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# Properties of Multiplication - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Properties of Multiplication' - ailis

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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

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

• 65 x 0 = 0

• 8 x 0 = 0

• 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

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

• Commutative Property – The order of the factors does not change the product.

• 6 x 8 = 8 x 6

• 14 x 3 = 3 x 14

• 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

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

• 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

• 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)

• 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

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

• 56 x 1 = 56

• 38 x 1 = 38

• 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

• 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

• 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)

• 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

• 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 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

• 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 multiplication over subtraction

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

9 multiplication over subtraction

Name the property…3 X 11 = 11 X 3

• Identity

• Commutative

• Zero

• associative

10 multiplication over subtraction

Name the property…13 X 1 = 13

• Identity

• Commutative

• Zero

• associative

10 multiplication over subtraction

Name the property…20 X 0

• Identity

• Commutative

• Zero

• associative

10 multiplication over subtraction

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

• Identity

• Commutative

• Zero

• associative

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

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… multiplication over subtraction

Let’s use those properties to solve some problems.

10 multiplication over subtraction

8 x 56

• 400

• 448

• 500

• 456

10 multiplication over subtraction

4 x (30 + 15)

• 120

• 140

• 160

• 180

10 multiplication over subtraction

(2000 x 0) x 16

• 32000

• 320000

• 0

• 16

10 multiplication over subtraction

(210 x 1) x 1

• 212

• 210

• 211

• 220

10 multiplication over subtraction

8 x (60 – 4)

• 416

• 420

• 406

• 448

10 multiplication over subtraction

4 x (80 – 5)

• 300

• 285

• 320

• 220