9 replies to this topic

[TyYann]

Hi everybody today I typed on my fx 9860 GII the infamous:
6/2(1+2)
and got the wrong answer, 1 instead of 9.
I don't want to debate which answer is right. I'm a math teacher, and I did some research specifically on the subject and 9 is the right answer.

I just want to know
1- what is the behaviour of other models?
2- is there any explanation of this in the manual (I couldn't find any)?

Cheers

Yann

[flyingfisch]

I am not sure what the other models do, but isn't 6/2(1+2) == 1?

PEMDAS:


Original: 6/2(1+2)
Parentheses: 6/2(3)
Multiplication: 6/6
Division: 1

Answer: 1

[TyYann]

I am not sure what the other models do, but isn't 6/2(1+2) == 1?

PEMDAS:


Original: 6/2(1+2)
Parentheses: 6/2(3)
Multiplication: 6/6
Division: 1

Answer: 1

Actually not:

PEMDAS
Paretheses 6/2(3)
Multiplication AND division, from left to right: 3(3)
 
Answer: 9

Type this:
6/2×(1+2)
the answer on your calculator will be the right one: 9, though the PEMDAS process is the same...

[MicroPro]

tl;dr: This is the way it is in fx, it's mentioned in the manual.

I remember this was discussed some time ago, too and there were pros and cons of what answer is right. I just can't find the topic.

No matter what your researches were, from fx's point of view the correct answer is 1, since the implied multiplications (multiplications with the multiplication symbol OMITTED) have a higher priority over the × and ÷ operators in fx. So calculation in fx is being more natural than being rock-algorithmic.

In the manual look at Chapter 2 (Manual Calculation) section "Calculation Priority Sequence": Number 7 (Abbreviation multiplication format in front of parenthesis) has a higher priority than Number 10 ( / ).

I think the thought beyond this is that people naturally prioritize implied multiplications in their calculations (and to some extent is correct, say what's the difference between sinxy and sinx×y?). Therefore you should not (!) assume there is a multiplication sign there already. Anyway PEMDAS doesn't mention implied calculations.

btw in ClassPad all forms of multiplication have the same priority and this results in 9.

[TyYann]

Thanks!

[flyingfisch]

Actually not:

PEMDAS
Paretheses 6/2(3)
Multiplication AND division, from left to right: 3(3)

Answer: 9

...

Ah, I see. I was taught that it was multiplication, then division, but I guess its not? Or are there two methods?

[TyYann]

Well, I found the page you mentionned, however, later, it is written this:

Multiplication Operations Without a Multiplication Sign
You can omit the multiplication sign (×) in any of the following operations.
[?]
Before an open parenthesis
Example 3 3(5+6), (A+1)(B-1), etc.

There is no warning that the result could be different. It is said as if it makes no difference, which is right mathematically, but wrong considering the behaviour of the calculator.

Once again, if I can omit the × sign as said in the manual, then writing
6/2×(2+1)
as
6/2(2+1)
should get me the same result, right?

[MicroPro]

I was taught that it was multiplication, then division

They have the same priority and have left-to-right associativity.

There is no warning that the result could be different.

Then they have to make it clearer and that the result can be different. And in the part you mentioned they have already put references to the priority section.

Once again, if I can omit the × sign as said in the manual, then writing 6/2×(2+1) as 6/2(2+1) should get me the same result, right?

"Being able to omit it" and "the result being changed" are two different stories. The manual didn't say result doesn't change -- it made a big mistake; yes.

You know, I'm not myself a big fan of this kind of prioritizing. It can confuse those newly learning algebra (am I an education specialist? ) Even ClassPad doesn't do this.

[noname11]

That's why they added automatic parentheses insertion in Prizm OS 1.04:
http://edu.casio.com..._20/#pagelink05

[MicroPro]

It's good they added it. Seems they were aware of the confusions it made (or they were just reading the previous thread in here! ) This should be added to fx'es too.

And they should elaborate more on it in their manual.