1/9
#MathsMonday
I have (unless someone comes up with yet ANOTHER way to get this wrong, which at this point wouldn't surprise me anymore!) finished covering #Math order of operations and will wrap this topic up with a summary of all relevant #Mathematics rules

First a reminder that the index for this thread is at https://dotnet.social/@SmartmanApps/110897908266416158, where these #Maths issues are discussed in depth

1. a pronumeral is literally a substitute for a numeral, and as such all arithmetic rules apply to them...

1/2
One more #MathsMonday post about order of operations - a short one this week(!) - and then I'll do a summary next week. This one is mainly just to address some objections I've seen to the correct answer, which amounts to "but that would mean a÷bc=a÷b÷c, and that can't be right!". That's exactly right actually(!), and is a #Math property that we use in #Maths things like factorising.

Let's illustrate this with an example...

1/11
Well, I THOUGHT I was nearly done with this #MathsMonday topic. This week ANOTHER thing that the "#Mathematics is ambiguous" lot don't understand turned up - #Maths Expressions and #Math Unary/Binary operators. Today we'll prove the order of operations rules #MathsIsNeverAmbiguous

We've discussed before that Terms consist of pronumerals and/or numbers. Expressions consist of Operators (+,-,*,/) and Operands (Terms)...

1/12
I'm essentially at the end of my #MathsMonday series on #Mathematics order of operations (might tidy up some loose ends next week, maybe do a summary), but what I wanted to do this week was address some #Maths #textbook #authors and #Math #Teachers as I have seen issues with #Education also. i.e. as much as many people have misremembered what they were taught, I've seen cases of incorrect things being taught to begin with also...

1/10
This week for #MathsMonday I'm going to talk about #calculators, in particular the current topic of #Mathematics order of operations (which I am nearly finished with now), and e-calculators (I'm looking at you #Developers #Programmers).

It's important to know where brackets go in #Maths expressions, and after last week's topic I ran a follow-up poll https://dotnet.social/@SmartmanApps/111145907574869556 to see how many people could remember the #Math FOIL acronym from High School, because I sensed a deeper issue...

1/9
#MathsMonday
Today I'm going to talk about adding/removing brackets, for 2 reasons...
- people prematurely remove them
- people adding them incorrectly
In #Mathematics we have many things which are the opposite of each other - add/subtract, multiply/divide, factorising/expanding - and so it is with brackets in #Math also. This is because if someone has put together an expression from a number, the rules of #Maths have to make sure we follow the exact opposite steps to get the same number...

1/6
#MathsMonday
I continue to see people who say that in #Mathematics ab=a*b, and thought of a good #Maths example to illustrate why ab is a single #Math Term (i.e. ab=(a*b))...

Let's say I was 2 metres tall (just for the sake of using whole numbers in the example). We write that as 2m - in this case m is short for metres, but it also looks like an algebraic term, right? So let's say m is a pronumeral, and in this case m is equal to 1 metre. In other words in both cases, m is the units...

1/4
#MathsMonday
1917 (iii) - Terms included in denominator
My investigation into (alleged) changes in #Mathematics rules in 1917 started with claims that the number of terms included in the denominator of a #Math expression was changed in 1917 (though I've yet to find any actual evidence of this - let me know if you have a reference for it). Some mentioned Lennes' letter, yet his letter says nothing at all about this! For now, let's assume it's true and see what that would mean for #Maths...

1/7
#MathsMonday
1917 (ii) - Lennes' letter (Terms and operators)
I've seen many refer to https://www.jstor.org/stable/2972726 as a change in #Mathematics precedence rules, and yet nothing at all actually changed! It does show that 100 years ago though, even then there were people #LoudlyNotUnderstandingThings #Math terms and rules!

On page 93 he says "it is agreed that each symbol applies only to the term immediately following it" which shows he understands #Maths Terms and Left Associativity...

1/6
#MathsMonday
1917 (part 1) - Left Associativity
I have seen many people who argue about this #Mathematics issue that refer to changes in 1917, and I started to research it this week. The #Maths change I thought was made, I have not been able to find any reference for it, and that is about /2(1+3) vs. /2*(1+3). Apparently in pre-1917 #Math the latter was also considered to be a single term (in the denominator) but now is 2 terms. If anyone has a reference for that then please let me know...

1/7
This week for #MathsMonday we are going to debunk the "implicit multiplication" (IM) claims (and also look at the mnemonics). I say claims, because there is actually no such thing as IM in #Mathematics. I find invariably the people who say there is have forgotten The Distributive Law (TDL) and/or Terms, but most often both! As we have already seen, these are both rules of #Maths, taught in many #Math textbooks, so that right away debunks any claims that "there is no convention in Maths"...

@denki @fortyseven @clement_la_baleine @schmutzie
2(2+2) is a single, factorised term, which must be expanded according to The Distributive Law. For full coverage of everything read my (still in progress) #MathsMonday thread on order of operations https://dotnet.social/@SmartmanApps/110807192608472798
TL;DR Google is wrong

1/4 #MathsMonday
Now we'll tie the previous 2 #Math rules together and see why #Mathematics order of operations means #MathsIsNeverAmbiguous provided you #DontForgetDistribution

Start with 1, also the result of any number divided by itself, so let's write 8/8

We can factorise, and 8 is even, so let's take out a 2, 8/2(4)

We can rewrite the stuff in brackets without changing the answer, so let's write 8/2(1+3)

I started with 1,so we have to make sure the rules of #Maths get us back there...

#MathsMonday week 2, Terms.
Simply put, in #Mathematics Terms are separated by operators and joined by brackets. The most common example is 2a=(2*a). This makes it simpler to write fractions. e.g. 1/2a rather than 1/(2*a). That also means 1/2a isn't mistaken as half a, which would actually be written as a/2. Notice in the latter that the a is to the left of the division, which means it's in the numerator, and vice-versa for the former (more about this aspect of #Maths #Math later, but first)...