How to apply BODMAS correctly in the given problem

[chwala]

Homework Statement

How do we apply BODMAS to this problem; this follows a discussion that i had with my colleague...

let me come up with the problem;

$4\div 6(4+1)$

Relevant Equations

Bodmas

$4\div 6(4+1)$

Now we both agreed on 1st step that is applying 'B';

$4\div 6(5)$

Now from this step; my understanding is that we apply 'O' that is 'Of' implying Multiplication.

$4\div30=\dfrac{4}{30}=\dfrac{2}{15}$

On the other hand;my colleague was of the thinking that 'O' just means order and has no implication whatsoever and therefore;

$\dfrac{4}{6} ×5=\dfrac{20}{6}=\dfrac{10}{3}$

Which is the correct approach?

Further to this; what of BIDMAS and PEDMAS? In my understanding, BODMAS is the form that is generally acceptable in Maths.

Cheers!

 

[pbuk]

• The $\div$ symbol is not used in "real" mathematics.
• Division and multiplication have the same "rank" and so are carried out left to right: the expression can be rewritten $\frac 4 6 (4 + 1) = \frac {10}3$.
• "O" does not feature in this expression.
• The acronyms BODMAS, BIDMAS and PEDMAS are equivalent and none is more "generally acceptable" than any other. To be clear, the first letter represents the synonymous terms "Brackets" and "Parentheses" and the second letter the equivalent concepts of "Order", "Indexation" and "Exponentiation".
• The order of arithmetical operations is well defined and does not depend on any acronym. These acronyms are used by children to help them learn how arithmetic works, not the other way round.
• For the avoidance of doubt, the word "order" has a different meaning in each of the two previous points: in the immediately preceding point it is synonymous with "sequence".

I don't understand why we are discussing this when you have other threads asking about partial differentiation?

 

[Gordianus]

Both my Casio and HP calculators say the answer is 10/3

 

[chwala]

• The $\div$ symbol is not used in "real" mathematics.
• Division and multiplication have the same "rank" and so are carried out left to right: the expression can be rewritten $\frac 4 6 (4 + 1) = \frac {10}3$.
• "O" does not feature in this expression.
• The acronyms BODMAS, BIDMAS and PEDMAS are equivalent and none is more "generally acceptable" than any other. To be clear, the first letter represents the synonymous terms "Brackets" and "Parentheses" and the second letter the equivalent concepts of "Order", "Indexation" and "Exponentiation".
• The order of arithmetical operations is well defined and does not depend on any acronym. These acronyms are used by children to help them learn how arithmetic works, not the other way round.
• For the avoidance of doubt, the word "order" has a different meaning in each of the two previous points: in the immediately preceding point it is synonymous with "sequence".

I don't understand why we are discussing this when you have other threads asking about partial differentiation?

Just wanted to be clear on this...thanks for your insight...children do have these kind of questions with division and brackets involved...I simply wanted to know on which part comes first (in particular the part mentioned on my post)...In my childhood I was taught of 'O' ie 'of' implying multiplication. .. looks like I will need to revisit my understanding on that part...I will nevertheless take into account your contribution. Thanks!

 

[Steve4Physics]

On the other hand;my colleague was of the thinking that 'O' just means order and has no implication whatsoever

Many decades ago, I was taught that the ‘O’ in BODMAS stood for ‘of’. This then allowed the teacher to present us with expressions such as $\frac 45$ of 10 +20 (which is of course equal to 28, not 24 ).

But times change (pun intended).

 

[chwala]

Many decades ago, I was taught that the ‘O’ in BODMAS stood for ‘of’. This then allowed the teacher to present us with expressions such as $\frac 45$ of 10 +20 (which is of course equal to 28, not 24 ).

But times change (pun intended).

That has all along been my understanding...i.e $a(b)$ being equivalent to $a$ of $b$... hence my post.

...keying the values in different calculators gives the two diverse values as answers...

 

[Steve4Physics]

That has all along been my understanding...i.e $a(b)$ being equivalent to $a$ of $b$... hence my post.

...keying the values in different calculators gives the two diverse values as answers...

Maybe you are working with very old textbooks (or very old teachers)!

Also, maybe there are regional differences in usage (i.e. from country to country).

If there is a risk of ambiguity, brackets can be used.

 

[pbuk]

...keying the values in different calculators gives the two diverse values as answers...

That's because one of them doesn't have ANY operator precedence, it just performs operations as they are entered. That is the difference between a so-called "scientific" calculator and ones that are given away as toys for adding up your shopping.

https://www.calculator.org/articles/Precedence.html

 

[pbuk]

Maybe you are working with very old textbooks (or very old teachers)!

But in 2022 we have the internet.

Also, maybe there are regional differences in usage (i.e. from country to country).

Regional differences in how arithmetic works? No, people can be wrong anywhere.

 

[DrClaude]

$4\div 6(4+1)$

I'm getting tired of being these in my social media. This is mathematically ambiguous and there is no right answer.

 

[Steve4Physics]

But in 2022 we have the internet.Regional differences in how arithmetic works? No, people can be wrong anywhere.

There are no issues about how arithmetic works! The (minor) issue is simply the meaning of the 'O' in 'BODMAS'.

With the dubious advantage of age, I would say there has been an actual change in the meaning of the 'O in 'BODMAS' over the decades.

In my youth 'O' represented 'of'. I remember having to work out silly sums such as $\frac {5}{240}$ of £11 10s 7d + 7guineas (which is probably only intelligible to elderly UK readers).

A quick search shows that nowadays, 'O' represent 'other' or 'order'.

I suspect that the changeover occurred in the 1970s here in the UK. Not sure about other countries.

And no idea what is taught in non-English speaking schools.

 

[PeroK]

I'm getting tired of being these in my social media. This is mathematically ambiguous and there is no right answer.

Arguments about "order of operations" is one of my pet peeves.