Solve 48

[Julius Caro]

/thread

Is this forreal?

To whoever said that multiplication takes precedence over division, pardon the rudeness, but that's just dumb. Mutiplication AND division take precedence over addition and subtraction. Considering you can express every division as a multiplication and viceversa, one taking precedence over the other doesn't make any sense. Same goes for addition and subtraction, they have equal precedence.

The ? symbol is confusing as hell, too.

48 / 2 * (9+3) = 48 * 0.5 * 12

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

I also thought at first that it was = 2, but no. It's not 48 / (2*(9+3)). And I highly doubt calculators are giving contradictory results, since the way they calculate the order of operations is straightforward.

[Jebadiah]

Yes, but multiplication, I've always been taught, takes precedence over division. So how come this doesn't apply here?

Division and Multiplication have equal precedence. Addition and Subtraction have equal precedence. In order of decreasing precedence: Parenthesis > division/multiplication > add/subtract.

What you have to notice is that there are no parenthesis in the denominator to indicate that 2 should be multiplied with (9 + 3).

Write it on a piece of paper properly the expression in the numerator and denominator form and you'll see what I am trying to say.

[skypx]

This may make it easier to understand.

[The Teej]

Division and Multiplication have equal precedence. Addition and Subtraction have equal precedence. In order of decreasing precedence: Parenthesis > division/multiplication > add/subtract.

What you have to notice is that there are no parenthesis in the denominator to indicate that 2 should be multiplied with (9 + 3).

Write it on a piece of paper properly the expression in the numerator and denominator form and you'll see what I am trying to say.

No no, I get the idea that there isn't parenthesis with parenthesis (that part is painstakingly obvious), the reason why I said 2(12) should come first is because I've always been taught multiplication > division > addition > subtraction is the logical order of all things - even going all the way back to Year 5 math classes. As multiplication and division are of equal precedence then the only real answer would be 288.

[giantpotato]

No no, I get the idea that there isn't parenthesis with parenthesis (that part is painstakingly obvious), the reason why I said 2(12) should come first is because I've always been taught multiplication > division > addition > subtraction is the logical order of all things - even going all the way back to Year 5 math classes. As multiplication and division are of equal precedence then the only real answer would be 288.

Whoever taught you, taught you wrong. multiplication = division > addition = subtraction. The operations that are of equal precedence are done left to right.

BEDMAS and PEMDAS have to have the same outcome, the answer to math equations has to be universal, it can't be dependant on where you were taught :unsure:

Personally, I was taught B E DM AS (Y)

[hondaa]

http://www.google.com/search?q=48%C3%B72%289%2B3%29&sourceid=ie7&rls=com.microsoft:en-us:IE-Address&ie=&oe=

[Rigby]

Four pages, what is going on here? This is grade school math. :laugh:

[Versanis]

If you will, simplify (ab+ac) for me.

The simplification is of course a(b+c).

The problem with writing it as in this question is that you cannot divide 48 by 2 as the 2 is a factor of the following sum, and not an independent term.

48 / 24 can be written as 48/2(9+3) because you cannot split the factor from its dependant terms for the purposes of order of operations as they should be considered 1 term.

If you could, you could just as equally do the following :-

48 / 24 = 48 / 4 * 6 = 72 which is clearly wrong.

[Julius Caro]

No no, I get the idea that there isn't parenthesis with parenthesis (that part is painstakingly obvious), the reason why I said 2(12) should come first is because I've always been taught multiplication > division > addition > subtraction is the logical order of all things - even going all the way back to Year 5 math classes. As multiplication and division are of equal precedence then the only real answer would be 288.

any multiplication can be expressed as a division, and every addition can be expressed as a subtraction. so what you are saying doesnt even make sense

[MikeFu84]

If it's PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction) shouldn't it me this:

Question: 48 ? 2 (9 + 3)

(9 + 3) = 12

12 * 2 = 24

48 / 24 = 2

[Draconian Guppy]

:)

Pretty sure Texas Instruments knows what they're doing.

Correct answer is:

48 / 2 * (9 + 3)

= 48 / 2 * 12

= 24 * 12

= 288

You cannot multiply 2 and 12 because 12 is not in the denominator. Do not make such incorrect assumptions just because of the way the expression is written.

+1

[Stetson]

If it's PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction) shouldn't it me this:

Question: 48 ? 2 (9 + 3)

(9 + 3) = 12

12 * 2 = 24

48 / 24 = 2

Well first PEMDAS is handy but misleading since multiplication and division are equal, as are addition and subtraction. Second you're correct in that apparently a distribution into parentheses takes higher presidence than normal multiplication.

Again I think the real issue is the formatting. Some calculators would take the given equation as meaning (my TI-89 for example, as well as Wolfram Alpha) while others would take it as .

If you take into account the rule about distributive multiplication presidence, which is probably correct but doesn't come up much, then the second interpretation is correct. Really the issue is that writing this equation out as 48 ? 2 (9 + 3) is unnecessarily confusing, and it isn't something you'd see in a real math class anyway.

I think that this is actually the correct way to write the original equation:

Here's a different way to show that:

1) 48/2(9+3)

2) let x=(9+3)

3) 48/2x

4) 24/x

5) 24/12

6) 2

I still think that the original equation is ambiguous, but that's how I see it now.

[Shadrack]

If it were written like 48/2(9+3) then I would say 2 because most people would assume that if a fraction is written like this then the left hand side of the slash is the numerator and the right hand side is the denominator. But because of the symbol used I'm thinking it goes by order of operation and is 288.

[Shokus]

My answer would be 2.

Not because multiplication takes precedence over division.

My reason is summarized here >

The answer is 2 based on the distributive law of multiplication taking precedence. If you want to know how PEMDAS factors in, you can just say that the digit next to the parentheses directly acts on the elements within the parentheses and therefore it's factored in before the rest of the order of operations.

This.

Edit: Actually the divide symbol defines that 48 divided by 2(9+3) so the answer is 2.

To get 288, the equation needs to be written as 48?2*(9+3).

Further readings:

http://physicsforums.com/showthread.php?t=488334

The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "?" sign) indicates that the juxtaposed values must be multiplied together before processing other operations.

Therefore,

48?2(9+3) = 2

48?2*(9+3) = 288

This is because I understand an algebraic statement 2x to be equal to 2(x), and this takes priority over regular multiplication and division. Therefore, 9?2x is equivalent to 9?2(x) which gives me 4.5 / x, instead of 4.5(x).

[Raa]

To me, the answer is 2.

Break it into words: 48, divided by 2 lots of (9 plus 3) -> 48 divided by 2 lots of 12 -> 48 divided by 24 -> 2.

That's how my mind reads it, it's been a long time since I did that sort of maths, but IIRC you don't suddenly do the right hand side of the equation before the left. It's left to right order - except parentheses of course.

Feel free to correct me if i'm wrong, and I probably am! :)

[Skyfrog]

Is this thread for real or is this all a big joke I'm missing?

[Versanis]

I think the joke is in how many people rely on computers to think for them.

[Jebadiah]

Is this thread for real or is this all a big joke I'm missing?

LOL It's for real and it has also become a joke.

[shockz]

Ahh math threads... a different answer for every post. Amazing.

[Stetson]

Ahh math threads... a different answer for every post. Amazing.

Yep, and each answer accompanied by "I don't see how you could see this any other way," when in the end we're all arguing about a problem which is poorly written in the first place.

[Jebadiah]

Yep, and each answer accompanied by "I don't see how you could see this any other way," when in the end we're all arguing about a problem which is poorly written in the first place.

No it's not poorly written, at least not this one. The expression is correct and there is only one answer, which is 288.

For one, people, please don't write math in a single line to try to solve it. It's supposed to be written on a piece of paper properly and solved manually, if you are solving it manually. And do NOT make random assumptions. Also, do NOT replace numbers with variables incorrectly with other random assumptions. That is all.

[Nayos]

If you will, simplify (ab+ac) for me.

The simplification is of course a(b+c).

The problem with writing it as in this question is that you cannot divide 48 by 2 as the 2 is a factor of the following sum, and not an independent term.

48 / 24 can be written as 48/2(9+3) because you cannot split the factor from its dependant terms for the purposes of order of operations as they should be considered 1 term.

If you could, you could just as equally do the following :-

48 / 24 = 48 / 4 * 6 = 72 which is clearly wrong.

48 / 24 would have to be written as 48 / (2(9+3)) if you're going to write it on one line.

And 48 / 24 = 48 / (4 * 6)

The brackets are important.

[Stetson]

No it's not poorly written, at least not this one. The expression is correct and there is only one answer, which is 288.

For one, people, please don't write math in a single line to try to solve it. It's supposed to be written on a piece of paper properly and solved manually, if you are solving it manually. And do NOT make random assumptions. Also, do NOT replace numbers with variables incorrectly with other random assumptions. That is all.

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

[seta-san]

#include <iostream>
using namespace std;

int main()
{
cout << 48 / 2 * (9+3);

return 0;
}

288

[pasty2k2]

I was getting in a pickle there, but the question isn't written in a correct format - you say solve, but the notation used is incorrect - the division symbol isnt used like that. Like on calculators (I'm not using one) it would be written as a fraction.

Now depending on how that was written in the question - 48 divided by 2(including everything in braces) or 48 divided by 2 * (everything in braces), you would end up with 2 or 288. Crude, but see below:

48

--------- = 2

2(9+3)

-OR-

48

--- (9+3) = 288

2

That was fun!