BIDMAS Questions with Answers and Solutions
Students can often run into problems when faced with what seem at first like fairly easy mathematical problems. Consider, for example, the equation 5 + 2 × (3 + 3) = y. What is the solution? Some might say y = 60, while others might say y = 17. The problem here is that we have multiple mathematical ‘operations’ (processes such as addition, subtraction, multiplication, and division) which people can choose to perform in a different order. This is where BIDMAS comes in. BIDMAS, or the ‘order of operations’, provides an easy guide which tells you how to break down these complex equations and solve them correctly. This handy post should help you to get to grips with how you can use BIDMAS to avoid confusions in your work.
What is BIDMAS?
BIDMAS is an acronym that stands for Brackets, Indices, Division, Multiplication, Addition, Subtraction. This list gives the order in which you should perform operations in an equation. You may be unfamiliar with the term ‘indices’ here. Indices are operations such as squaring, cubing, or anything of the form ‘x to the power of y’.
BIDMAS tells us to always perform operations inside brackets first, and then to perform any operation before or after the brackets with whatever number results from the operation inside the brackets. Next, operations including powers should be performed before other operations. Finally, division, multiplication, addition, and subtraction operations should be performed in that order.
Example of using BIDMAS
Consider this equation: 2 + (5 − 3)² × 4 = y
In order to reach a solution, we must perform four operations: addition, subtraction, squaring, and multiplication. BIDMAS can help us to break this complex equation down into its individual operations so that we can then to perform them in order.
First, we must consider the brackets. The operation in brackets is 5 – 3, which leaves us with 2.
Now our equation looks like this: 2 + (2)² × 4 = y
Secondly, we must deal with the indices. Here we have 2² which is equal to 4.
We are then left with this: 2 + 4 × 4 = y
The last two operations are a multiplication and an addition. BIDMAS tells us to do the former first. Therefore, we start with 4 × 4 which gives us 16.
We are then left with the equation, 2 + 16 = y, which we can easily solve to give us our solution: y =18.
Hopefully, this has cleared up a bit how BIDMAS can be used to work through a complex equation without getting confused or making mistakes.
Other hints and tips about BIDMAS
Over the last few years, an equation has been circling Facebook and Twitter that has caused a lot of arguments. Take a look at it: 8 ÷ 2(2 + 2) = y. Some people think that y = 1, while others think y = 16. We can use BIDMAS to help us to find out which answer is correct.
First, we perform the operation within parentheses. This leaves us with: 8 ÷ 2(4) = y.
Then, we perform the division. This leaves u with: 4(4) = y.
When a number comes before a set of brackets, this means that we must multiply that number by whatever is in the brackets. As such, we must perform 4 × 4, which leaves us with y = 16
Why, then, do some people think that the answer is y = 1? The problem comes at the last step. Because this equation leaves out the multiplication symbol, people don’t see this operation as a normal multiplication just like any other. This leads to a confusion whereby the multiplication is performed before the division, which goes against the BIDMAS rules we looked at above. It is important to recognise this way of writing multiplications so that you don't make the same mistake in your own work.
Sometimes when studying science subjects, especially physics, you might be asked to formulate your own equations using information provided to you along with whatever equations are involved in the scientific theory that you’re studying. These equations can often involve multiple different operations. As such, you can be easily led into the kind of BIDMAS problems that we’ve looked at so far. One helpful way to avoid this is to simply put all operations in brackets. As brackets always have priority in BIDMAS, you won’t have to remember the other order of operations when dealing with equations.
So, for example, instead of writing ‘y = 4 × 10 ÷ 5 + 2’, you could write ‘y = (4 × (10 ÷ 5)) + 2’. Doing this will make it clear which order you must perform the multiplication, division, and addition in; simply by looking at the equation. In this way, you won't have to try and remember the order of operations from memory in stressful situations where other considerations are more important.
Don’t be scared of brackets
Formulating and solving equations which contain multiple operations can sometimes lead students into easily avoidable confusions. The BIDMAS rules outlined here provide a simple guide which can help students to break down these complex equations and to solve them in the right way. These problems can catch out students particularly when they’re forming and solving equations in science exams, where the order of operations is not their primary concern. As such, using lots of brackets to break up these equations and to make visible the order in which you have to perform operations can be a real help.
Explore resources available on studysquare.co.uk for other helpful hints and tips for successfully navigating the world of maths and science. Specifically for BIDMAS visit:
Logic Enthusiast is an independent writer and is studying for an MA in Philosophy at the University of Edinburgh. He is particularly interested in Logic and the philosophy of science.