You sneered about 1/ab five minutes ago
Yet again, I have no idea what you're talking about
Troll
says person who can't back up anything they say about Terms with textbook references 🙄
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That’s convention for notation
Nope, still rules
not a distinction between a*b and ab
says person who only read 2 sentences out of the book, the book which proves the statement wrong 😂
a*b and ab both being the product of a and b
Nope, only ab is the product, and you would already know that if you had read more than 2 sentences 😂
You have to slap 1/ in front of things and pretend that’s the subject
"identically equal", which you claimed it means, means it will give the same answer regardless of what's put in front of it. You claimed it was identical, I proved it wasn't.
avoid these textbooks telling you
It kills you actually, but you didn't read any of the parts which prove you are wrong 🙄just cherry pick a couple of sentences out of a whole chapter about order of operations 🙄
They are the same thing. They are one term
Nope! If they were both 1 term then they would give the same answer 🙄
1/ab=1/(axb)=1/(2x3)=1/6
1/axb=1/2x3=3/2=1.5
Welcome to why axb is not listed as a Term on Page 37, which if you had read all the pages up until that point, you would understand why it's not 1 Term 🙄
You poor thing…
You don't know what Maths textbooks say because you were too poor to go to school? I'm sorry to hear that
You can’t keep your own horseshit straight
No idea what you're talking about, again, I've been saying the same thing the whole time
You insist they’re not the same. How?
Not difficult, I already did in another post. If a=2 and b=3...
1/ab=1/(axb)=1/(2x3)=1/6
1/axb=1/2x3=3/2=1.5
Convention saying 1/a(b+c)2 is 1/(a(b+c)2)
There's no such convention, given it would violate The Distributive Law 🙄
By all means, humiliate yourself by splitting that hair
I'll take that as an admission that you're wrong then, given you can't defend your wrong interpretation of it (which you would know is wrong if you had read more than 1 paragraph of the book!) 😂
They’re more than equal
They're not equal at all 🙄
If a=2, b=3...
1/ab=1/(2x3)=1/6
1/axb=1/2x3=3/2=1.5
It’s an identity, which you’d understand
Nope! axb==ab is an identity, which is NOT how it's written, "illiterate fraud" as per your other comment
if you weren’t lying about being a teacher
says person who is lying about what the textbook says 🙄
Illiterate fraud
says person who thinks "means" and "equals" mean the same thing 😂
“a X b is written ab and means a times b.”
Notice that it doesn't say equals, speaking of Illiterate fraud, as per your other comment 🙄
So b * c, which is a product of the variables b and c
Nope. bc is the product of b and c. bxc is Multiplication of the 2 Terms b and c.
according to this textbook
Says person who clearly didn't read more than 2 sentences out of it 🙄
none of the examples on this particular page feature the multiplication symbol ×
and why do you think that is? Do explain. We're all waiting 😂 Spoiler alert: if you had read more than 2 sentences you would know why
That means that the expression bc is just another way of writing b×c;
No it doesn't. it means bxc is Multiplication, and bc is the product 🙄 Again you would've already known this is you had read more than 2 sentences of the book.
it is treated the same other than requiring fewer strokes of the pen
No it isn't, and again you would already know this if you had read more than 2 sentences. If a=2 and b=3, then...
1/ab=1/(2x3)=1/6
1/axb=1/2x3=3/2
this is just a custom
Nope, an actual rule of Maths. If you meant 1/axb, but wrote 1/ab, you've gonna get a different answer 🙄
That should clear up your confusion in interpreting this textbook
says person who only read 2 sentences out of it 🙄
though really, the language is clear:
It sure is when the read the rest of the page 🙄
you don’t dispute that b×c - or b * c - are products, do you
What don't you understand about only ab is the product of a and b?
Elsewhere in this thread you are clearly confused about what brackets mean
Not me, must be you! 😂
They are explained on page 20 of your textbook, where it says that you evaluate the expression inside the (innermost) brackets before doing anything else.
Until all brackets have been removed. on the very next page. 🙄 See what happens when you read more than 2 sentences out of a textbook? Who would've thought you need to read more than 2 sentences! 😂
the “distributive law” is not mentioned, because the distributive law has nothing to do with brackets
And yet, right there on Page 21, they Distribute in the last step of removing Brackets, 🙄 5(17)=85, and throughout the whole rest of the book they write Products in that form, a(b) (or just ab as the case may be).
is not an operation
Brackets aren't an operator, they are grouping symbols, and solving grouping symbols is done in the first 2 steps of order of operations, then we solve the operators.
Thus the expression 3 × (2 + 4) can be evaluated by first performing the summation inside the brackets to get 3 × 6 and then the product to get 1
3x6 isn't a Product, it's a Multiplication, done in the Multiplication step of order of operations.
The textbook then says that it is customary to omit the multiplication symbol and instead write 3(2+4)
It says you omit the multiplication sign if it's a Product, and 3x6 is not a Product. I'm not sure how many times you need to be told that 🙄
again indicating that these expressions are merely different ways of writing the same thing
Nope, completely different giving different answers
1/3x(2+4)=1/3x6=6/3=2
1/3(2+4)=1/3(6)=1/18
You have suggested that you must evaluate this as (2a+2b)² because you must “do brackets first”
Yep
this is not what “doing brackets” means.
Yes it is! 😂
Not what is outside the brackets.
Yes it is! 😂 Until all Brackets have been removed, which they can't be if you haven't Distributed yet. Again, last step of the working out...
Distributing 2 over a+b is not “doing brackets”;
Yes it is! 😂 Until all Brackets have been removed
it is multiplication and comes afterwards
Nope, it's Distribution, done in the Brackets step, before doing anything else, as per Page 21
following your textbook’s instruction to do what is inside the brackets first, this is equal to 2(4)²
Which, when you finish doing the brackets, is 8²
The next highest-priority operation is the exponent
After you have finished the Brackets 🙄
giving us 2×16
Nope. Giving us 8²=64
we now must write the × because it is an expression purely in numerals
Nope! If you write it at all, which you don't actually need to (the textbook never does), then you write (2x4)², per The Distributive Law, where you cannot remove the brackets if you haven't Distributed yet. There's no such rule as the one you just made up
The fact that these two answers are different is because
You disobeyed The Distributive Law in the second case, and the fact that you got a different answer should've been a clue to you that you did it wrong 🙄
what it means to “do brackets” and the distributive law are wrong
No, that would be your understanding is wrong, the person who only read 2 sentences 🙄 I'm not sure what you think the rest of the chapter is about.
Since I’m working off the textbook you gave
Says person who only read 2 sentences out of it 🙄
I referred liberally to things in that textbook
Yep, ignoring all the parts that prove you are wrong 🙄
I’m sure if you still disagree you will be able to back up your interpretations with reference to it
Exact same reference! 😂
it does rather seem like this rule is one established not by the fundamental laws of mathematics but by agreement as they say
You know Mathematicians tend to agree when something has been proven, right? 😂
Care to comment?
Yep, read the whole chapter 🙄
Because they're not identically equal 🙄 Welcome to you almost getting the point
means, isn't equal
Nope, it's because ab==(axb) <== note the brackets duuuhhh!!! 😂
No you can't! 😂
Nope! An actual rule, as found not only in Maths textbooks (see above), but in all textbooks - Physics, Engineering, Chemistry, etc. - they all obey ab==(axb)
says person still ignoring all these textbooks