BODMAS

So we see questions like this a lot online...

3 - 4 * 7 + 5 = ?

So what's the answer? I see a lot of people aren't being taught, or don't pay attention, to maths rules.




I can't say I'm actually any good at maths. I just know enough to aid me in my generation of 3D visuals. I can explain the few things I was taught, through the years, to understand how to answers questions like that...

LTR - The initial rule

At an early point in my mathematical understand I was taught, what I was told, was the left-to-right (LTR) method.

This essentially means executing things from the left to the right, in the order you find them...

3 - 4 * 7 + 5

Breaking it down

3 - 4 = -1

=> -1 * 7 + 5

-1*7 = -7

=> -7 + 5 

-2

Now, this is a perfectly valid way of executing these things. For now...

MDF - Slightly more complex rule

The nest thing I was taught about was "Multiplication and Divison First" (MDF).

As it implies, it's saying to do multiplication and division first.

So again

3 - 4 * 7 + 5

4 * 7 = 28

=> 3 - 28 + 5

But, now, there is nothing in this rule what to do with addition and subtraction. However, due to the orders of things being learnt, it implies to carry on left-to-right now...

3 - 28 = -25

=> -25 + 5

=> -20

So, a totally different answer.

BODMAS - Finally

(or BEDMAS or PEDMAS )

At the time of learning MDF, we weren't being taught about other things, like brackets and exponents. BODMAS was taught when this happened...

Brackets

Order

Division 

   & Multiplication

Addition 

   & Subtraction

note: The B can be Parentheses. The O can be Exponent. 

These 6 letters define the 4 levels of importance to an equation. The 'Precedence'.

The only thing it doesn't say is what to do when everything has the same precedence is what to do? Without knowing anything else what is there? Default to the LTR method.

What I have seen sometimes is the DMAS being executed in order, Division, Multiplication, Addition, Subtraction...

3 - 4 * 7 + 5

=> 4 *7 = 28

3-28+5

=> 28+5 = 33

3 - 33

=> -30

So, different answer again. It's not entirely wrong, except this is a different answer that others will get.

The problem being, like I said, people follow the words of BODMAS, but not the meaning.

Division and Multiplcation

Addition and Subtraction