MasteringMaths.co.uk

Number Mastery for School Age Children

Number Mastery for School Age Children


How to do Order of Operations

This page is designed to help you correctly solve problems by using the 'Order of Operations'.
Why is this important? An operation is a calculation. When there is more than one calculation involved in the same mathematical problem, it is important to use the correct order of operations because going out of sequence will produce the wrong answer.

Example:- 7 + 2 × 3 = ? You could do this sum in two ways. Let's see:
You could add the 7 and 2, making 9, then multiply it by 3, or multiply the 2 and 3, then add the answer to 7.
9 × 3 = 27 and 7 + 6 = 13
Very clearly, maths couldn't work if everyone did the same sum differently and got a different answer. So, long ago a set of rules was agreed upon so that anyone faced with a problem would reach the same answer. Let's look at these rules in detail. By the way, the correct answer is 13, and you'll see why in a minute.

The order in which mathematical operations need to be solved.

  1. Calculations must be done from left to right
  2. Calculations in Brackets (Parenthesis) are done first. With more than one set of brackets, do the inner brackets first
  3. Exponents (radicals, square roots, powers or orders) must be done next
  4. Then Multiply and Divide, from left to right
  5. Then Add and Subtract, from left to right
  6. Using Brackets, Exponents, Divide, Multiply, Subtract and Add, use this phrase to help you memorize the sequence:
    Big Elephants Do Massive Sneezes, Atchoo!
So in the example above, multiply comes before add and so you would perform the operation 2 × 3 first, then add 7, giving you 13. I'm sure the best way to explain this fully is to give you some examples and show you how they are worked out.

Example 1. 4 × ( 5 + 3 ) =
4 × 8 = 32
Work out the Brackets first; 5 + 3 = 8
Multiply second


Example 2. 3 × 2² =
3 × 4 = 12
Work out the Exponents first; 2² = 4
Multiply second


Example 3. 30 ÷ 2 × 2² =
30 ÷ 2 × 4 =
15 × 4 = 60
Work out the Exponents first; 2² = 4
Now, do you divide or multiply first? They both carry the same weight so just work left to right. Divide 30 by 2 first = 15, then multiply by 4 = 60


Example 4. 7 + ( 5 × 5 ) - 3² =
7 + 25 - 3² =
7 + 25 - 9 =
32 - 9 = 23
Work out the Brackets first. 5 x 5 = 25
Restate the equation with the 25 in place
Work out the Exponents next. 3² is 3 x 3 = 9
Restate the equation with the 9 in place
Work left to right. Take 9 away from 32 = 23


Example 5. 6 × 2² + 5 × ( 4 + 1 ) =
6 × 2² + 5 × 5 =
6 × 4 + 5 × 5 =
24 + 25 = 49
Work out the Brackets first. 4 + 1 = 5
Restate the equation with the 5 in place
Work out the Exponents next. 2² is 2 x 2 = 4
Restate the equation with the 4 in place
Next take care of the multiplying
Work left to right and add the two numbers 24 + 25 = 49


Example 6.
Last one.
4 × ( 4 + 6 ) + 2² ÷ ( 6 - 2 ) =
4 × 10 + 2² ÷ ( 6 - 2 ) =
4 × 10 + 2² ÷ 4 =
4 × 10 + 4 ÷ 4 =
40 + 4 ÷ 4 =
40 + 1 = 41
Work out the left bracket first. 4 + 6 = 10
Restate the equation with the 10 in place and do second bracket
Restate the equation with the 4 from the second bracket
Work out the exponents next. 2² is 2 x 2 = 4
Restate the equation with the 4 in place
Next multiply from the left 4 x 10 = 40
Restate the equation with the 40 in place
Next divide the 4 ÷ 4 = 1
Add the two numbers 40 + 1 = 41

If you remember the order of operations, these types of sums are a piece of cake!


REMEMBER:- Big Elephants Do Massive Sneezes, Atchoo!

Home | Order Page | Free Practice Pages | Contact | The Solution | Math Jokes | News | Privacy | Bookmark and Share
Copyright Philip Chave MMX - MMXII masteringmaths.co.uk and mathsmaster.co.uk. All rights reserved.