Commutative and associative properties

As you have seen in our math classes, we've been studying the properties of numbers. So, let's take a look at them:

• The Commutative Property of Addition and Multiplication

3 + 2 = 2 + 3

(5 = 5)

3 x 6 = 6 x 3

(18 = 18)

If you change the order of the numbers, the results won't change.

Remember: You can only use the Commutative Property with Addition or Multiplication. Don't use it with Subtraction or Division.

• The Associative Property of Addition and Multiplication

(2 + 3) + 7 = 2 + (3 + 7)

(5) + 7 = 2 + (10)

12 = 12

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

(6) x 4 = 2 x (12)

24 = 24

Moving the parentheses will not affect the results.

Let's Practice

Use the commutative property to solve the equations:

a) 2 x 3 x 2 = 2 x 2 x 3

b) 3 + 4 + 12 = 3 + 12 + 4

c) 32 x 2 = 2 x 32

d) 44 + 3 + 15 = 44 + 15 + 3

 

 

Now use the associative property to solve:

a) (123 + 3) + 23 = 123 + (3 + 23)

b) (9 x 8) x 2 = 9 x (8 x 2)

Order of Operations

Welcome back for our new term!!! Hope you had a great holiday.
 

This week we've begun studying the Order of Operations. Why is it important? Because if we don't follow the order we may not come to the right solution.

 

There are two ways to help you remember, choose the one you prefer:

 

Please excuse my dear Aunt Sally

   or

                                                PEMDAS

 

 

P - parentheses

E - exponents

M - multiplication

D - division

A - addition

S- subtraction

 

 

Let's give it a try. Solve:

 

 

2 - 2 x 2 + 2 = ?

 

1st: 2 x 2 = 4

 

2nd: 2 - 4 + 2 = 0

 

The answer is 0.

 

 

Here are some more. Post your answers!!!

 

a) 9 - (2 x 3) + 15 : 3 = __________

 

b) 8 x (4 + 3) - 46 = __________

 

c) 12 : 3 - 3 + 2 x 6 = __________