There's only 1 set of rules, and 2 sets of people - those who follow the rules and those who don't.
SmartmanApps
joined 1 year ago
6 / 2 * 3 into 6 * 3 / 2 (note that I moved the division with the 2)
And note that it doesn't work if the multiply was an addition. e.g. 6/2+3=6 but 6+3/2=7.5. Multiplication and division are both binary operators, and you can't move them around unless you also move the term to the left with it. i.e. 6/2+3=6. 3+6/2=6.
Just remember that left to the six is an “imaginary” (don’t quote me ^^) multiplication
No, to the left of the 6 is an actual plus sign, but we don't write plus signs if it's at the start of an expression. +6 and x6 aren't the same thing at all (and, since x is a binary operator, you couldn't write just x6 anyway - there would have to be a term to it's left). No expression ever starts with x6.
That’s not really possible with multiplication because “/2” is not a valid notation for “1/2”
It's not a valid notation for multiplication either - both multiplication and division are binary operators and must be written with 2 terms.
Semi-related: something in me wants to read that as 6 / (2*3)
100% related actually, since that's the actual next line of working out. i.e. you cannot remove brackets unless there is only 1 term left inside, a mistake which those who have prematurely removed brackets have made and ended up with the wrong answer (because it flips the 3 from being in the denominator to being in the numerator).
when you read a paper that contains math, you won’t see a declaration about what country’s notation is used for things that aren’t defined
Not hard to work out. It'll be , for decimal point and : for division, or . for decimal point and ÷ or / for division, and those 2 notations never get mixed with each other, so never any ambiguity about which it is. The question here is using ÷ so there's no ambiguity about what that means - it's a division operator (and being an operator, it is separating the terms).
Probably a cop-out from the teacher
No, that's an actual convention of Maths, to make sure people (who don't know better) obey the actual rule of left associativity.
Neither is ambiguous. #MathsIsNeverAmbiguous ab=(axb) by definition. Here it is referred to in Cajori nearly 100 years ago (1928), and literally every textbook example quoted by Lennes (1917) follows the same definition, as do all modern textbooks. Did you not notice that the blog didn't refer to any Maths textbooks? Nor asked any Maths teachers about it.
you can’t prove that some notation is correct and an alternative one isn’t
I never said any of it wasn't correct. It's all correct, just depends on what notation is used in your country as to what's correct in your country.
It’s all just convention.
No, it's all defined. In Australia we use the obelus, which by definition is division. In European countries they use colon, which by definition in those countries means division. 1+1=2 by definition. If you wanna say 1+1=2 is just a convention then you don't understand how Maths works at all.
What you are saying is like saying "there's no such things as dictionaries, there are no definitions, only conventions".
Maths is pure logic. Notation is communication, which isn’t necessarily super logical. Don’t mix the two up.
Don't mix up super logical Maths notation with "communication" - it's all defined (just like words which are used to communicate are defined in a dictionary, except Maths definitions don't evolve - we can see the same definitions being used more than 100 years ago. See Lennes' letter).
Yep, that's the "quote" in the blog, but if you click on the link not only is it not on page 21, it's not in there at all. i.e. the quote - if it even is a quote - is out of context.
It was incredibly thorough and well researched
It never mentions the 2 relevant rules of Maths, nor any textbooks, nor speaks to any Maths teachers. You can find all those thing here
That’s the correct answer if you follow
...the rules of Maths.
They're arguing about whether Distribution is Multiplication or not. Spoiler alert: it isn't, it's Brackets.