Algebra - Order of Operations

BODMAS or BIDMAS

This all sounds very complicated and confusing, but as with most other topics,
the key is to break it down and work through it slowly and thoroughly.

Why do we need an Order of Operations?

Look at this calculation ... 5 + 2 x 4

If you work from left to right - you would get, 5 + 2 = 7 and then 7 x 4 = 28

try this with a scientific calculator .... the result is 13!

Which answer is correct? You guessed it - the calculator. It did the multiplication first,
2 x 4 = 8, and then added the 5, 8 + 5 = 13

So, we need to know which calculation to do first - which order to do the operations in.

The Order of Operations is just a set rules to tell you which order you must do operations (like add, subtract, multiply etc) to get the correct answer.

Is it BODMAS or BIDMAS? - They both mean the same. It doesn't matter
what you call it as long as your child understands it,

B

Stands for Brackets - If there are any brackets in your calculation, work out whatever is inside them first.

O or I

Stands for Order or Indices - Next you must work out any powers. like 4².

D
M

Stands for Divide and Multiply - Next, work out any division or multiplication calculations in the order that they appear (left to right).

A
S

Stands for Add and Subtract - work out any additions or subtraction calculations in the order that they appear (left to right)..

Lets work through an example ... 10 + (8-6) x 5

                        1st - Deal with the brackets, 8 - 6 = 2, which results in ... 10 + 2 x 5

                      2nd - Any powers? No

                      3rd - Any multiplications or divisions? Yes -
                                              work them out, 2 x 5 = 10 leaving ... 10 + 10

                      Lastly, Any additions or subtractions? Yes, work them out, 10 + 10 = 20

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How about a tougher one? ... 9 - (5 x 2 ²) ÷ 5

                      1st - Deal with the brackets. Inside the brackets there are two operations, a                                multiplication and a power. You must do the power first and then the                                multiplication.     2² = 2 x 2 = 4 and then 5 x 4 = 20 leaving   9 - 20 ÷ 5

                      2nd - Any powers left? No

                      3rd - Any divisions or multiplications? Yes ...   20 ÷ 5 = 4 leaving 9 - 4

                      Lastly, any subtractions or additions? Yes ..... 9 - 4 = 5

 

Practice working with BODMAS / BIDMAS with these worksheets from Mathsblog

Order of Operations 1      Order of Operations 2       Order of Operations 3

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