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Math Question





izcool
I learned in my Algebra 2 class today (on a side note, we are doing logs right now) that 2+2*2 = 6. When I did it in my head, it was 8. How is this true ? Why did the problem come out that way in my calculator ? My teacher wouldn't explain, she only said that we didn't remember what we learned in Algebra 1. Rolling Eyes

I did it as so :
2+2*2 = ?
2+2 = 4
4*2 = 8

- Mike.
bluefossil
I believe if you look you will find that math problems follow a certain order.

when you have a problem with a + and a * you multiplyu first and do the addition second.

so in your case 2 + 2 * 2 would go

2 * 2 = 4
2 + 4 = 6

it may ge * / + - but i'm not positive, You can search online and find it.

if it was written (2+2)*2 it would be 8
(2+2)*2
(4)*2
8
mOrpheuS
izcool wrote:
I learned in my Algebra 2 class today (on a side note, we are doing logs right now) that 2+2*2 = 6. When I did it in my head, it was 8. How is this true ? Why did the problem come out that way in my calculator ? My teacher wouldn't explain, she only said that we didn't remember what we learned in Algebra 1.


Sigh ... the calculator/computer generation of today Laughing

In our times, we used to learn BODMAS very very early in school.

I think that's what your teacher is referring to as Algebra 1.
caroline
It's called order of operations! Smile
I think it goes something like
Please
Excuse
My
Dear
Aunt
Sally

Which is:

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

You do those which are further up on the list first, so 2+2*2 =
2+ (2*2) = 2 + 4 = 6!
Smile
n0obie4life
You always do the multiplication first.

So in the case of 2+2*2.

2*2 is done first. Then the +2 is added.

If it were

2+2/2

2/2 would have been done first.

If it were

2+2/2*2

2/2 would have been done first then 2*2, then +2.
Liu
I could swear you're supposed to learn order of operations in elementary school; more importantly before algebra.

What kind of calculator are you using? If it's a postfix calculator, or a calculator that doesn't evaluate input expressions, it's understandable that you're getting 8, thus the user's fault for the wrong answer in what you're trying to do. Calculators like those depend on the human user to understand order of operations -- i.e. inputing 2*2 first, then add 2. More advanced calculators that allows input of expressions will parse and evaluate the expression according to order of operations.
Pyxel
Ug, math.

You would think that being a programer, I would either love math or have extensive practice in it.

But the opposite is true. I hate it, and I cant do it worth squat.

Yet this I remember. Multiply first. It is the simple answer of the order of operations. If you entered it into your calculator as (2=2)*2 you would get an answer of 8. If you entered it as 2+(2*2) you would get 6.

I think I just repeated like four people, though .. hehe.
Blaster
First rule of them problems.
P ()
Epoints
Multiply or
Divide
Addor
Ssubtract

2*2=4+2=6
DoctorBeaver
I remember back in the days when I was studying for my computer science degree I had to write an algorithm for RPN (Reverse Polish Notation). That involved taking a formula and rearranging it into the correct order of priority. Not only that, but 2 + 3 would have to rearrange as 2 3 +. I can't remember how the hell I did it.
A lot of early Hewlett Packard calculators used RPN.
acamas
Ahh good old maths!
It is really easy if you put your mind to it. we learnt about all this stuff when I was like 12 maybe the syllabus is different over there.. actually make that it definitely is
Jack_Hammer
bluefossil wrote:
I believe if you look you will find that math problems follow a certain order.

when you have a problem with a + and a * you multiplyu first and do the addition second.

so in your case 2 + 2 * 2 would go

2 * 2 = 4
2 + 4 = 6

it may ge * / + - but i'm not positive, You can search online and find it.

if it was written (2+2)*2 it would be 8
(2+2)*2
(4)*2
8


That is what I was going to say, but you beat me to it.
izcool
I use a TI-83+ calculator (Mine's purple, like this one http://www.albion.edu/mathcs/MBollman/TI83+UV.gif becuase it would be easy to identify if it were stolen), graphing calculator, where it doesn't go ahead and explains what it does on the screen.

I learned the order of operations in my Algebra 1 class but I clearly forgotten them.

I do some programming for websites, but I don't really do any mathematical equations for what I need to do. Often times, I use percentages when doing designs, and very simple adding and subtracting in programming, that's about it.

- Mike.
snowboardalliance
wow....
yeah 2+2*2=6
(2+2)*2=8

there's a difference
wumingsden
People keep on saying that a certain function is always done frist, the problem is your saying the wrong functions.
It goes in the order of Brackets, Order, Division, Multiplication, Addition, Subtraction. Like mOrpheuS kind of points out, the beginning letter of each word spells out BODMAS.
Blaster
We were taught PENDAS
Liu
wumingsden wrote:

It goes in the order of Brackets, Order, Division, Multiplication, Addition, Subtraction.

What does "Order" represent than being seemingly superfluous?
wumingsden
@ Blaster - Exactly the same thing about from different uses for different cultures.

@ Liu - The "order" means to the power of
Daniel15
Liu wrote:
wumingsden wrote:

It goes in the order of Brackets, Order, Division, Multiplication, Addition, Subtraction.

What does "Order" represent than being seemingly superfluous?

It helps to make "BODMAS" pronouncable (How would you pronounce "BDMAS"?)

The only difference between BODMAS and PEMDAS is that PEMDAS mentions exponents, whereas BODMAS doesn't.

@izcool: I've got a TI-84+ calculator. One of my teachers showed my a CAS calculator (the TI-89) and now I want it! It's so much more powerful. Very Happy
wumingsden
OK, daniel, you've officially confused me (this isn't that hard to do at the moment). How do you pronounce BODMAS ? Er... BODMAS.

Brackets
Order
Divide
Multiply
Addition
Subtract
Blaster
I fell like i am in pre alegrabra again. I am in alegrabra 1 now.
suntzu3500
http://en.wikipedia.org/wiki/Order_of_operations

Summarises everything pretty effectively.

Yeah, order of operations is easily forgettable, I'm starting college calculus in three weeks and I regularly forget stuff like that. Razz
CrestedLova
I find it easier to remember PEMDAS
P arenthese
E xponents
M uliplacation
D ivision
A ddition
S ubtraction
Daniel15
Quote:
How do you pronounce BODMAS ? Er... BODMAS.


Teachers here usually pronounce it like "Bod-Mass" (ie. in 2 syllables)
benwhite
BOSMAS does mention exponents, as order refers to the power of a number (just like an exponent). They're just different mnemonics. We learned PEMDAS back in the day. I think it has a nicer ring to it. Besides, we call [] brackets and () parenthesis, so I'll take PEMDAS anyday.
Liu
wumingsden wrote:

@ Liu - The "order" means to the power of

Ah that makes sense. duh on me.
adiutrix
In logarithms, + means multiply, - means divide and vise versa. Don't let it confuse you as I do Agebra 2 as well and it's really easy ones you get used to it.
Nyizsa
Everybody seems to be talking about BODMAS, PEMDAS, and similar abbreviations. I would like to put one thing clear: multiplication and division, and then addition and substraction have the same priority. The abbreviations suggest otherwise. So it should be P E [M-D] [A-S], or something similar. To put it clear, the precedence is:
( ) Parentheses,
^ Exponentials,
* / Multiplication and division,
+ - Addition and substraction.
wumingsden
Liu wrote:
wumingsden wrote:

@ Liu - The "order" means to the power of

Ah that makes sense. duh on me.


Sorry, as you notice from this entire thread there are different people with different cultures therefore are taught a little bit different. An example is http://en.wikipedia.org/wiki/Root_%28mathematics%29
mOrpheuS
Nyizsa wrote:
So it should be P E [M-D] [A-S], or something similar. To put it clear, the precedence is:
( ) Parentheses,
^ Exponentials,
* / Multiplication and division,
+ - Addition and substraction.

True ... but BODMAS OR PEMDAS are so much easier to pronounce.

How would you pronounce "P E [M-D] [A-S]" anyway ? Laughing


as a footnote, for anybody wondering what happens if they encounter multiplication and division in the same expression ... eg.,
4 / 2 x 2

if you literally follow BODMAS (division before nultiplication)
you get :
4 / 2 x 2 = 2 x 2 = 4

and if you follow PEMDAS literally (multiplication before division)
you get :
4 / 2 x 2 = 4 / 4 = 1

While the fact is that multiplication and division both should be treated with the same priority in an expression !

The last rule, usually missed out in clever acronyms like BODMAS and PEMDAS (and their cleverer acrostics) is that of always solving an expression from left to right.

therefore,
4 / 2 x 2 = 2 x 2 = 4 is the correct way to tackle this expression.
Nyizsa
mOrpheuS wrote:
The last rule, usually missed out in clever acronyms like BODMAS and PEMDAS is that of always solving an expression from left to right.

Yes, I forgot to mention the left-to-right rule - thanks.
mOrpheuS wrote:
How would you pronounce "P E [M-D] [A-S]" anyway ? Laughing

Well... I will think about it if you really wish to pronounce it...
Very Happy
mOrpheuS
Nyizsa wrote:
Yes, I forgot to mention the left-to-right rule - thanks.

Well, you weren't supposed to be responsible for it.
However the people who devised the clever acronyms (BODMAS, PEMDAS) apparently are. Wink
Many textbooks and websites that talk about the order of operations go only as far as expanding/explaining these popular acronyms, often missing talking about the left-to-right convention.

And I have seen kids get confused over this.

Nyizsa wrote:
Well... I will think about it if you really wish to pronounce it...
Very Happy

nevermind, I am not desperate about pronouncing it.
Don't lose your sleep over it. Laughing
seodfac
I don't understand why people have to buy a $100 calculator and then realize they use it for nothing more than simple arithmetic. Most people will never use 90% of the functions on the TI-83/84/86 and 98% of the functions on the 89/92. However, schools feel it necessary to have them for graphing capabilities. No offense but if you don't know your order of operations you should not be using a TI-83, it may not be your fault though. The TI-83 is capable of solving systems of linear equations with matrices, evaluating definite integrals and derivatives at a point, not to mention doing statistical analysis. The TI-89 can solve many differential equations, do symbolic algebra, and so much more. There is a huge world of math beyond Algebra 2 and the fact that your TI-83 gave you the answer lets me know that more time needs to be spent understanding the fundamentals of basic mathematics. I also think your teacher needs to care just a bit more about your math education. But this is just what I think.
seodfac
[quote="mOrpheuS"]
Nyizsa wrote:
Yes, I forgot to mention the left-to-right rule - thanks.

Well, you weren't supposed to be responsible for it.
However the people who devised the clever acronyms (BODMAS, PEMDAS) apparently are. Wink
Many textbooks and websites that talk about the order of operations go only as far as expanding/explaining these popular acronyms, often missing talking about the left-to-right convention.

Can you give me an example when this supposed left to right rule applies? If I wanted to solve an equation/evaluate an expression I could do it in any order I wish provided I follow the basic order of operations. I may be mistaken, but I cannot think of anytime when I was required to go from left to right.
Nyizsa
seodfac wrote:
...more time needs to be spent understanding the fundamentals of basic mathematics.


EXACTLY. In high school, we were not allowed to use calculators in most of the cases! We ahd to know for example the sine and cosine of 0, 30, 45, 60 and 90 degrees by heart, as well as some squareroots (2 and 10, for example), and some other facts. Also trigonometric and logarithmic identities. Precedence of operations never was an issue - it was obvious.
mOrpheuS
seodfac wrote:
Can you give me an example when this supposed left to right rule applies? If I wanted to solve an equation/evaluate an expression I could do it in any order I wish provided I follow the basic order of operations. I may be mistaken, but I cannot think of anytime when I was required to go from left to right.


http://www.frihost.com/forums/vp-240212.html#240212

Same topic, just a few posts ago. Wink


Nyizsa wrote:
seodfac wrote:
...more time needs to be spent understanding the fundamentals of basic mathematics.


EXACTLY. In high school, we were not allowed to use calculators in most of the cases! We ahd to know for example the sine and cosine of 0, 30, 45, 60 and 90 degrees by heart, as well as some squareroots (2 and 10, for example), and some other facts. Also trigonometric and logarithmic identities. Precedence of operations never was an issue - it was obvious.

At many places, use of calculators is prohibited in schools.
Where I live, for example, calculators do not become a part of a student's kit until University.


seodfac wrote:
I don't understand why people have to buy a $100 calculator and then realize they use it for nothing more than simple arithmetic.

Exactly what I thought when I saw that image of the humongous TI-83 that somebody posted in this thread. Shocked

We managed with not-so-advanced calculators, even during professional courses which involved advanced mathematics.

p.s. - This calculator costs around 5 USD Smile
Daniel15
Quote:
here I live, for example, calculators do not become a part of a student's kit until University.


Here, for Specialist maths, we have two exams at the middle and end of the year: A calculator-free exam (1 hour) and a calculator-active exam (2 hours). About half of our tests are also calculator-free

But I love my calculator. It's really useful for factorising cubics using the program 'FACTOR9'. And I also wrote a half life calculator for my calculator Smile
n0obie4life
mOrpheuS wrote:
seodfac wrote:
I don't understand why people have to buy a $100 calculator and then realize they use it for nothing more than simple arithmetic.

Exactly what I thought when I saw that image of the humongous TI-83 that somebody posted in this thread. Shocked

We managed with not-so-advanced calculators, even during professional courses which involved advanced mathematics.

p.s. - This calculator costs around 5 USD Smile


mOrp, do you use that? Because I do (I took that from my dad).

Yes, I get to use calculators in school, but not for every single subject. For the easier ones like algebra (teachers don't want us to spend hours trying to calculate simple stuff).
cfackler
Good old order of operations. I personally own and use a TI-89 and TI-83+SE. I'm studying Calculus II in high school and many of the symbolic functions of the 89 frequently come in handy.
Blaster
I am still wondering how you can forget somthing as basic as that. That should be somthing that everyone abouve 7th grade should know. Now taking alegrabra 1 in 8th grade.
Daniel15
n0obie4life wrote:
mOrpheuS wrote:
seodfac wrote:
I don't understand why people have to buy a $100 calculator and then realize they use it for nothing more than simple arithmetic.

Exactly what I thought when I saw that image of the humongous TI-83 that somebody posted in this thread. Shocked

We managed with not-so-advanced calculators, even during professional courses which involved advanced mathematics.

p.s. - This calculator costs around 5 USD Smile


mOrp, do you use that? Because I do (I took that from my dad).

Yes, I get to use calculators in school, but not for every single subject. For the easier ones like algebra (teachers don't want us to spend hours trying to calculate simple stuff).


What an ugly looking calculator Razz
Until I got my TI-84+, I used this calculator: here or here . It cost about AU$15
izcool
seodfac wrote:
I don't understand why people have to buy a $100 calculator and then realize they use it for nothing more than simple arithmetic. Most people will never use 90% of the functions on the TI-83/84/86 and 98% of the functions on the 89/92. However, schools feel it necessary to have them for graphing capabilities. No offense but if you don't know your order of operations you should not be using a TI-83, it may not be your fault though. The TI-83 is capable of solving systems of linear equations with matrices, evaluating definite integrals and derivatives at a point, not to mention doing statistical analysis. The TI-89 can solve many differential equations, do symbolic algebra, and so much more. There is a huge world of math beyond Algebra 2 and the fact that your TI-83 gave you the answer lets me know that more time needs to be spent understanding the fundamentals of basic mathematics. I also think your teacher needs to care just a bit more about your math education. But this is just what I think.


It's required at my school to have TI-83+ calculators for the graphing capabilities on it. I know many functions on the TI-83+ but I don't exactly need to know the order-of-operations when I have my calculator there to do it for me. Infact, I've done programming in my TI-83+ calculator and made an entire GAME out of it in the internal programming language ("PGRM" button near the middle). Don't assume that I don't know what that thing can do. There's more than what meets the eye.

- Mike.
Blaster


That is my sexy calculator. You are just jelous. Razz The graphing calculator is one of the coolest things ever.
jveezy
I'm in Calculus IV (multivariable on quarter system here) and we're not even allowed to use calculators anymore. The only reason I need mine is for my science and engineering classes so I can calculate actual values.

And schools do mess around with calculators way too much. Especially in elementary school. Nobody knows how to do arithmetic any more by the time they get to high school.

In fact, when doing basic arithmetic, if you learn one of the speed methods (like all that soroban stuff) then you could probably calculate stuff in your head in less time than it takes for you to punch all the numbers into a calculator and hit a function key in between each number.
Liu
izcool wrote:

It's required at my school to have TI-83+ calculators for the graphing capabilities on it.

What is the most complicated function that you've graphed so far?

Quote:
I know many functions on the TI-83+ but I don't exactly need to know the order-of-operations when I have my calculator there to do it for me.

No wonder kids these days are so horrible with math. I don't think you understand how basic and fundamental order of operations are. Calculators aren't even allowed at most universities while taking the tests. I've been through three quarters of calculus, differential equations, linear algebra, upper division statistics, and multivariable calculus all without a calculator. You will need to know how to do simple math if you want to get anywhere in your future educational endeavors.

Quote:

Infact, I've done programming in my TI-83+ calculator and made an entire GAME out of it in the internal programming language ("PGRM" button near the middle). Don't assume that I don't know what that thing can do. There's more than what meets the eye.

Perhaps more time should be spent learning really simple math than making a game on a calculator.
mOrpheuS
n0obie4life wrote:
mOrp, do you use that? Because I do (I took that from my dad).

Why, yes I did !
It was given to me by my seniors when I joined Uni and I passed it on to my juniors when I left.
It's not like we had to spend even the $5 to buy that calculator.

Books, calculators, drawing kits ... were all part of a rich legacy Laughing

n0obie4life wrote:
teachers don't want us to spend hours trying to calculate simple stuff

Students are supposed to "use" math, not "do" it.

I agree, and yet I doubt if students ever spend hours trying to calculate simple stuff ... especially if they're used to doing so without the aid of a calculator.

Atleast I somehow never felt the need for a calculator during school.Honestly, solving a simple expression hardly takes longer than a minute or so ... less if the problem has been cleverly crafted (eg., with most terms simplifying or cancelling out).

The curriculum makers spent a lot of effort so that the students didn't have to.
There was hardly a case where we needed to do numerical operations which we couldn't do in our heads.

Perhaps it was the curriculum, perhaps it was the teachers (or the lack thereof) or perhaps it's just me.


daniel15 wrote:
What an ugly looking calculator Razz

Umm...well ...

  • While it may seem like a small amount to few ... Aus$15 for a calculator is considered extravagant by many students in not-so-rich places(not to mention the $100+ ones).
  • it does its job well.
  • this calculator used to be so common that we didn't feel "ashamed" of having to use it.
  • a more advanced(expensive) calculator would get stolen.
  • if I had a more advanced calculator I wouldn't know what to do with it.
  • and most importantly - Never look a gift horse in the mouth ... Laughing


That said, I find schools making a certain expensive calculator compulsory for students (as izcool's school does) as plain funny.
lukeropro
yep, I learnt BODMAS in my primary school too. Always to multiplication and division first before doing subtraction and addition...
Daniel15
Quote:
That said, I find schools making a certain expensive calculator compulsory for students (as izcool's school does) as plain funny.


Well, at my school, a TI-83 or higher is complusory for the higher maths classes (eg. Maths Methods and Specialist Maths). We do stuff like calculus, matrices, vectors, cubic division, partial fractions, etc. I can do stuff like partial fractions, completing the square, simplification, etc. but stuff like cubic division and multiplying of factors is pretty hard Razz
izcool
Liu wrote:
izcool wrote:

It's required at my school to have TI-83+ calculators for the graphing capabilities on it.

What is the most complicated function that you've graphed so far?

Quote:
I know many functions on the TI-83+ but I don't exactly need to know the order-of-operations when I have my calculator there to do it for me.

No wonder kids these days are so horrible with math. I don't think you understand how basic and fundamental order of operations are. Calculators aren't even allowed at most universities while taking the tests. I've been through three quarters of calculus, differential equations, linear algebra, upper division statistics, and multivariable calculus all without a calculator. You will need to know how to do simple math if you want to get anywhere in your future educational endeavors.

Quote:

Infact, I've done programming in my TI-83+ calculator and made an entire GAME out of it in the internal programming language ("PGRM" button near the middle). Don't assume that I don't know what that thing can do. There's more than what meets the eye.

Perhaps more time should be spent learning really simple math than making a game on a calculator.


I'm only stating that I made a game to show that I'm not exactly foreign to my calculator, I know quite a lot of what the thing can do. To be honest $100.00 is not a lot, I bought that thing used on eBay for a little bit cheaper than to go to the store and get a new one. I used that one for several years and it's definately paid off.

Hmm, well let's see some of the things I've done in it :

- Matrixes
- Graphs
- Probability
- Logs
- Sin/Cos/Tan
- Plotting Points
- Using the table feature

I'm sure there are more but that's all off the top of my head. Those functions are what I use this thing most for.

So is it against the law to own a calculator like this one to do a "simple" math problem to figure out what the answer is ? Or do I have to carry this one around for my school work, and then a cheapie $5.00 one to do the "simple" math like that ? Why is everyone jumping on me because I started this thread asking a question. I've got my answer, it's the order of operations. Thanks to those who pointed it out.

- Mike.
Nyizsa
izcool wrote:
So is it against the law to own a calculator like this one to do a "simple" math problem to figure out what the answer is ? Or do I have to carry this one around for my school work, and then a cheapie $5.00 one to do the "simple" math like that ?

Hey, don't take it seriously. There isn't any problem with using any kind of calculator. We only say that calculators are for calculating (I mean actual values), and not for remembering basic rules instead of you. In other words: You first need to know exactly what will you calculate.
Gieter
I agree with Nyizsa, it's always useful to be able to work without a calculator. However, if you need to draw a sinus-function, it's more easier with a calculator than drawing it by hand, isn't it? And also for statistics it comes in very handy! I don't think calculators are something bad in our education, you can make more exercises/see more theory because the calculators save you a lot of time.

In my school, calculators are allowed, and we always use them, and nobody sees a reason to prohibit them. Algebra, statistics, functions, matrices,... what's wrong with using a calculator in these areas of mathematics? Nothing I think Smile
the_mariska
Well, if you don't know what to count, even your calculator can't help you. I don't even have a one, if I am to work on big numbers or take a square root I use the one built in my mobile. However, I've noticed that getting used to it made me do more mistakes in the basic arithetmics, so I try to count on my own the most I can. Heard somewhere than 60% of teenage americans cannot solve the equotation x + 7 = 12 without using a calculator. Don't think it is true, but I don't wanna be like this :]
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