Mathematical Properties

Mr. Kenrick made three deposits to his account in this order: $460, $185, and $240. Show how to use the Commutative Property to find the sum of the deposits mentally.

$460 + $185 + $240 = $460 + $240 + $185 = $885

Mrs. Perez was looking at her bank account statement. She noticed that her beginning balance was $500, and she had added nothing to her account. What was the ending balance on her statement? What property did you apply?

$500; Identity Property

Mr. Escalante and Mrs. Turner plan to take their music classes to a musical revue. Tickets cost $6 each. They need a total of 48 tickets. Use the Commutative Property to write two equivalent expressions that could be used to find the total cost.

$6 ⋅ 48 or 48 ⋅ $6

A grocery store sells an imported specialty cheese for $11 and its own store-brand cheese for $5. Write two equivalent expressions for buying one of each cheese and an unknown amount of other groceries.

(11 + g) + 5 and 11 + (g + 5)

Luzon has 8 fish, 3 cats, and 2 dogs. Write two equivalent expressions using the Associative Property that can be used to find the total number of pets.

(8 + 3) + 2 and 8 + (3 + 2)

Using one or more properties, rewrite the expression 9 ⋅ (k ⋅ 5) as an expression that does not use parentheses.

k ⋅ 45

Bik was working on memorizing her multiplication facts. She noticed that anytime she multiplied a number by 1, she got the same number she started with. What property allows this to be true?

Identity Property

What property is represented by 2 + 0= 2?

Identity Property

What property is represented by 5 ⋅ 1= 5?

Identity Property

Taylor noticed that for a rectangle that had a length of 3 inches and a width of 2 inches, she could multiply 2 times 3 to get its area of 6 square inches. How else could she find the area?

Multiply 3 times 2.

Using one or more properties, rewrite the expression (b + 3) + 6 as an expression that does not use parentheses.

b + 9

Using one or more properties, rewrite the expression (p ⋅ 1) ⋅ 6 as an expression that does not use parentheses.

p ⋅ 6

What is the distributive property?

When you multiply the number(s) outside the parenthesis with each number inside the parenthesis.

Using one or more properties, rewrite the expression (a + 5) + 23 as an expression that does not use parentheses.

a + 28

Using one or more properties, rewrite the expression 7 + (3 + t) as an expression that does not use parentheses.

10 + t

Students in Mr. Rivas' class were practicing their multiplication skills by rolling three 6-sided number cubes. Wapi rolled a 2, a 3, and a 5. He multiplied the three numbers as follows using the order of operations: (2 ⋅ 3) ⋅ 5 = 30. Write another way Wapi could have performed the multiplication without changing the order of the numbers. State the property you used.

2 ⋅ (3 ⋅ 5) = 30; Associative Property

Using one or more properties, rewrite the expression 1 + (h + 2) as an expression that does not use parentheses.

3 + h

What is the identity property?

When you add or multiply numbers to equal that same number.

What property is represented by 3(a + 2) = 3a + 6?

Distributive Property

What property is represented by 4(7x + 4y) = 28x + 16y?

Distributive Property

What property is represented by 10x + 15y = 5(2x +3y)?

Factor Property

What property is represented by 36k + 12z + 60 = 12(3k + z + 5)?

Factor Property

What property is represented by (18 + 24) + 8 = 18 + (24 + 8)?

Associative Property

What property is represented by (2 + 5) + 3 = 2 + (5 + 3)?

Associative Property

What property is represented by 3 + 2 = 2 + 3?

Commutative Property

What property is represented by 5 ⋅ 2 = 2 ⋅ 5?

Commutative Property

Mr. Brooks was working on addition using dominos with a group of 1st graders. When picking the domino with 3 dots on one end and 5 dots on the other, some students read, "3 plus 5 equals 8" while others read it as, "5 plus 3 equals 8." What property were these children using? Explain.

Commutative Property; the order was different.

What is the factor property?

When you find a common factor of the numbers in an expression and then make it distributive property.

What is the associative property?

When adding or multiplying you can group numbers in any order.

What is the commutative property?

When adding or multiplying you can place the numbers in any order.