2.1: Number Properties

2.1: Number Properties

Thursday 10/15/20

Commutative Property of Addition or Multiplication

Changing the order of addends or factors does not change the sum or product.

3 + 5 = 5 + 3

3 × 5 = 5 × 3

Associative Property of Addition or Multiplication

Changing the grouping of addends or factors does not change the sum or product.

(2 + 4) + 1 = 2 + (4 + 1)

(2 × 4) × 1 = 2 × (4 × 1)

Addition Property of Zero

The sum of any number and 0 is that number.

8 + 0 = 0

Multiplication Property of Zero

The product of any number and 0 is 0.

5 × 0 = 0

Multiplication Property of One

The product of any number and 1 is that number.

7 × 1 = 7

Distributive Property

Multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products.

4 × (3 + 1) = (4 × 3) + (4 × 1)

6 × (5 - 2) = (6 × 5) - (6 × 2)

Multiple Choice

Example 1

Identify the property shown.

32 + 29 + 8 = 29 + 32 + 8

• Associative Property of Addition

• Commutative Property of Addition

• Addition Property of Zero

• Distributive Property

Multiple Choice

Example 2

Identify the property shown.

6 × (4 × 8) = (6 × 4) × 8

• Associative Property of Multiplication

• Commutative Property of Multiplication

• Multiplication Property of Zero

• Distributive Property

Now for some practice! You will get

6 questions and you must identify the property shown.

Multiple Choice

#1

Identify the property shown.

25 × 4 = 4 × 25

• Distributive Property

• Commutative Property of Multiplication

• Associative Property of Multiplication

• Distributive Property

Multiple Choice

#2

Identify the property shown.

0 × 71 = 0

• Multiplication Property of Zero

• Commutative Property of Multiplication

• Associative Property of Multiplication

• Multiplication Property of One

Multiple Choice

#3

Identify the property shown.

4 × (10 - 6) = (4 × 10) - (4 × 6)

• Multiplication Property of One

• Commutative Property of Multiplication

• Associative Property of Multiplication

• Distributive Property

Multiple Choice

#4

Identify the property shown.

19 × 1 = 19

• Multiplication Property of One

• Commutative Property of Multiplication

• Associative Property of Multiplication

• Distributive Property

Multiple Choice

#5

Identify the property shown.

(8 + 4) + 10 = 8 + (4 + 10)

• Addition Property of Zero

• Commutative Property of Addition

• Associative Property of Addition

• Distributive Property

Multiple Choice

#6

Identify the property shown.

750 + 0 = 750

• Addition Property of Zero

• Commutative Property of Addition

• Associative Property of Addition

• Distributive Property

Using the Distributive Property

The Distributive Property is used to multiply a number by a sum or difference. This lets us break larger numbers into the sum or difference of simpler numbers. The number outside is then multiplied to both addends before finding the sum or difference.

Multiple Choice

Example 3

Which of the following is a possible way to use the Distributive Property for  $8\times64$  ?

•  $\left(8\times60\right)-\left(8\times4\right)$  

•  $\left(10-2\right)\times\left(60-4\right)$  

•  $\left(8\times60\right)+\left(8\times4\right)$  

•  $\left(8\times70\right)+\left(8\times4\right)$