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Properties of Multiplication. 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

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Properties of multiplication

Properties of Multiplication

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
Definitions

  • Zero Property – The product of any factor and 0 equals 0.

  • 65 x 0 = 0

  • 8 x 0 = 0


Zero property
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
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


Definitions1
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
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
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


Definitions2
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
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
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


Definitions3
Definitions

  • Identity Property –The product of any factor and 1 equals the factor.

  • 56 x 1 = 56

  • 38 x 1 = 38


Identity property
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
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


Definitions4
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
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
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


Definitions5
Definitions multiplication over addition

  • 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
Distributive Property of Multiplication over Subtraction 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 subtraction
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
Properties with Beans multiplication over subtraction

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


Name the property 3 x 11 11 x 3

9 multiplication over subtraction

Name the property…3 X 11 = 11 X 3

  • Identity

  • Commutative

  • Zero

  • associative


Name the property 13 x 1 13

10 multiplication over subtraction

Name the property…13 X 1 = 13

  • Identity

  • Commutative

  • Zero

  • associative


Name the property 20 x 0

10 multiplication over subtraction

Name the property…20 X 0

  • Identity

  • Commutative

  • Zero

  • associative


Name the property 12 x 4 x 3 12 x 4 x 3

10 multiplication over subtraction

Name the property…(12 X 4) X 3 = 12 X (4 X 3)

  • Identity

  • Commutative

  • Zero

  • associative


Name the property 3 x 9 1 3 x 9 3 x 1

10 multiplication over subtraction

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

  • Identity

  • Commutative

  • Distributive of multiplication over subtraction

  • Distributive of multiplication over addition


Name the property 5 x 6 2 5 x 6 5 x 2

10 multiplication over subtraction

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

  • Identity

  • Commutative

  • Distributive of multiplication over subtraction

  • Distributive of multiplication over addition


Now that you can identify the properties

Now that you can identify the properties… multiplication over subtraction

Let’s use those properties to solve some problems.


8 x 56

10 multiplication over subtraction

8 x 56

  • 400

  • 448

  • 500

  • 456


4 x 30 15

10 multiplication over subtraction

4 x (30 + 15)

  • 120

  • 140

  • 160

  • 180


2000 x 0 x 16

10 multiplication over subtraction

(2000 x 0) x 16

  • 32000

  • 320000

  • 0

  • 16


210 x 1 x 1

10 multiplication over subtraction

(210 x 1) x 1

  • 212

  • 210

  • 211

  • 220


8 x 60 4

10 multiplication over subtraction

8 x (60 – 4)

  • 416

  • 420

  • 406

  • 448


4 x 80 5

10 multiplication over subtraction

4 x (80 – 5)

  • 300

  • 285

  • 320

  • 220


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