- 13 x (6 + 3) =

(10 x 5) + (10 x 2)

= 70

(3 x 3) + (3 x 4)

= 21

(8 x 9) + (8 x 2)

= 88

(12 x 4) + (12 x 8)

= 144

(15 x 10) + (15 x 11)

= 315

(13 x 6) + (13 x 3)

= 117

Definitions

- Distributive Property of Multiplication over Subtraction – To multiply a difference of two numbers by a third number, you can multiply the first two numbers by the third, and then find the difference of the products.
- 7 x (23 – 9) = (7 x 23) – (7 x 9)
- 5 x (9 – 3) = (5 x 9) – (5 x 3)

Distributive Property of Multiplication over Subtraction

- 5 x (7 - 4) = (5 x 7) - (5 x 4)
- a x (b - c) = (a x b) - (a x c)
- 6 x (3 - 2) = (6 x 3) - (6 x 2)
- 12 x (8 - 1) = (12 x 8) - (12 x 1)
- 9 x (10 - 2) = (9 x 10) - (9 x 2)

Solve these equations using the distributive property of multiplication over subtraction

- 10 x (5 - 2) =
- 3 x (4 - 3) =
- 8 x (9 - 2) =
- 12 x (8 - 4) =
- 15 x (11 - 10) =
- 13 x (6 - 3) =

(10 x 5) - (10 x 2)

= 30

(3 x 4) - (3 x 3)

= 3

(8 x 9) - (8 x 2)

= 56

(12 x 8) - (12 x 4)

= 48

(15 x 11) - (15 x 10)

= 15

(13 x 6) - (13 x 3)

= 39

Properties with Beans

- Now that you have learned about the different properties we are going to do a hands-on activity.

10Name the property…3 X (9 – 1) = (3 X 9) – (3 X 1)

- Identity
- Commutative
- Distributive of multiplication over subtraction
- Distributive of multiplication over addition

10Name the property…5 X (6 + 2) = (5 X 6) + (5 X 2)

- Identity
- Commutative
- Distributive of multiplication over subtraction
- Distributive of multiplication over addition

Let’s use those properties to solve some problems.

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