The Written Podcast: BIDMAS Vs PEMDAS

You may have already seen this math problem circulating the internet as of late:

8 / 2 (2 + 2) = ?

I was pitched this question by a friend who tasked me to solve it, and so I did, using these specific steps:

2 + 2 = 4.

8 / 2 = 4.

4 * 4 = 16.

So the answer is 16.

I used the BODMAS method. Brackets, Indices, Division, Multiplication, Addition, Subtraction. By following that rule, you can’t go wrong when solving these types of math problems, only if you calculate the individual sums wrong will you get the wrong answer.

This was when my friend revealed there is another way of solving this problem. Sure, there may be many ways you can solve this problem; with maths, with some equations, there are multiple ways you can reach the same answer. However, my friend then revealed that you wouldn’t get the same result, but the other way is perfectly valid. I was confused. He explained to me the act of using PEMDAS. Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. PEMDAS swaps the two stages of multiplication and division around, resulting in an entirely different answer.

I went ahead and calculated the question using the PEMDAS method:

2 + 2 = 4.

2(4) = 8.

8 / 8 = 1.

So the answer is 1.

He said the method is perfectly valid, and by researching that method, I discovered it actually was a used method a hundred years ago. Upon further research, I unfortunately didn’t come up with a time frame when BIDMAS started coming into effect, but that PEMDAS was used for quite a while beforehand. Modern calculators will interpret that equation by today’s accepted method, and to make the computer believe the answer is 1, you’ll actually have to change the question by adding an extra Bracket. 8 / (2(2 + 2)) = 1. For modern calculators to accept that the answer to that question is 1, you’ll have to change the question, which then, logically stats it is a different question. What I did find out via my research is that BIDMAS started fading into view around about the same time as computers did. Does this mean that computers are wrong? Have we accepted the method they showed us as a way to slowly conquer our world one mathematically wrong answer at a time until it’s too late? Er… no. Or at least I like to think so anyway.

If you insert that equation into a computer, its interpretation is thus:

(8 / 2) (2 + 2) = ?

By following that method, the answer will always be 16. A computer would separate the equation into smaller questions, then calculate the answer.

8 / 2 = 4.

2 + 2 = 4.

4 * 4 = 16.

So the answer by a modern day computer is 16.

There is an old episode of QI where they brought up an equation comprised of symbolic logic. Bertrand Russell set out to prove that mathematics made sense. He discovered there were too many paradoxes and illogical solutions regarding his modern day interpretation of maths, and so he decided to write a book proving that maths did in fact make sense. The symbolic logic equation which appeared on the big screens behind the panellists was the one which proved that 1 + 1 = 2.

David Mitchell’s response was one of an understandable reaction, stating that it was a bit late within the 20^th century to prove that 1 + 1 did indeed make 2, because what would’ve happened if Bertrand discovered that it didn’t?

My reaction regarding the BIDMAS and PEMDAS debate was synonymous to that of David’s concerning the very different answers and that we have a lot riding on the specific method of BIDMAS. What happens if we discover that BIDMAS isn’t actually the correct way but instead another way is? What the heck would happen to our society as we know it?

You can actually get a third answer from this equation if you ignore both methods but instead just go straight across from left to right:

8 / 2 = 4

4 * 2 = 8

8 + 2 = 10.

So the answer if you ignore the equation’s layout is 10. Will that soon become the next accepted method of calculating the equation?

Three different answers to one equation. Two of which were perfectly acceptable methods so why not logically accept the third way and state the answer is also 10. This equation has turned into an engineer’s nightmare. If they were designing a building, one will build one that’s 16-metres-tall, the other will build one 1-metre-tall and the third will build one that’s 10-metres-tall; and now we’ve got that classic joke where “three engineers walk into bar…” Is the reason the Burg Khalifa so tall is because they used BIDMAS instead of PEMDAS?

Mathematics is supposed to be fixed. There may be different methods upon solving the problem, but usually the answer is the same, and the other ways which result in a different answer is tossed to one side. But it now appears it’s in a constant state of flux. It changes much like language does, every now and again. We may have accepted BIDMAS as the accepted method, but according to those who were living a hundred years ago, PEMDAS was also accepted and they may have completely disregarded BIDMAS as the wrong way of doing things. Makes you wonder if BIDMAS will no longer be the correct method but instead another one will be used, resulting in a completely different answer, and society as we know it will change forever, for better or for worse.

All I know at this present time is BIDMAS must be the correct method because if it’s discovered to be wrong, I wouldn’t want to be living in the resulting society. It’d probably be a little apocalyptic… may be a little over-exaggerated, or not… who the heck knows anymore…

Thanks for reading

Antony Hudson

(TonyHadNouns)