Properties of Addition & Multiplication

Properties ofAddition &

Multiplication

Why do we need rules or properties in math?

Lets see what can happen if we didn’t have rules.

Before We Begin…• What is a VARIABLE?

A variable is an unknown amount in a number sentence represented as a letter:

5 + n 8x 6(g) t + d = s

Before We Begin…• What do these symbols mean?

( ) = multiply: 6(a) or group: (6 + a)

* = multiply

· = multiply

÷ = divide

/ = divide

Commutative Property• To COMMUTE something is to change it

• The COMMUTATIVE property says that the order of numbers in a number sentence can be changed

• Addition & multiplication have COMMUTATIVE properties

Commutative Property

Examples: (a + b = b + a)

7 + 5 = 5 + 7

9 x 3 = 3 x 9Note: subtraction & division DO NOT have commutative properties!

a b

b a

As you can see, when you have two lengths a and b, you get the same length whether you put a first or b first.

a

b a

bThe commutative property of multiplication says that you may multiply quantities in any order and you will get the same result. When computing the area of a rectangle it doesn’t matter which side you consider the width, you will get the same area either way.

Commutative PropertyPractice: Show the

commutative property of each number sentence.

1. 13 + 18 =

2. 42 x 77 =

3. 5 + y =

4. 7(b) =

Commutative PropertyPractice: Show the

commutative property of each number sentence.

1. 13 + 18 = 18 + 13

2. 42 x 77 = 77 x 42

3. 5 + y = y + 5

4. 7(b) = b(7) or (b)7

+ +toYou can change

You can change to And the result will not change

Keep in mind the and do not have to be numbers.

They can be expressions that evaluate to a number.

Example:(2 * 7) + (8 – 5)

+

*_

2 7 8 5

14 + 3

17 17

(8 - 5) + (2 * 7) +

_*

8 5 2 7

3 + 14

Lets see why subtraction and division are NOT commutative.

The commutative property: a + b = b + a and a * b = b * a

7 + 3 = 3 + 7 and 7 * 3 = 3 * 7

Try this subtraction: 8 – 4 = 4 – 8 8 ÷ 4 = 4 ÷ 8and division

10 = 10 21 = 21

4 ≠ -4 2 ≠ 0.5

Associative PropertyPractice: Show the associative

property of each number sentence.

1. (7 + 2) + 5 = 7 + (2 + 5)

2. 4 x (8 x 3) = (4 x 8) x 3

3. 5 + (y + 2) = (5 + y) + 2

4. 7(b x 4) = (7b) x 4 or (7 x b)4

Distributive Property• To DISTRIBUTE something is give it out or share it.

• The DISTRIBUTIVE property says that we can distribute a multiplier out to each number in a group to make it easier to solve

• The DISTRIBUTIVE property uses MULTIPLICATION and ADDITION!

Distributive PropertyExamples: a(b + c) = a(b) + a(c)

2 x (3 + 4) = (2 x 3) + (2 x 4)

5(3 + 7) = 5(3) + 5(7)Note: Do you see that the 2 and the 5 were shared (distributed) with the other numbers in the group?

Distributive PropertyPractice: Show the distributive

property of each number sentence.

1. 8 x (5 + 6) =

2. 4(8 + 3) =

3. 5 x (y + 2) =

4. 7(4 + b) =

(8 x 5) + (8 x 6)

4(8) + 4(3)

(5y) + (5 x 2)

7(4) + 7b

Ella sold 37 necklaces for $20.00 each at the craft fair. She is going to donate half the money she earned to charity. Use the Commutative Property to mentally find how much money she will donate. Explain the steps you used.

Use the Associative Property to write two equivalent expressions for the perimeter of the triangle

€

6

€

6€

41

2

€

51

2€

51

2

Six Friends are going to the state fair. The cost of one admission is $9.50, and the cost for one ride on the Ferris wheel is $1.50. Write two equivalent expressions and then find the total cost.