#mathsmonday

1/6 This week for #MathsMonday I'm going do - again - a #mathematics order of operations proof, but the simple version. 🙂 Last time there were people who were claiming that + and - "can be a binary operator", and I was actually addressing that, but in the process proved that #Maths binary operators have to be solved before #Math unary operators, thus proving the order of operations rules, but this time an arithmetic approach, based on the operator definitions...

1/5 #MathsMonday #Maths #Math This week a commonly-forgotten rule of #Mathematics - because we usually skip these lines of working out and go straight to the solution - when we substitute a value for a pronumeral, the value goes in brackets. i.e. if a=3, then 2a=2(3), not 23, because 2a=6, not 23. We can see this explicitly demonstrated on page 36 of Modern Algebra https://archive.org/details/modernalgebrastr01dolc_2 If showing full working out (which Modern Algebra skips) then the next step is to apply...

1/5 #MathsMonday I'm coming back to a point I've covered before, but this time adding #Mathematics textbooks for the sake of completeness, that being the history of what Division meant in #Maths, with emphasis on what it means now in #Math Up until at least the 17th Century everything that followed a division symbol was in the Divisor. We can see that in Teutsche Algebra (1659), on page 76, where 7÷GG+1 means 7÷(GG+1)....

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...

1/4 #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...

1/6 #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...

1/9 #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...

1/7 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"...

Thread index https://dotnet.social/@SmartmanApps/110897908266416158 Before I say what it is, I am NOT posting this as clickbait (which is how it's often used)! 😂 I'm posting this as a Maths teacher who knows this topic inside-out and wants to help people to understand it better. There are MANY mistakes that people make and get the wrong answer, and I'm going to cover them in bite-size chunks each week for a few weeks So 8÷2(1+3)=? What is the answer (bonus: and WHY is it the answer)? #Maths #Mathematics #MathsMonday

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...

1/6 I have a #MathsMonday #FactFriday cross-over event post for you this week 🙂 The #fact is that #Mathematics is universal. We may use different notation in different countries, but the underlying #Maths is the same everywhere. i.e. there is nothing "arbitrary" about #Math I saw someone question if there might be "different" Maths somewhere else in the universe. No. If I have 1 thing, and I get another thing, I now have 2 things. i.e. 1+1=2 (or your country's notation)...

#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)...

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/x #MathsMonday I'm coming back to #Mathematics order of operations (hopefully) one last time, just to flesh it out with some more #Maths textbook references, for those who want it (having only initially given one in each case). Not going overboard, just 4 #Math textbook screenshots per post (since Mastodon only allows 4 pics per post, that's a good number to finish it off with). I may come back in future, if some particularly good ones come along, hence unknown post count for now...

@bemmesr@mathstodon.xyz you don't want to pay attention to @SmartmanApps@dotnet.social on this. Check out any of his "#MathsMonday" pinned posts that have replies from others and you'll see what I mean. In this case, you are right that you *could* just use a single variable that is equal to a polynomial expression, but this is missing the point of the technique: when we create the placeholder variables A, B, etc, there is in fact an assumption that these are not dependent on x (or whatever the unknown is), and this assumption makes the technique work, together with the assumption that the equation you set up holds for all values of x. Because they don't vary with x, if you know that, for example, Ax + B = 3x + 5, it must be that A = 3, B = 5. For particular values of x, you could pick other values of A,B, but these are the only ones which work for all values of x. Unless, that is, A and B may themselves depend on x! For example, A=5/x, B=3x would work if they could. In general it is better to make the dependencies of variables on other variables explicit, by using functional notation, so that "A" always stands for an independent variable, with "A(x)" meaning some quantity which depends on x. But this is not how mathematics is taught in practice, so you end up with these situations where you may not realise what all the assumptions are. Sorry you had to read the charlatan's answer before getting a proper explanation.