Why * and / parts of a sum must be done before + and - AKA: Not all calculators follow the rules and you can't just go left to right

An easy explanation why * and / come before + and -

Here is a story  :

I went to the doctor and he says 

“That’s a bad case of mathology I want you to take three blue pills, four red pills and one yellow pill.”

"Wow that’s a lot of pills" I replied. "Must be a serious condition." 

“Let me add that up  3 * Blue + 4 * Red + 1 * Yellow = 8 pills to take.”

Next week I go to the doctor and he says :

“Things are looking better and I want you to take the same but zero yellow pills.”

Try this on your calculator .......

    Blue * 3 + Red * 4 + Yellow * 0  is the sum ....... 

    1 * 3       + 1 * 4     +  1 * 0  =  ?

 Some older calculators will says I don’t have to take any pills now ...... but is that what the what the doctor ment ?

Math rules say that all the multiplications must be done before you start doing any of the additions when you have a mixed sum.

    1 * 3   + 1 * 4  + 1 * 0 

after the multiplication parts are done this becomes :

   3 + 4 + 0 = 7 pills.

Which is what the doctor intended. In a longer multi part sum the order in which the sub-sums are done is vitally important.  * and / parts of a sum must be done before + and -   

The same rules, explained differently, are available Google BODMAS  or see image below.