Properties of Multiplication Lesson

Properties of Multiplication

Today you will learn about the Properties of Multiplication! Let's begin!

What is a property?

Remember from our last unit - a property is a rule that is always true. Properties of multiplication are rules that are always true about multiplication. Let's learn about them!

There are five properties of multiplication

• Associative Property

• Commutative Property

• Distributive Property

• Identity Property

• Zero Property

Associative Property of Multiplication

The way you group numbers in a problem will not change the product. For example, 5 x (3 x 4) = (5 x 3) x 4.

Multiple Choice

Which is an example of the Associative Property of Multiplication?

• 8 x 7 = 56

  7 x 8 = 56

• 2 x ( 5 x 4 ) = 40

  ( 2 x 5 ) x 4 = 40

• 18 x 0 = 0

• 1 x 9 = 9

Multiple Select

Select the equation that shows the CORRECT use of the Associative Property.

• (9 x 6) x 2 = 9 x (6 x 2)

• (3 x 5) x 1 = 3 x (5 + 1)

Commutative Property of Multiplication

The order in which you multiply numbers will not change the product. For example, 3 x 4 = 4 x 3.

Multiple Choice

3 x ____ = 9 x 3

• 7

• 9

• 27

• 11

Multiple Choice

Which represents the Commutative Property of Multiplication?

• 8 + 2 = 2 + 8

• 7 x 1 = 7

• 7 + 0 = 7

• 7 x 6 = 6 x 7

Multiple Choice

Using the Commutative Property what is another way you could write this multiplication equation?

• 6 + 6

• 6 x 6

• 7 x 6

• 7 + 6

Distributive Property of Multiplication

A problem can be broken into the sum of two smaller parts. For example, 12 x 5 = (10 x 5) + (2 x 5). We decomposed 12 into 10 + 2, and then "distributed" the 5 to both addends.

Multiple Choice

What is the simplified version of this expression? $$5(a+6)$$  

• $$5a+6$$  

• $$a+30$$  

• $$5a+30$$  

• $$5a-30$$  

Identity Property of Multiplication

The product of any number and 1 is that number. For example, 12 x 1 = 12.

Multiple Choice

The Identity property tells us that any number multiplied by 1 is that number.  Which expression below is an example of this property?

• 2x0=0
• 2x2=4
• 2+1=3
• 2x1=2

Zero Property of Multiplication

The product of any number and zero is ZERO. For example, 11 x 0 = 0.

Multiple Choice

Which of these illustrates the zero property of multiplication?

• 4 x (5 x 6) = (4 x 5) x 6
• 6 (9 + 1) = (6 x 9) + (6 x 1)
• 4 x (56) = (45) x 6
• 5 x 0 = 0

Multiple Choice

Which property is demonstrated by the following: 4 x 5 = 5 x 4

• Associative

• Distributive

• Commutative

• Identity

Multiple Choice

Which property is demonstrated by the following: 6 x 4 = (2 x 4) + (4 x 4).

• Zero

• Associative

• Distributive

• Commutative

Multiple Choice

Which property is demonstrated by the following: 0 x 43 = 0.

• Zero

• Associative

• Commutative

• Identity

Multiple Choice

Which property is demonstrated by the following: (3 x 4) x 2 = 3 x (4 x 2).

• Commutative

• Identity

• Distributive

• Associative

Multiple Choice

Which property is demonstrated by the following: 14 x 1 = 14.

• Identity

• Associative

• Zero

• Distributive

Multiple Choice

Rewrite (9 x 6) x 5 using the associative property.

• 270
• 9 x 30
• 9 x (6 x 5)
• 5 x 9 + 5 x 6

Multiple Choice

Use the commutative property of multiplication to solve the equation.
5 x 2 = 10, so ____ x 5 = 10

• 10
• 5
• 2
• 7

Multiple Choice

Which property is being used in the equation below?
10 x 8 = 8 x 10

• Identity Property
• Equality Property
• Commutative Property
• Associative Property