Maths question, apparently gone viral ion 2019

[67Dino]

Gandahar said:

OK, the solution is that it can be either 1 or 16 using mathematical rules due to the equation being badly written so being ambiguous.

Note that PEDMAS or PEMDAS or BODMAS or BIDMAS is not a mathematical rule, it's a mnemonic and prone to misinterpretation. So it is no wonder people are getting that wrong.

The reasoning for 1 and 16 both being correct --

The equation of 8÷2(2×2) = ? can obviously be reduced first without any argument to

8÷2(4) = ?

and then again

8÷2×4 = ? or 8 / 2 × 4 = ?

This where the problem starts and it is not the maths rules but how people have learnt how to do it. People may grasp at

1. It is always division first.
2. It is done left to right.

Both are wrong. M and D do not have priority in maths, neither are they done left to right, unlike Add and Subtraction which is. PEDMAS or PEMDAS or BODMAS etc is not a maths rule. It's a memory aid which is being used wrongly.

With 8÷2×4 or 8 / 2 × 4 there is not enough information as written to decide which operation to do first as no priority. If you choose one way you get one answer, the other way the 2nd answer.

The equation is badly written. It can be better written on 2 lines using / or on one line using parentheses, ie

8÷(2×4) or (8÷2)×4


8
-------
2 × 4

or

8 × 4
---
2

No doubt it will pop up again in a few years time using different numbers ( to protect the innocent )


PS Note that PEDMAS is better written P -- E -- DM ( MD) -- AS (SA) left to right


if you wish to use it

Edited by Gandahar on Friday 2nd August 15:01

^This
In reality, anyone writing an equation like this whilst trying to solve something would either know the context or would have made it clearer to themselves. Personally, if I ever wrote this it would be because I wanted to multiply the 2 by the brackets first, as otherwise I’d have written it with the 8 divided by 2 in brackets.

This sort of ambiguity is equivalent to writing “Fruit flies like a banana”. Technically it is ambiguous whether it describes the projectile properties of fruit or the eating habits of drosophila. In reality, no one writing about either would write the sentence without context.

[otolith]

Gandahar said:

otolith said:

This has been going on for ages. It's a classic clickbait trick, pick something that people will argue about. That division operator is the problem - it's poorly defined. Grown-ups doing mathematics don't use it, it's for children doing arithmetic.

That's wrong actually.

Wrong in that it's the division symbol used that it is just clickbait. Instead think of it as a way to correct your maths assumptions. You are correct that it is an old issue and it is poorly defined.

This was all over social media two years ago. It's a classic way to drive clicks - find something ambiguous that people will have strong opinions on and watch the clicks roll in.

The correct answer is that if you want to write an equation, write it properly, not how an 8 year old would do it!

[Gandahar]

otolith said:

Gandahar said:

otolith said:

This has been going on for ages. It's a classic clickbait trick, pick something that people will argue about. That division operator is the problem - it's poorly defined. Grown-ups doing mathematics don't use it, it's for children doing arithmetic.

That's wrong actually.

Wrong in that it's the division symbol used that it is just clickbait. Instead think of it as a way to correct your maths assumptions. You are correct that it is an old issue and it is poorly defined.

This was all over social media two years ago. It's a classic way to drive clicks - find something ambiguous that people will have strong opinions on and watch the clicks roll in.

The correct answer is that if you want to write an equation, write it properly, not how an 8 year old would do it!

The first instance was in 2011.

It's still not clickbait though because that does not expand your knowledge, this does.

[Abbott]

tribalsurfer said:

MECHENG84 said:

I'm not sure this is the right way to solve this equation and happy for somebody to point out the error of my ways, but I sometimes like to give a real world scenario to these and see what the result is. 8 Footballers run out on to the pitch and divide themselves in 1/2 so they can have a 4 vs 4 match. They are each wearing 2 football boots and 2 gloves, how many gloves and football boots are there in total?

8/2(2+2) = well in the scenario above it'd be 16.

You are both the giver of a good example and more importantly correct.

Feeling dim but in the story above, each player has 2 boots and 2 gloves so 4 items to each player. There are 8 Players therefore the answer is 32 items.
Happy to be shot down

[Gandahar]

ash73 said:

It's not ambiguous at all.

1. No operator implies multiplication, e.g. 2a means 2 x a
2. Parentheses are needed when there are two numbers, e.g. 2 x 4 can be written as 2(4) but not 24

Similarly, 2(2+2) = 2(4) which means 2 x 4

Therefore 8 / 2(2+2) = 8 / 2 x 4 = 16

Wrong. Parenthesis are needed also when there is an operand, to tell you which order to do them in.

What order do you do this in

8÷2×4 ?

given the mathematical rule that neither division and multiplication has any priority ? You chose to do the division first to get 16 .. why ?

You have two choices to do this badly written equation, one gives you 1 and one gives you 16.

If written 8÷(2×4) or (8÷2)×4 with parenthesis there is no ambiguity.

[John_S4x4]

MECHENG84 said:

I'm not sure this is the right way to solve this equation and happy for somebody to point out the error of my ways, but I sometimes like to give a real world scenario to these and see what the result is. 8 Footballers run out on to the pitch and divide themselves in 1/2 so they can have a 4 vs 4 match. They are each wearing 2 football boots and 2 gloves, how many gloves and football boots are there in total?

8/2(2+2) = well in the scenario above it'd be 16.

I think you're right, we need a real world example....so you know 8 young ladies needing a lift to your stag-do and you have 2 cars which are 2+2's , like a BMW M3. How many car seats does each lady get and will she end up, sitting on my lap ?

Edited by John_S4x4 on Friday 2nd August 21:52