Algebra: Properties

Properties of Addition and Multiplication

Characteristics of operations that are always true.

Commutative Property of Addition

Order of addends does not matter

Commutative Property of Multiplication

Order of the factors does not matter.

Associative Property of Addition

Order stays the same - grouped differently

Associative Property of Multiplication

Order remains the same - groupings are different

Identity Property of Addition

Any number is added to 0 the sum will be the same.

Multiple Choice

Determine whether the two expressions are equivalent. 
2⋅(3⋅7) and (2⋅3) ⋅7

• Yes

• No

Multiple Choice

Determine whether the two expressions are equivalent. 
7⋅2 and 2⋅7

• Yes

• No

Multiple Choice

Determine whether the two expressions are equivalent. 
26 - (9 - 7) and (26 - 9) - 7

• Yes

• No

Multiple Choice

Determine whether the two expressions are equivalent. 
40 ÷ 10 and 10 ÷ 40

• Yes

• No

Multiple Choice

Determine whether the two expressions are equivalent.
625 + 421 and 421 + 625 

• Yes

• No

Multiple Choice

7 + 9 = 9 + 7
This is an example of which property?

• Commutative 

• Associative

• Identity 

Multiple Choice

3 + ( 9 + 5) and (3 + 9) + 5
This is an example of which property?

• Commutative

• Associative

• Identity 

Multiple Choice

13 + 0 
This is an example of which property? 

• Commutative

• Associative

• Identity

Multiple Choice

(2 ⋅ 9) ⋅ 5 and 2 ⋅ (9 ⋅ 5) 
This is an example of which property? 

• Commutative

• Associative

• Identity 

Multiple Choice

9 + 0 = 9

• Multiplicative Identity

• Associative Property

• Additive Identity

• Additive Inverse

Multiple Choice

5(0) = 0

• Multiplicative Property of Zero

• Additive Inverse

• Additive Identity

• Multiplicative Identity

Multiple Choice

Find an equivalent expression using the associative property:

7 + (8 + 9)

• 7 + 8 + 9

• 8 + (7 + 9)

• (7 + 8) + 9

• 7 + 10

Multiple Choice

1 • 12 =12

• Multiplicative Identity

• Commutative Property

• Multiplicative Inverse

• Distributive Property

Multiple Choice

Find an equivalent expression using the Commutative property:
4 x 3 x 5 = 

• 4 + 3 x 5

• 5 x 4 x 3

• 5 + 4 + 3

• 3x + 5

Multiple Choice

Translate: twelve less than a number

• $$12-x$$  

• $$x-12$$  

• $$12x$$  

• $$x+12$$  

Multiple Choice

Translate: the sum of eight and the product of a number and nine

• $$9x+8$$  

• $$8x+9$$  

• $$\frac{x}{9}+8$$  

• $$9x-8$$  

Multiple Choice

Translate: five times the sum of a number and four

• $$5x+4$$  

• $$5\left(x+4\right)$$  

• $$5\left(4x\right)$$  

• $$4\left(x+5\right)$$  

Multiple Choice

Translate: the product of three and four less than a number

• $$3\left(4-x\right)$$  

• $$3\left(x-4\right)$$  

• $$3x-4$$  

• $$4-3x$$  

Multiple Choice

Translate: thirteen less than the product of negative six and a number

• $$13--6x$$  

• $$13-6x$$  

• $$6x-13$$  

• $$-6x-13$$  

Match

Match each phrase with the expression that accurately represents it.

• 5 times a number

• 5 more than a number

• 5 added to 5 times a number

• a number decreased by 5

• 5 decreased by a number

5x

x+5

5+5x

x-5

5-x

• 5x

• x+5

• 5+5x

• x-5

• 5-x

Match

Match each phrase to the math operation that it represents.

• decrease

• create equal groups

• total

• product

subtraction

division

addition

multiplication

• subtraction

• division

• addition

• multiplication

Multiple Choice

m divided by 16

• m + 16

• m - 16

• 16m

• m/16

Multiple Choice

Select the expression that would represent friends splitting $60

• 60/f

• 60f

• f+60

• f+60

Multiple Choice

The sum of 5 and f

• 5 + f

• 5 - f

• 5f

• 5/f

Multiple Choice

The product of 5 and f

• 5 + f

• 5 - f

• 5f

• 5/f

Multiple Choice

The difference between 8 and m

• 8 + m

• 8 - m

• 8m

• 8/m

Multiple Choice

m increased by 16

• m + 16

• m - 16

• 16m

• m/16

Multiple Choice

m decreased by 16

• m + 16

• m - 16

• 16m

• m/16

Multiple Choice

s increased by 10

• n + 10

• n - 10

• 10n

• n/10

Multiple Choice

Half the amount of yards.

• m + 16

• m - 16

• 16m

• $$y\div2$$

Multiple Choice

$5 less than Brett had.

• b-5

• 5-b

• 5b

• b+5

Multiple Choice

Define the variable.

• m = miles traveled

• c = cost per mile

• c = cabs ridden in

• t = total cost

Multiple Choice

Define the variable.

• c = total cost of membership

• c = cost per month

• r = registration fee

• m = number of months for membership