Order Of Operations And BIDMAS Explained

Imagine this: You’re scrolling through Facebook, and a friend has shared one of those simple “Are you as smart as a Year 6 student?” challenges.

4 + 3 x 2

It may look easy, but the answers in the comments are far from unanimous, being equally split between two answers: 14 or 10.

Some people are performing the operations as 4 + 3 = 7, then 7 x 2 = 14

Others are performing the operations as 3 x 2 = 6, then 4 + 6 = 10

Which is the right answer?

Mathematical problems with multiple operations follow an order. This order makes the maths easy and reliable so that everyone will evaluate it the exact same way. Known as the order of operations, it allows us to tackle many different operations that may show up together in a single mathematical problem. An easy way to remember this rule is with BIDMAS.

B = Brackets
I = Indices (or Order if you learned BODMAS)

D = Division

M = Multiplication

A = Addition

S = Subtraction

The BIDMAS rule reminds us to always start by solving the part of the equation in brackets, working from the innermost brackets outward. Next tackle the indices. After that, solve the multiplication and division operations, working left to right. Finally, solve the addition and subtraction operations, working left to right. Work through all the multiplication and division together, you don't have to do all the division then the multiplication - our friends in America remember the rule using PEMDAS, but we all come up with the same answer!

Let’s practice together with an example:

2 + 3(8 - 6)

1. Begin with the innermost brackets: 8 - 6 = 2 We now have 2 + 3(2)
2. Having solved what was in the brackets, and having no indices, our next step is to multiply 3(2), or 3 x 2 = 6, giving us: 2 + 6
3. Our final step is the addition of 2 + 6, giving us our answer!

Answer: 8

Once you know the BIDMAS rule, you can use it to evaluate any expression with multiple operations! By the way, the correct answer to your friend’s Facebook maths problem in the example at the top of this post is 10. Did you get it right?

Practice evaluating expressions using the order of operations BIDMAS rule with these sample problems and then check the answer key below. 

1) 30 ÷ 6 + 2 x 4 - 3 = ____ 2) 32 ÷ (15 - 7) + 12 x 2 = ____

3) 13 + (11 - 9) 3 x 9 + 4 = ____ 4) 34 + 5 [2 + 3(23 + 2)] = ____

Click here to download the Order of Operations answer key

We invite parents and adults to do these practice exercises with their children. As with reading, children who see adult role models doing maths on a regular basis are more likely to be comfortable doing maths themselves. (Adults may want to check their mastery as well. You would be surprised at how easy it is to lose the knowledge learned in school when you’re no longer practicing it every day!)

Check back here regularly for more maths mastery tips to help primary and secondary students gain maths understanding. With understanding comes passion, and with passion comes growth — a treasure is unlocked!