Solve 48

[Pikey]

It's not April 1st again is it?

I think I learnt this sort of stuff when I was about 7 or 8 years old ...

[Nayos]

It's not April 1st again is it?

I think I learnt this sort of stuff when I was about 7 or 8 years old ...

You must have been doing pretty advanced stuff at your school if you were learning distributive multiplication then

[Soulsiphon]

(9+3) = 12

2(12) = 24

48 / 24 = 2

this is how it always shook out for me too, basically it's numeric 48 divided by a quantity aka the denominator with a value of 24.

edit: actually, there isn't a whole quantity below due to the lack of parenthetical notation making it so. So, yeah, 288 in strictly order of ops.

[WickedScribbler]

anything/anything(anything+anything)

(anything[9]+anything[3])=anything[12]. Parenthesis are ALWAYS solved first when both factors are known.

Anything[48]/anything[2]=anything[24]=anything[24] is solved next.

Anything[24](anything[12] is a multiplication problem.. i.e. PiR2 PiD etc.

Anything[24]Xanything[12]-answer[288].

Punch in the numbers (exactly) as stated on on anything TI, or if you are old school use a slipstick, and you will reach the same conclusion. I know that Mrs. Foster is waiting in the after life to give me a bad grade for anything less than this.

[+theblazingangel MVC]

It is because this is what my son is studing right now in 5th grade math. He laughed at this and did this and the answer is: 288 and not 2.

Oh well that just proves it then, who could possibly question the knowledge of your 5 yr old son /sarcasm

You think you are smarter, better and can compute faster than your Casio FX-85es?

When the hell did I say that? Go troll somewhere else. :angry:

[Nayos]

If you go with basic math (the BODMAS rule) then the equation would be treated like this:

48 / 2 * (9 + 3)

I think everyone is overthinking it.

2(9 + 3) should not be treated as (2(9 + 3)) because the second set of () were not specified.

That's the whole debate. Multiplication by juxtaposition says that 2(9+3) should be treated as (2(9+3)) and there's no Mathematics council that we can ask, so all we can do is debate amongst ourselves.

[inferniac]

http://www.wolframalpha.com/input/?i=48%C3%B72%289%2B3%29

:whistle:

[Draconian Guppy]

For everyone's info, Google Calc gets '2' when a second set of parenthesis is used to control the order of evaluation:

48 / (2(9 + 3))

= 2

48 / 2(9 + 3)

= 288

Both of which are correct answers :)

No. only the latter is correct, based on what the OP gave us, since it didn't have a second set of parenthesis.

This thread makes me sad.

Agreed, again, based on what we have, there is only one solution.

[Nayos]

Guys, if you're just jumping in now, at least read what some people have said regarding distributive multiplication and multiplication by juxtaposition.

[Draconian Guppy]

Guys, if you're just jumping in now, at least read what some people have said regarding distributive multiplication and multiplication by juxtaposition.

i'm not I was one the first to reply

[primexx]

So what do you say to the evidence earlier that distributive multiplication does indeed have a higher order-of-operations presidence than other multiplication?

As I have already shown with examples that nobody has disputed, that is a stupid rule to apply to this equation. (aka they're doing it wrong)

Typing this into C++ or C# or python etc is useless because you are inserting a * in so the 'juxtaposition rule' won't take effect. Adding a multiplication symbol changes the equation.

that's ludicrous. explicitly writing the multiplication sign gives you the exact same equation as the original simply omitted it in type as a shorthand, it's simply an implied multiplication.

[Rigby]

Oh well that just proves it then, who could possibly question the knowledge of your 5 yr old son /sarcasm

When the hell did I say that? Go troll somewhere else. :angry:

Let's not lose our tempers.

[Hardcore Til I Die]

No. only the latter is correct, based on what the OP gave us, since it didn't have a second set of parenthesis.

I'm saying that both of those answers I posted are mathematically correct, not that they're both the same as the sum posted in this thread.

[Draconian Guppy]

^^ point taken.

[Gutierrez]

answer: FRIDAY!

[Versanis]

that's ludicrous. explicitly writing the multiplication sign gives you the exact same equation as the original simply omitted it in type as a shorthand, it's simply an implied multiplication.

So 2z = 2*z ?

4z?2z = 2z? ??

Would you naturally interpret it that way?

Note that the above equation is exactly the same as the OP's for the case z=12.

[Draconian Guppy]

answer: FRIDAY!

:rofl: prove that mathematically :shifty:

So 2z = 2*z ?

:laugh:

[Nayos]

:laugh:

Answer him

4z ? 2z = 2

or

4z ? 2z = 2z?

Which is correct?

How about

4*z ? 2*z = 2

or

4*z ? 2*z = 2z?

Wolfram Alpha for 4z/2z

Wolfram Alpha for 4*z/2*z

[Ambroos]

God. It's just a badly written equitation. Nothing is completely correct.

If you want to try and solve it, the 'most correct' solution would be 2. Juxtapositioning the 2 before the brackets implies that the 2 and the (9+3) are treated as one element, thus resulting in adding brackets around them, leading to this:

48?2(9+3) = 48?[2(12)] = 48?24 = 2

It's well-demonstrated by nevann's example in the post above.

You get 4z/2z. Will you treat it as 4*z/2*z = 2z*z = 2z??

No. Juxtaposition implies you treat 4z and 2z as elements within brackets. (4z)/(2z) = 2.

In the end, it comes down to just being an unclear equitation. Every single teacher will tell you that it's just not good to write an equitation like that. In mathematics, you're supposed to add brackets to avoid any possible confusion.

Conclusion:

48?2(9+3) can not be solved correctly because it is unclear what is meant exactly.

[primexx]

So 2z = 2*z ?

4z?2z = 2z? ??

Would you naturally interpret it that way?

Note that the above equation is exactly the same as the OP's for the case z=12.

the difference, of course, is that 2z is one entity (the number quantifies the variable), whereas 2(4) is two entities with an implied multiplication.

edit: but you can certainly express it as (2*z),

edit 2: i don't understand everyone who say that the ? symbol is confusing. It's the exact same thing as / just a different way of writing it. The meaning and scope of the operator is the same either way.

[Ambroos]

the difference, of course, is that 2z is one entity (the number quantifies the variable), whereas 2(4) is two entities with an implied multiplication.

We never defined z as a variable. It's only a variable if you say something like f(z)=2z.

Juxtaposition, like we do in 2(4) still suggests you treat it as one entity being 8.

[Julius Caro]

http://en.wikipedia.org/wiki/Order_of_operations

As mentioned before, 4-7+3 should be viewed as 4+(-7)+3=0. This is because subtraction is just adding the additive inverse.

Likewise, 48?2(9+3) should be viewed as 48*(1/2)*(9+3)=288, because division is multiplying by multiplicative inverse. When in doubt, turn "?y" to "*(1/y)" just like "-y" to "+(-y)". Then, it becomes unambiguous because multiplication is associative and commutative. This is why some math teachers say "division before multiplication" in BEDMAS etc. That really isn't accurate though. Division takes the same precedence as multiplication, but you just need the perspective that division means multiplying by multiplicative inverse. I'm pretty sure all TI calculators will agree on this.

+1.

[primexx]

We never defined z as a variable. It's only a variable if you say something like f(z)=2z.

Juxtaposition, like we do in 2(4) still suggests you treat it as one entity being 8.

you use a letter, it's a variable (or constant, depending on the letter/context). in fact you even used it as a variable (where you said z=12).

the f(z) thing is a function.

2(4) is just another way of writing 2*4, just because you write something beside something else doesn't make it special.

[WickedScribbler]

God. It's just a badly written equitation. Nothing is completely correct.

If you want to try and solve it, the 'most correct' solution would be 2. Juxtapositioning the 2 before the brackets implies that the 2 and the (9+3) are treated as one element, thus resulting in adding brackets around them, leading to this:

48?2(9+3) = 48?[2(12)] = 48?24 = 2

It's well-demonstrated by nevann's example in the post above.

You get 4z/2z. Will you treat it as 4*z/2*z = 2z*z = 2z??

No. Juxtaposition implies you treat 4z and 2z as elements within brackets. (4z)/(2z) = 2.

In the end, it comes down to just being an unclear equitation. Every single teacher will tell you that it's just not good to write an equitation like that. In mathematics, you're supposed to add brackets to avoid any possible confusion.

Conclusion:

48?2(9+3) can not be solved correctly because it is unclear what is meant exactly.

Amen. After much cogitating, this should be expressed as:

(48/2)(2(9+3))=288 or

48/(2[9+3])=2 or

48

2(9+3)

[Ambroos]

http://en.wikipedia.org/wiki/Order_of_operations

As mentioned before, 4-7+3 should be viewed as 4+(-7)+3=0. This is because subtraction is just adding the additive inverse.

Likewise, 48?2(9+3) should be viewed as 48*(1/2)*(9+3)=288, because division is multiplying by multiplicative inverse. When in doubt, turn "?y" to "*(1/y)" just like "-y" to "+(-y)". Then, it becomes unambiguous because multiplication is associative and commutative. This is why some math teachers say "division before multiplication" in BEDMAS etc. That really isn't accurate though. Division takes the same precedence as multiplication, but you just need the perspective that division means multiplying by multiplicative inverse. I'm pretty sure all TI calculators will agree on this.

Does not matter at all. You can still change 48/2(9+3) into 48*[1/(2(9+3))]. It all depends on if you see "2(9+3)" as one number or not. And since there is no official rule about juxtapositioning, the original equitation is just a case of bad maths, and should not be considered correct or even possible to solve. It's just unclear.