Sometimes in maths, you’ll find a question that you look at, and it just baffles you how you’re supposed to get to the answer. This could be because it uses symbols that you don’t recognise, or it could be because the alphabet has been thrown in there.
But sometimes, you recognise what all of the numbers and the symbols mean, yet you still have no clue how you’re supposed to approach the question. For example, if there are multiple sums that you need to do in one.
What is the result of 5-5×5+5?
If we take 5-5×5+5, the answer is -15. But to get to this answer, you need to understand the rules of BIDMAS.
BIDMAS: How 5-5×5+5 is calculated
BIDMAS might sound like something a cockney might say when he’s not in a good mood, but it’s a rule that helps us to understand how we should approach sums with more than one sum in them.
It stands for Brackets, Indices, Division, Multiplication, Addition, Subtraction. By approaching the sum using BIDMAS, we can see that you must always do division before subtraction, even if subtraction is the first symbol within the sum.
If we were to ignore BIDMAS and just work left to right, the sum would be like this.
As you can see, this does not give us the correct answer.
BIDMAS, however, is not perfect, as there will be some circumstances where you need to avoid it to get the right answer.
Let’s take a new sum, 1-2+4
If we were to follow BIDMAS to the letter, it would go like this…
1-2+4= 1-6= -5
If you were to type the original sum into a calculator, you would see that the answer is actually 3.
The issue is not BIDMAS, the problem is how I have written it. The correct way to approach multifunction sums would be by using BI(DM)(AS).
Work from left to right if the sums contain only division and multiplication or only addition and subtraction.
Why the 5 times tables are so easy
I can remember being at primary school many years ago and learning my times tables. I remember the feeling of dread whenever the teacher announced we would have a surprise times tables quiz.
There are some which I could not get my head around, like the 7 times tables. Some I started off needing my fingers but quickly learnt them off by heart like 3s and 4s. Others I just doubled another times tables, like the 6 and 7s.
With the nines there were loads of tips and tricks.
But one of the easiest was the 5. Not only did it have a nice rhythm to it, but every number ended in either 5 or 0.
Step One: 5×5
But for now, let’s get back into 5-5×5+5. And we’ll be tackling this using the rules of BI(DM)(AS).
Therefore, the first thing to do is to find out 5 times 5.
Most of you will already know the answer to be 25.
If we want to overcomplicate things for the hell of it, we can say that 5×0.5= 2.5.
And 2.5×10 is 25.
We could also say that 52 is 25. But there really is no need to get into all of that when you know that 5×5 is 25.
Step Two: 5-25
The sum is now 5-25+5.
If we were to use BIDMAS, the answer would be 5-25+5=5-30=-25
Since this sum only has addition and subtraction, we should instead just answer the sums from left the right.
Therefore, the first sum should be 5-25. This might look scary as we’re taking a bigger number away from a smaller number, but it’s really not too bad.
If we take 5 away from 5, we’ll get nothing. Take another 20 away from that, and we’re left with -20.
Step three: -20+5
So now, the final sum which we need to figure out to get the answer is -20+5.
I’m sure that many of you will know automatically that this will give you -15. There may be some of you who need to use your fingers to figure this out (I shall neither confirm nor deny if I am one of them).
If you’re still confused, think of it this way.
You’re in debt by $20, and I was to put $5 into your account, you are now in debt by only $15.
BIDMAS in the real world
As with most things in maths, when I was 13, I used to think that this is all going to be pointless rubbish that won’t serve me any use once I finish my GCSEs. But I was wrong.
Using BI(DM)(AS) can be essential for calculating income vs spending, or profits.
Let’s say I spend $2 on a bottle of juice, which can cover 4 ice lollies. I sell the Ice lollies for $1 each. 2 people give me a tip of 50cents, but one wants a refund.
I want to figure out my profit.
Writing this as a sum would be $1×4+$0.5×2-$1-$2
This would turn into $4+$1-$1-$2
Which would then become $2.
I have made a $2 profit from my ice lollies.
Let’s take a quick look at some more examples.
As you can see from all of the examples above, we have used the rules of BI(DM)(AS) to get to the correct answer. Sometimes, you might find a sum that uses brackets or indices, if you do, you will first need to figure out the sum of the brackets, and then the indices.
Multiplication and division first, working them out from left to right.
Addition and subtraction next, again, figuring them out from left to right.
When looking at 5-5×5+5, many of you may feel overwhelmed. Which is odd because 5 is a very easy number to work with and you know how to subtract, multiply and divide. You just don’t know what order you need to do it.
BI(DM)(AS) stands for brackets, indices, (division, multiplication), (addition, subtraction). And it’s the order you should do the maths in when more than one symbol comes up in the same equation.