48÷2(9+3) = ?

[grundle]

Texas Instruments TI-85 says:

48÷2(9+3) = 2

But Texas Instruments TI-86 says:

48÷2(9+3) = 288

[SoothingDave]

http://amby.com/educate/ord-op/pretest.html

Answer number 7. Maybe it’s a conspiracy?

[SeaHawkFan]

Go and continue to wallow on your ignorance. If you could not follow the example at the link which I had copied in post #429, you are beyond help. And to claim you are more lnowledgable than an award-winning math teacher is just plain stupid.

[SoothingDave]

I heard you the first time. You cite one website, and even he admits that his juxtaposition theory is not final and that most software doesn’t follow his theory.

And the idea that teachers are infallible is laughable. I’m worried that she is really teaching kids that 9 / 3 * 3 is 1.

[GreenAccord]

Excel evaluates to 288

CELL A1 equal to 48
CELL B1 equal to 2
CELL C1 equal to 9
CELL D1 equal to 3

CELL E1 equal to “=A1/B1*(C1+D1)”
(double quotes surround the cell contents in my example only to provide the boundaries for the formula entered in E1)

CELL E1 evaluates to 288

You’re free to try and make Excel multiply CELL B1 by the sum of C1 and D1 without the “*”. Good luck with that.

[re_nortex]

Maybe it’s a conspiracy?

The conspiracy aspect of this matter will occur when it hits the magic number of 666 for responses. At that point, we should kindly ask the moderator to lock the thread to preserve it for posterity.

51 / 2 * (14 + 12) + 3

C'mon gang, we can do it! Just a few more followups to go! :-)

[Ironfocus]

The answer is 2.

48/x(9+3)=288
48/12x=288
48=288*12x
48/288=12x
1/6=12x
0.16667=12x
0.16667/12=x
x=0.0138888

Putting the x back in:
48/0.0138888(9+3)=x
48/0.0138888(12)=x
48/0.1666667=x
288=x

48/x(9+3)=2
48/12x=2
12x=48/2
12x=24
x=24/12
x=2

[grateful]

Of course x=2. You took the 2 and replaced it with x. Why would you set the equation equal to 288 if it was not the answer?

48/2(9+3) = x
48(9+3) = 2x
48*12 = 2x
576 = 2x
288 = x

[grateful]

Or, this, doing parens first following standard order of operations.

48/2(9+3) = x
48/2(12) = x
48*12 = 2x
576 = 2x
288 = x

[Ironfocus]

Where did the division go in your step 2? Should it not be 48/(9+3)=2x?

I tested both equations for the two suggested answers of 2 and 288, look more closely.

[SoothingDave]

48/x(9+3)=288
48/12x=288

You beg the question in your first step. You assume that (9 + 3) is in the denominator of the expression. If you express this expression in a linear fashion (entering into a calculator or programming a computer), you need to add parentheses to make this so.

48/(x(9 + 3))

[Ironfocus]

No, nothing to do with question begging, it is simple testing of the two proposed answers.

[grateful]

You beg the question in your first step. You assume that (9 + 3) is in the denominator of the expression. If you express this expression in a linear fashion (entering into a calculator or programming a computer), you need to add parentheses to make this so.

Exactly. And a point I made earlier is that this is not an algebraic equation. Therefore, parens trumps multiplication. Once you do the equation in the parens, 2(12) becomes 2*12. There is no such thing as "implied parentheses", otherwise I could write the equation this way:

48/2*9 +3

... and argue there is an implied parentheses around the 9+3. Parentheses are always explicit. They have to be. That is their purpose.

(Btw, award winning calculus gal here, too.)

[SoothingDave]

I don’t know what you are trying to do, but you are begging the question.

But, it’s simple math. No need to make it into an expression with variables.

If you are trying to back-calculate, it’s to no purpose. If you calculate it the way the 288ers do, you’ll get 288. If you calculate it the way the 2ers do, you get 2.

Proves nothing.

[SoothingDave]

Glad for your support. One major disconnect here is that people view the original expression however they want, rather than viewing it as an input to a computer/calculator. There are rules and syntax.

[grateful]

There are rules and syntax.

There have to be because machines are only as smart as we make them. (Computer programmer here.) Ambiguity leads to problems like this and if we want to tell a computer or calculator that we want certain multiplicative operations to take precedence over others, we must add other parentheses. I think that also can be said about how humans solve the equation because if it was this...

48÷(2(9+3))

I'd be firmly on the 2 side. As of yet, implicit multiplication does not trump explicit multiplication, they are equal, for most standards.

[Ironfocus]

How do you test equations that are ambiguous?

[SoothingDave]

I see how people can be easily misled (and a few parentheses wouldn’t hurt), but if you follow the rules, there is no ambiguity. It’s really a question of syntax and the order in which operations are supposed to be evaluated.

[SoothingDave]

If those parentheses were there, then the answer would be 2. No question about it.

I can even see how implicit multiplication can come into play when discussing higher math. It’s a pain to write 1/(2x) when it’s obvious from context that you mean 1/2x. But that’s context and that’s higher math.

This is arithmetic.

[Mr.Unique]

Question 1: Sister Mary Catherine has 48 students in her math class, seated two to a desk. To each desk she distributes a cup containing nine orange jelly beans and 3 red jelly beans. Shared out equally, regardless of flavour, how many pieces of candy does each student receive? 6

Question 2: Sister Mary Catherine has 48 students in her math class. To each student she distributes two cups, each containing nine orange jelly beans and 3 red jelly beans. How many pieces of candy has Sister Mary Catherine distributed? 576

Please show your work....

That's the issue here. In my view, mathematics represents something. Depicting that which is represented in a form that others understand is what is important. I'm curious what the correct answers are...

[BoringGuy]

This is arithmetic.

We should be able to prove out the arithmetic. I believe this is what Ironfocus was attempting.

If the correct solution is 42/2(9+3)=288, then we should be able to replace ANY of the numbers above with a variable and solve. The answer should always resolve to the replaced value.

I cannot get that to work with 42/2(9+3)=288, but I can with 42/2(9+3)=2.