Multiplication Properties Commutative Associative Identity Distributive and Zero

Multiplication Properties Commutative, Associative, Identity, Distributive, and Zero

• One classroom has 3 rows of 6 desks. Another has 6 rows of 3 desks. Do both classrooms have the same number of desks? • How do you know?

Commutative Property • Do 2 groups of 5 marbles equal 5 groups of 2 beach balls? 2 x 5=5 x 2

• You can change the order of the numbers • The answer stays the same. • The numbers commute, they go from one place to another. 2 x 5=5 x 2

Associative Property • You can change the grouping of the factors. • The Product stays the same. (2 x 5) x 3 = 2 x (5 x 3) 10 x 3 = 2 x 15 30 = 30

Identity Property • Any number times 1 equals the original number. 5 x 1=5

Zero Property • When you multiply any number by 0, the product is 0. • No groups, nothing there • 12 x 0 = 0

Distributive Property • Multiplying each term inside the parentheses with the term outside of the parentheses. • You distribute or give a digit to the others.

Name that property • 537 x 1 = 537 – How do you know? • 5 x (40 x 9) = (5 x 40) x 9 – What changed? • 24 x 32 = 32 x 24 – What changed? • 400 x 0 = 0 – How do you know?

Name that property • 73 x 14 = 14 x 73 – How do you know? • 1 x 111 = 111 – How do you know? • 0 x 1, 247 = 0 – How do you know? • 8 x (4 x 3) = (8 x 4) x 3 – How do you know?

Name that Property • (9 x 3) x 5 = 9 x (3 x 5) – Why? • 1 x 90 = 90 x 1 – Why? • 76 x 1 = 76 – Why? • 0 x 563 = 0 – Why?

What’s missing? • 1, 037 x = 1, 037 – Which property is it? – How do you know? • (635 x 47 ) x =0 – Which property is it? – How do you know? • 75 x = 42 x 75 – Which property is it? – How do you know?

What’s Missing • 5 x (20 x 9) = (5 x 20) x – Which property is it? – How do you know? • 8 x 5= x 8 – Which property is it? – How do you know? • (9 x 6) x 4= 4 x (9 x ) – Which properties is it? – How do you know?

• What is the missing number in the number sentence? • Which property does this show? Why? (6 x 3) x 8 = 6 x ( x 8)

• Two bags with 3 marbles in each bag is the same amount as 3 bags with 2 marbles in each bag. Which property of multiplication does this represent? • Write a number sentence and Explain why you chose that property.

• Two sets of 3 bags with 5 marbles in each bag is the same as 3 sets of 2 bags with 5 marbles in each bag. Which property of multiplication does this represent? • Write a number sentence and explain your property choice.