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

• 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

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

n = 0

s = 0

g = 0

z = 0

m = 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 + 7 = 7 + 4

• m + 2 = 2 + 5

• z + 3 = 3 + 9

• g + 6 = 6 + 11

• s + 4 = 4 + 20

• c + 8 = 8 + 32

n = 4

m = 5z = 9

g = 11s = 20c = 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

m = 3

b = 7

n = 8

v = 5

r = 2

w = 4

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.

Name the property…3 X 11 = 11 X 3

a. Identity

b. Commutative

c. Zero

d. associative

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

Name the property…13 X 1 = 13

a. Identity

b. Commutative

c. Zero

d. associative

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

Name the property…20 X 0

a. Identity

b. Commutative

c. Zero

d. associative

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

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

a. Identity

b. Commutative

c. Zero

d. associative

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

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

a. Identity

b. Commutativec. Distributive of

multiplication over subtraction

d. Distributive of multiplication over addition

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

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

a. Identity

b. Commutativec. Distributive of

multiplication over subtraction

d. Distributive of multiplication over addition

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

Now that you can identify the properties…

Let’s use those properties to solve some problems.

8 x 56

400

448

500

456

25% 25%25%25%10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

1. 400

2. 448

3. 500

4. 456

4 x (30 + 15)

120

140

160

180

25% 25%25%25%10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

1. 120

2. 140

3. 160

4. 180

(2000 x 0) x 16

32000

320000 0 16

25% 25%25%25%10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

1. 32000

2. 320000

3. 0

4. 16

(210 x 1) x 1

212

210

211

220

25% 25%25%25%10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

1. 212

2. 210

3. 211

4. 220

8 x (60 – 4)

416

420

406

448

25% 25%25%25%10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

1. 416

2. 420

3. 406

4. 448

4 x (80 – 5)

300

285

320

220

25% 25%25%25%10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

1. 300

2. 285

3. 320

4. 220