48÷2(9+3) = ????

[Bill Verburg]

Originally Posted by DanielDudley

I'm thinking that there is a distinct lack of additional parenthesis.

Parenthal Guidance is strongly suggested.

It boils down to a lack of understanding of the order of operations sans parenthesis which alter normal order of operation

in simplest terms most would get these wrong because they think that math rules are more like guidelines than actual rules

48/2*3

or this

48*2/3

[winders]

Originally Posted by fast_e_man

Just saw this revived thread --- Wow, Speachless

This is right up there with the question: Which weighs more, a pound of feathers or a pound of nails?

It's more complicated than that....

48÷2(9+3) = ????

That is a poorly written equation that is quite ambiguous.

If you follow the standard order of precedence rule, you get 288. But, if follow the school of thought that says implicit multiplication has precedence of explicit multiplication and division, you get 2.

Also, what if you do this:

48/2(9+x)=288

48/2(9+x)=2

Solve for x in both cases. Which one works out as 3?

Scott

[sammyg2]

Originally Posted by winders

It's more complicated than that....

48÷2(9+3) = ????

That is a poorly written equation that is quite ambiguous.

If you follow the standard order of precedence rule, you get 288. But, if follow the school of thought that says implicit multiplication has precedence of explicit multiplication and division, you get 2.

Also, what if you do this:

48/2(9+x)=288

48/2(9+x)=2

Solve for x in both cases. Which one works out as 3?

Scott

[RWebb]

school of thought?

I mean... I'm cool with Riemann Geometry and Klein Bottles; I'm down with the whole stable limit cycle bit, and I once tried to use a Lyapunov function to Lasso a thang while I wus ridin' the Range on the Complex Plane, and I even used to date a hot Group Theory graduate student, but...

[sammyg2]

.
when this question came up on a MATH forum the thread got locked

Order of operations question.

[svandamme]

Originally Posted by winders

That is a poorly written equation that is quite ambiguous.

it's math, there's no ambiguity about it.
Either you understand math, or you don't.

[svandamme]

Originally Posted by winders

Also, what if you do this:

48/2(9+x)=288

48/2(9+x)=2

Solve for x in both cases. Which one works out as 3?

Scott

48/2(9+x)=288

24(9+x)=288
9+x = 288 /24
9+x = 12
x= 12-9
x = 3


48/2(9+x)=2
24(9+x) = 2
9+x = 2/24
9+x= 0.08333333333
x = 0.08333333 - 9
x = -8.916666666666667

[T77911S]

i was told there would be no math involved

[RWebb]

Originally Posted by sammyg2

.
when this question came up on a MATH forum the thread got locked

Order of operations question.

"theres a big argument going on at on a different forum full of retards..."

[winders]

Let's make it more clear:

Looking at it like this:

48 ÷ x(9 + 3) = 288
48 ÷ (9x + 3x) = 288
48/12x = 288
4/x = 288
4 = 288x
4/288 = x
1/72 = x

Or:

48 ÷ x(9 + 3) = 2
48 ÷ (9x + 3x) = 2
48/12x = 2
4/x = 2
4 = 2x
4/2 = x
2 = x

Would suggest that 288 is wrong, and that 2 is correct.

Like I said, the equation is poorly written as is designed to cause this kind of problem.

The equation should be written as:

48 ÷ 2 x (9 + 3) = 288

Or:

48 ÷ (2(9 + 3)) = 2

Scott

[Bill Verburg]

Originally Posted by winders

Let's make it more clear:

Looking at it like this:

48 ÷ x(9 + 3) = 288
48 ÷ (9x + 3x) = 288
48/12x = 288
4/x = 288
4 = 288x
4/288 = x
1/72 = x

Or:

48 ÷ x(9 + 3) = 2
48 ÷ (9x + 3x) = 2
48/12x = 2
4/x = 2
4 = 2x
4/2 = x
2 = x

Would suggest that 288 is wrong, and that 2 is correct.

Like I said, the equation is poorly written as is designed to cause this kind of problem.

The equation should be written as:

48 ÷ 2 x (9 + 3) = 288

Or:

48 ÷ (2(9 + 3)) = 2

Scott

multiplication and addition are associative so one can add parentheses where one wants

3*4*5 = (3*4)*5 = 3*(4*5) implicit or explicit has no bearing on this 3(4*5) = (3*4)5

but division and subtraction are not associative (3-4)-5 is not = 3-(4-5) in the absence of parenthesis in mixed expressions that contain operators of equal precedence are performed in strict left to right order


multiplication and division have equal precedence and so must be performed left to right, the parenthesis alters the precedence of addition
48 ÷ x(9 + 3) = 288
48 ÷ x(12) = 288 is correct but the next operation is division 48÷x then the multiplication by 12

here' are more that most will get wrong, what does each of these reduce to

2x/2x

2*x/2*x

2(x)/2(x)

[winders]

There you are Bill, living in your world of "only you are right". As I said, there is a reason this equation is used. It is ambiguous and poorly written. Not even the math community agrees on the answer because the ambiguity. And yes, some in the math community think that implicit multiplication take precedence over explicit.... So on you!

Scott

[Bill Verburg]

Originally Posted by winders

There you are Bill, living in your world of "only you are right". As I said, there is a reason this equation is used. It is ambiguous and poorly written. Not even the math community agrees on the answer because the ambiguity. And yes, some in the math community think that implicit multiplication take precedence over explicit.... So on you!

Scott

There goes windbag(again), he hasn't a clue so he resorts to spewing bullsh**

[winders]

Originally Posted by Bill Verburg

There goes windbag(again), he hasn't a clue so he resorts to spewing bullsh**

You are the windbag spewing bullsh**.

Look here:

Order of arithmetic operations; in particular, the 48/2(9+3) question.

To quote:

"A problem that hit the Internet in early 2011 is, "What is the value of 48/2(9+3) ?"

Depending on whether one interprets the expression as (48/2)(9+3) or as 48/(2(9+3)) one gets 288 or 2. There is no standard convention as to which of these two ways the expression should be interpreted, so, in fact, 48/2(9+3) is ambiguous. To render it unambiguous, one should write it either as (48/2)(9+3) or 48/(2(9+3)). This applies, in general, to any expression of the form a/bc : one needs to insert parentheses to show whether one means (a/b)c or a/(bc)."

Are you a published Professor Emeritus from an institution as prestigious as the University of California, Berkeley?

George M. Bergman | Department of Mathematics at University of California Berkeley

George M. Bergman -- publications and preprints

Scott

[dad911]

Originally Posted by winders

There you are Bill, living in your world of "only you are right". As I said, there is a reason this equation is used. It is ambiguous and poorly written. Not even the math community agrees on the answer because the ambiguity. And yes, some in the math community think that implicit multiplication take precedence over explicit.... So on you!

Scott

Algebraic Expressions, Order of Operations/P.E.M.D.A.S. I

"Perform the operations inside a parenthesis first
Then exponents
Then multiplication and division, from left to right
Then addition and subtraction, from left to right
You can also create a little phrase to memorize, as the sequence:
Please Excuse My Dear Aunt Sally"

48÷2(9+3) = x Perform the operations inside a parenthesis first
48÷2(12) = x Then multiplication and division, from left to right
24(12) = x
288 = x

If you rewrite to remove the ambiguity/convention that 'some' believe multiply before divide, by converting division to multiplying by the inverse:

48*(1/2)*(9+3) = x Perform the operations inside a parenthesis first
48*(.5)*(12) = x Then multiplication and division, from left to right
24*(12) = x
288 = x

You still get 288

[winders]

dad911,

All I have to say is:

See post post #512.

Jeez....

Scott

[dad911]

Originally Posted by winders

dad911,

All I have to say is:

See post post #512.

Jeez....

Scott

A lone prof spouting ambiguity and interpretation doth not a reference make.

1/2*4 = .5*4 = 2
Not
1/2*4 = 1/8 = .125

Or is than ambiguous also?
Multiplication and division evaluated left to right, in the whole world except in Bergman's classroom?

[dad911]

Let me google that for you

[winders]

Originally Posted by dad911

Let me google that for you

Do you see what Google does with the equation? It converts it to:

(48 / 2) * (9+3)=

And then solves it to "288".

Well, that's correct based on how it interpreted the equation.

Of the calculators that let you enter the equation as written, some come back with "2" and some with "288".

The equation " 48÷2(9+3) = ????" is like a poorly written sentence that could be taken two mean to different things. The author of the equation knew what he wanted to convey but did not do so clearly in this case.

The answer is that both "288" and "2" are correct answers. Which one you get is based on how your interpret the equation. In other words, it is ambiguous!

Scott

[winders]

Look at this link:

Math Forum - Ask Dr. Math

It states in the "Mathematical Reviews Database - Guide for Reviewers" that "multiplication indicated by juxtaposition is carried out before division."

Like I said, ambiguous!

Scott