There’s quite a few calculators that get this wrong. In college, I found out that Casio calculators do things the right way, are affordable, and readily available. I stuck with it through the rest of my classes.
Casio does a wonderful job, and it’s a shame they aren’t more standard in American schooling. Texas Instruments costs more of the same jobs, and is mandatory for certain systems or tests. You need to pay like $40 for a calculator that hasn’t changed much if at all from the 1990’s.
Meanwhile I have a Casio fx-115ES Plus and it does everything that one did, plus some nice quality of life features, for less money.
TI did the same thing Quark and Adobe did later on – got dominance in their markets, killed off their competition, and then sat back and rested on their laurels thinking they were untouchable
EDIT: although in part, we should thank TI for one thing – if they hadn’t monopolized the calculator market, Commodore would’ve gone into calculators instead of computers
Huge failure my ass. Come at me on munch man, Alpiner, or Tombstone City. Or coding vaguely racist things like Mr. Bojangles, one of the first codes in the early books.
Had one at home and used the hell out of it, don’t get me wrong. Was my first computer. Played the Zork series on that thing. But, it had issues and wasn’t a financial success.
It had fewer issues than almost anything I’ve owned since. I bet it would still work if I got the right adaptors. Wasn’t a huge financial success though. They seemed content with early coding and games, and didn’t move into word processing etc.
If you’re lucky, you can find these TI calculators in thrift shops or other similar places. I’ve been lucky since I got both of my last 2 graphing calculators at a yard sale and thrift shop respectively, for maybe around $40-$50 for both.
prefix notation doesn’t need parentheses either though, at least in this case. lisp uses them for readability and to get multiple arity operators. infix doesn’t have any ambiguity either if you parenthesize all operations like that.
16 is the right answer if you use PEMDAS only: (8 ÷ 2) × (2 + 2)
You added brackets and changed the answer. 2(2+2) is a single term, and if you break it up then you change the answer (because now the (2+2) is in the numerator instead of in the denominator).
1 is the right answer
The only right answer
both are correct answers
Nope, 1 is the only correct answer.
this is also one of the reasons why postfix and prefix notations have an advantage over infix notation
Except they don’t. This isn’t a notation problem, it’s a people don’t remember the rules of Maths problem.
That’s wrong. Multiplication and division have equal precedence, same as addition and subtraction. You do them left to right. PEMDAS could be rewritten like PE(MD)(AS). After parentheses and exponents, it"s Multiplication and division together, then addition and subtraction together. They also teach BODMAS some places, which is “brackets, order, division and multiplication, addition and subtraction” Despite reversing the division and multiplication, it doesn’t change the order of operations. They have the same priority, so they are just done left to right. PEMDAS and BODMAS are the different shorthand for the same order of operations.
They were right but for the wrong reason. Implied multiplication–that is, a(b) or ab–often comes before explicit multiplication and division. Apparently it’s up to the person writing the equation, so the meme is intentionally and explicitly ambiguous
They’re still wrong, in my humble opinion. I’m aware of this notion, and I’ve even had people share a snip from some book that states this as fact. However, this is not standardized and without the convention being widely understood and recognized as the standard in the world of mathematics (which generally doesn’t use the symbol (÷) at all at post-algebra levels), there is no reason to treat it as such just because a few people assert it is should be.
It doesn’t make sense at all to me that implied multiplication would be treated any differently, let alone at a higher priority, than explicit multiplication. They’re both the same operation, just with different notations, the former of which we use as shorthand.
There are obviously examples that show the use of the division symbol without parentheses sometimes leads to misunderstandings like this. It’s why that symbol is not used by real mathematicians at all. It is just abundantly more clear what you’re saying if you use the fraction bar notation (the line with numerator on top and denominator on bottom). But the rules as actually written, when followed, only reach one conclusion for this problem and others like it. x÷y(z) is the SAME as x÷y*z. There’s no mathematical or logical reason to treat it differently. If you meant for the implicit multiplication to have priority it should be in parentheses, x÷(y(z)), or written with the fraction bar notation.
There’s an argument to be made that implicit multiplication comes before division, resulting in the answer 1, but all multiplication? That’s wrong, full-stop. You calculate (explicit) multiplication and division in one step, left to right. Reason being that division is technically just multiplying by the reciprocal.
I don’t mean when they’re explaining “here’s how the order of operations works”. I mean in the basic way that they write more advanced problems and the answers they give for them.
This video, and the prequel to it linked in the description, go into some detail showing who uses what convention and why.
That’s exactly where the calculators in the op differ. For more examples, Casio calculators do implicit multiplication first, while ti’s treat it the same as explicit multiplication and division. I think that the latter is more predictable personally, but really you just need to know your calculator.
There’s quite a few calculators that get this wrong. In college, I found out that Casio calculators do things the right way, are affordable, and readily available. I stuck with it through the rest of my classes.
Casio does a wonderful job, and it’s a shame they aren’t more standard in American schooling. Texas Instruments costs more of the same jobs, and is mandatory for certain systems or tests. You need to pay like $40 for a calculator that hasn’t changed much if at all from the 1990’s.
Meanwhile I have a Casio fx-115ES Plus and it does everything that one did, plus some nice quality of life features, for less money.
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TI did the same thing Quark and Adobe did later on – got dominance in their markets, killed off their competition, and then sat back and rested on their laurels thinking they were untouchable
EDIT: although in part, we should thank TI for one thing – if they hadn’t monopolized the calculator market, Commodore would’ve gone into calculators instead of computers
https://en.wikipedia.org/wiki/TI-99/4A
It was a huge failure, but they tried.
Huge failure my ass. Come at me on munch man, Alpiner, or Tombstone City. Or coding vaguely racist things like Mr. Bojangles, one of the first codes in the early books.
Had one at home and used the hell out of it, don’t get me wrong. Was my first computer. Played the Zork series on that thing. But, it had issues and wasn’t a financial success.
It had fewer issues than almost anything I’ve owned since. I bet it would still work if I got the right adaptors. Wasn’t a huge financial success though. They seemed content with early coding and games, and didn’t move into word processing etc.
If you’re lucky, you can find these TI calculators in thrift shops or other similar places. I’ve been lucky since I got both of my last 2 graphing calculators at a yard sale and thrift shop respectively, for maybe around $40-$50 for both.
The TI equivalent to the Casio fx-115ES Plus is the TI-36X Pro, and they both cost $20 at Walmart.
My Casio calculators get this wrong, even the newer ones. BTW the correct answer is 16, right?
(8 ÷ 2) × (2 + 2)8 ÷ (2 × (2 + 2))2 2 + 8 2 ÷ × .(× (÷ 8 2) (+ 2 2))prefix notation doesn’t need parentheses either though, at least in this case. lisp uses them for readability and to get multiple arity operators. infix doesn’t have any ambiguity either if you parenthesize all operations like that.
There isn’t any ambiguity even if you don’t.
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PEMDAS is actually (PE)(MD)(AS). Those that are grouped together have equal precedence and are evaluated left to right.
8 / 2 * (2+2)
8 / 2 * 4
4 * 4
16
Edit to fix formatting, maybe?
When you added the multiply you changed the answer, because the (2+2) is now in the numerator instead of in the denominator.
You added brackets and changed the answer. 2(2+2) is a single term, and if you break it up then you change the answer (because now the (2+2) is in the numerator instead of in the denominator).
The only right answer
Nope, 1 is the only correct answer.
Except they don’t. This isn’t a notation problem, it’s a people don’t remember the rules of Maths problem.
Yes
8 / 2 (2+2)
8 / 2 (4)
4 (4)
16
No
8 / 2 (2+2)
8 / 2 (4)
8 / 8
1
No. Order of operations is left to right, not right to left. 1 is wrong.
Order of operations is BEDMAS, THEN left to right within each operator.
1 is the only correct answer.
Pemdas.
Multiplication comes before division.
1 is the correct answer.
That’s wrong. Multiplication and division have equal precedence, same as addition and subtraction. You do them left to right. PEMDAS could be rewritten like PE(MD)(AS). After parentheses and exponents, it"s Multiplication and division together, then addition and subtraction together. They also teach BODMAS some places, which is “brackets, order, division and multiplication, addition and subtraction” Despite reversing the division and multiplication, it doesn’t change the order of operations. They have the same priority, so they are just done left to right. PEMDAS and BODMAS are the different shorthand for the same order of operations.
They were right but for the wrong reason. Implied multiplication–that is, a(b) or ab–often comes before explicit multiplication and division. Apparently it’s up to the person writing the equation, so the meme is intentionally and explicitly ambiguous
They’re still wrong, in my humble opinion. I’m aware of this notion, and I’ve even had people share a snip from some book that states this as fact. However, this is not standardized and without the convention being widely understood and recognized as the standard in the world of mathematics (which generally doesn’t use the symbol (÷) at all at post-algebra levels), there is no reason to treat it as such just because a few people assert it is should be.
It doesn’t make sense at all to me that implied multiplication would be treated any differently, let alone at a higher priority, than explicit multiplication. They’re both the same operation, just with different notations, the former of which we use as shorthand.
There are obviously examples that show the use of the division symbol without parentheses sometimes leads to misunderstandings like this. It’s why that symbol is not used by real mathematicians at all. It is just abundantly more clear what you’re saying if you use the fraction bar notation (the line with numerator on top and denominator on bottom). But the rules as actually written, when followed, only reach one conclusion for this problem and others like it. x÷y(z) is the SAME as x÷y*z. There’s no mathematical or logical reason to treat it differently. If you meant for the implicit multiplication to have priority it should be in parentheses, x÷(y(z)), or written with the fraction bar notation.
As are you. There is no such thing as implicit multiplication - the actual relevant rules are Terms and The Distributive Law.
#MathsIsNeverAmbiguous #DontForgetDistribution
There’s an argument to be made that implicit multiplication comes before division, resulting in the answer 1, but all multiplication? That’s wrong, full-stop. You calculate (explicit) multiplication and division in one step, left to right. Reason being that division is technically just multiplying by the reciprocal.
There’s no such thing as implicit multiplication.
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1 is the correct answer, but it’s because Brackets comes before Division - there is no Multiplication in this problem.
a(b) is a×b. Step 2 could be rewritten as 8 / 2 × 4. Working left to right, step 3 becomes 4 × 4.
No, because implicit multiplication binds more tightly than explicit. a/b© becomes a/(bש)
Says who?
Most maths textbooks written by mathematicians.
I don’t mean when they’re explaining “here’s how the order of operations works”. I mean in the basic way that they write more advanced problems and the answers they give for them.
This video, and the prequel to it linked in the description, go into some detail showing who uses what convention and why.
Interestingly I’ve wondered if this is regional, as a fellow Aussie I learned the same as you but it seems in other places they learn the other way
Huh, I’ll be darned. I’m not as much of a math nerd as I thought
Here is an alternative Piped link(s):
This video
Piped is a privacy-respecting open-source alternative frontend to YouTube.
I’m open-source; check me out at GitHub.
Ignore the video - she completely ignored Maths textbooks (and yes, you’re right, the rules are in Maths textbooks - quoted multiple times here).
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The rules of Maths
That’s exactly where the calculators in the op differ. For more examples, Casio calculators do implicit multiplication first, while ti’s treat it the same as explicit multiplication and division. I think that the latter is more predictable personally, but really you just need to know your calculator.
Actually they follow the actual rules of Maths - Terms and The Distributive Law.
Right answer, wrong words. The actual rules are Terms and The Distributive Law.
a(b) is (a×b) - you can’t remove brackets unless there is only 1 term left inside.
8/(2x4)=8/8=1
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Write it out on paper, with numerator above the denominator. You’d have to write 8(2+2), 2(2+2) can only be written if both are in the denominator.
No.
8 / 2 (4) 8/(2x4) 8/8 1
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That’s (2x4). Doing division before brackets goes against the order of operations rules.
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I didn’t say they weren’t. I said…
You did 8/2x4, which is the same as (8/2)(2+2), which isn’t the same as 8/2(2+2)=8/2(4)=8/(2x4).
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Depends on the system you use. Most common system worldwide and in the academic circles (the oldest of the two) has 1 as the answer.
There are no other systems - only people who are following the actual rules of Maths and those who aren’t. And yes, 1 is the correct answer
No, the correct answer is 1.
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Casio calculators FTW. I got one that could do polar conversions, was basically essential for engineering.
Ditto for Sharp. It’s really only Texas Instruments that is the ongoing exception to the rule.
Sharp as well.