Order of Operations:

 

 

Today we are going to explore a math topic called order of operations

Order of operations are simply instructions which tells you which math rule to apply first when doing calculations.

The order of operations governs 4 mathematical rules used in mathematical calculations

 

  1. Parentheses & Brackets – Parentheses are written like this ( ), brackets are written like this [ ]. When numbers are written or included within the parentheses or brackets like this (2 x 2) or [2 x 2], it is called a Group. You always calculate what is written within the parentheses or brackets first. This is the first order of operations.

This simply means do all calculations in parentheses and brackets first, next do exponents after, thirdly, do multiplication and division after, and lastly, do addition and subtraction.

 Let’s examine Example 1:

2 + (2 x 3)

The order of operations tells us we need to work out what is in parentheses first, before adding.

This means we must first multiply 2 x 3, which is 6, then we add the 6 to the number 2 and we get the answer 8

So 2 + (2 x 3) = 8 (this is correct)

And not, 2 + (2 x 3) = 12 (this is wrong)

 

  1. Exponents

 

Next on our list of Order of Operations are: Exponents

What are exponents?

An exponent is simply a shortcut way of multiplying the same number by itself, and is usually called raising a number to a Power. And it is written as shown in the examples below.

 

Examples 1:

4 x 4 = 4 2  

Because the number 4 is being multiplied by itself 2 times, it is written as 4 2   and is called 4 raised to the power 2 or 4 squared.

 

Examples 2:

4 x 4 x 4= 4

Because the number 3 is being multiplied by itself 4 times, it is written as 4 3   and is called 4 raised to the power 3 or 4 cubed.

 

Examples 3:

4 x 4 x 4 x 4 = 4 4  

Because the number 4 is being multiplied by itself 4 times, it is written as 4 4   and is called 4 raised to the power 4.

 

Let do an example:

3 x 22 = 3 x 4 = 12 (this answer is correct)

3 x 22 = 6 x 6 = 36 (this answer is wrong)

 

Remember, exponents, numbers raised to a certain number have to be worked out first, before multiplication, division, addition or subtraction.

 

 

  1. Multiplication and Division

Third on the order of operations is: Multiplication and Division

Example:

5 + 5 x 4

An easier way would be to use brackets or parentheses when using the order of operations to perform calculations.

If you do this with the example above it would look like this:

5 +  (5 x 4)=5 + 20=25

Let’s work out another sum using the third order of operations.

5 + 25 ÷ 5

Please remember multiplication and division comes before addition and subtraction.

Let’s use brackets to help us calculate the above sum.

5 + [25 ÷ 5]

5 + 5 = 10

Work out what is in the brackets first [25 ÷ 5], then add the number 5.

The answer is 10.

 

You try it now. Using brackets and the order of operations, work out the sums below.

5 x 8 – 25 =

9 + 16 x 3 =

3 x 4 x 3 – 6 =

3 x 4 + 12 ÷ 6 =

 

 

  1. Addition and Subtraction (from left to right)

 

Let’s show by examples how the order of operations applies to each of the 4 mathematical rules mentioned.

Remember, always multiply first before you add or subtract.

Wasn’t that easy?

 

You do the following sums to get the hand of it.

 

4 x 5 + 5 =

7 + 3 x 9 =

4+ 4 x 4 =

 

 

  1. The last item on the order of operations is: Addition and Subtraction

You work out the sums below.

 

6 + 5 – 5 =

9 – 3 + 9 =

7 – 4 + 4 =