Properties of real numbers

Properties of Real Numbers

The ORDER of the numbers will not change the outcome of the problem.

(Multiplication and Addition)

​Commutative Property

Multiple Select

Which of the following are true?

• 3 + 5 = 5 + 3

• 3 - 5 = 5 - 3

• 9 • 3 = 3 • 9

• 9 ÷ 3 = 3 ÷ 9

​The way the numbers are GROUPED will not change the outcome of the problem

(multiplication and addition)

Associative property

Multiple Select

Which of the following are true?

• 8 + (3 + 1) = (8 + 3) + 1

• 8 - (3 - 1) = (8 - 3) - 1

• 12 • (6 • 2) = (12 • 6) • 2

Adding zero OR multiplying by one does NOT change the value of the problem

​

Identity Property

Multiple Select

Which of the following are true?

• 5 • 0 = 5

• 6 + 0 = 6

• 5 • 1 = 5

• 6 + 1 = 6

Inverse Property

​Use the OPPOSITE to "cancel out a value

Multiple Choice

What is the ADDITIVE INVERSE of
-7

• -7

• ^-1/₇

• ¹/₇

• 7

Multiple Choice

What is the MULTIPLICATIVE INVERSE of
8

• -8

• ^-1/₈

• ¹/₈

• 1

Multiple Select

Which of the following are true?

• 5 • 0 = 0

• 5 + 0 = 0

• 0.25 • 0 = 0

• 0.25 + 0 = 0

Multiply a value to an expression inside parenthesis

​

Distributive property

Multiple Choice

Which of the following shows the correct use of the distributive property

• $$3\left(a+b\right)=3a+3b$$

• $$3\left(a+b\right)=3ab$$

• $$3\left(a+b\right)=3a+b$$

• $$3\left(a+b\right)=3\cdot a+b$$

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

What is the property shown in this equation?
8(5 + 3) = 8(5) + 8(3)

• Associative Property of Addition

• Commutative Property of Addition

• Additive Identity Property

• Distributive Property

Multiple Choice

Identify the property:

11 + 36 = 36 + 11

• Commutative Property of Addition

• Associative Property of Addition

• Commutative Property of Multiplication

• Associative Property of Mulitplication

Multiple Choice

Identify the property:

(5 • 4) • 2 = 5 • (4 • 2)

• Commutative Property of Addition

• Associative Property of Addition

• Commutative Property of Multiplication

• Associative Property of Multiplication

Multiple Choice

This property tells us that when we change the order of numbers when we are adding, the answer does not change.  

• Commutative Addition

• Commutative Multiplication

• Associative Addition

• Associative Multiplication

Multiple Choice

3(w + 4) = 3w + 12 is an example of...

• Inverse Property

• Distributive Property

• Multiplicative Inverse

• Associative Property