Review of Algebraic Properties

Review of Algebraic Properties

​Hobbs

Commutative Property

This property is about "reordering" the addends or factors to get the same sum or product

Fill in the Blank

The __________ Property refers to "reordering" parts a of an addition or multiplication problem.

Multiple Select

Which of the following are examples of the commutative property of addition or multiplication?

• a + b = b + a

• a - b = b - a

• 7(5) = 5(7)

• 2 * 8 = 12 * 8

• 8 + 9 = 9 + 12

The Associative Property

This property is about "regrouping" your addends or factors without changing the sum or product.

Multiple Choice

Which of the following is NOT an example of the associative property?

• (a + b) + c = a + (b + c)

• 3 * (4 * a) = (3 * 4) * a

• 5 (a + b) = 5a + 5b

• 3(ab) = (3a)b

Multiple Choice

The associative Property is about _____ ?

• Reordering

• Regrouping

• Distributing

• Subtracting

The Identity Property

This property is about not changing the value of a number using addition or multiplication.

Multiple Select

Select all that apply: Which of the following is an example of the identity property?

• a * 1 = a

• 7 + 9 = 9 + 7

• 8(a + b) = 8a + 8b

• 7 + 0 = 7

The Inverse Property

Think about "canceling" the values out.

Key words to remember:

Addition - Opposite

Multiplication - Reciprocal

Multiple Choice

What is the reciprocal of 7?

• 7x

• x

• 7/1

• 1/7

Multiple Choice

Which problem is an example of the Inverse Property of Addition

• 8 * (1/8) = 1

• 9 + 0 = 9

• 9 + (-9) = 0

• 8 + 9 = 9 + 8

The Distributive Property

This property is about "distributing" or sharing one value with a sum or difference.

This property tells us its OK to work outside of GEMDAS in certain problems.

Multiple Choice

Which is NOT an example of the distributive property?

• a(4 + 5) = 4a + 5a

• 8(5 -2) = 40 - 16

• b( 1 + 9) = b + 9b

• 3(ab) = 3(ba)

Multiple Choice

a+ b = b + a is an example of the _______?

• Associative Property of Multiplication

• Associative Property of Addition

• Commutative Property of Addition

• Commutative Property of Multiplication

Multiple Choice

Which property is about "regrouping"

• Associative

• Distributive

• Commutative

• Inverse

Multiple Choice

The goal of the identity property is...

• to cancel out the numbers

• to not change the number's value

Multiple Choice

Complete the equation using the distributive property:

5 (9 - 4) =

• 45 - 9

• 45 - 4

• 45 + 20

• 45 - 20

Multiple Choice

1/5 is the ________ of 5.

• Opposite

• Reciprocal

• Identity

• Friend

Multiple Select

Based on the COMMUTATIVE Property, check all of the equations that are true.

• a + b = b + a

• (a + b) + c = a + (b + c)

• 5(6) = 6(5)

• 5(a + b) = 5a + 5b