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

One classroom has 3 rows of 6 desks. Another has 6 rows of 3 desks 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 2 x 5 = 5 x 2 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 5 x (40 x 9) = (5 x 40) x 9 How do you know? 5 x (40 x 9) = (5 x 40) x 9 What changed? 24 x 32 = 32 x 24 400 x 0 = 0 Identity- multiplied by 1, answer is the same as the original factor Associative- the groups changed Commutative- the order changed Zero Property- mutiplied by zero, the answer is zero

Name that property 73 x 14 = 14 x 73 1 x 111 = 111 0 x 1,247 = 0 How do you know? 1 x 111 = 111 0 x 1,247 = 0 8 x (4 x 3) = (8 x 4) x 3 Commutative- the order changed but the numbers and answer are the same Identity- multiplied by 1, answer is the same as the factor zero- multiplied by zero, answer is 0 associative- groups changed, not the order

Name that Property (9 x 3) x 5 = 9 x (3 x 5) 1 x 90 = 90 x 1 Why? 1 x 90 = 90 x 1 76 x 1 = 76 0 x 563 = 0 associative- groups changed Identity- multiplied by 1, answer is the factor identity- multiplied by 1, answer is the factor zero- multiplied by zero, answer is zero

What’s missing? 1,037 x = 1,037 (635 x 47 ) x = 0 75 x = 42 x 75 Which property is it? How do you know? (635 x 47 ) x = 0 75 x = 42 x 75 1- identity property, the answer and the factor are the same 0- zero, the product is 0 42- commutative, the group is the same, the order is different

What’s Missing 5 x (20 x 9) = (5 x 20) x 8 x 5 = x 8 Which property is it? How do you know? 8 x 5 = x 8 (9 x 6) x 4= 4 x (9 x ) Which properties is it? 9-associative, order is the same, groups change 5- commutative, group stays, order changes 6- commutative and associative, the order and groups change

What is the missing number in the number sentence? Which property does this show? Why? (6 x 3) x 8 = 6 x ( x 8) 3 associative because the groups change, not the order, there is no 1 or 0

Write a number sentence and Explain why you chose that property. 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. commutative; the order is reversed 2 x 3 = 3 x 2

Write a number sentence and explain your property choice. 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. 3 (5 x 2) = 3 x (5 x 2) associative; the groups change 2 sets of 3, 3 sets of 2 but the number of marbles in side stays the same