48÷2(9+3)


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But...

If you have 1 bottle of portwine

+

ten cans of beer.

=

Hangover next morning.

I'm pretty sure about that... DOH!

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BODMAS indicates when there is both multiplication and division, you go from left to right first. So you should be dividing 48 by 2, then multiplying what was in the brackets.

BODMAS has nothing to do with left to right (or right to left for that matter).

It is the order that you do the operations.

Brackets

Of

Division

Multipication

Addition

Substraction

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This is an equation.

48

---------- = 2

2(9+3)

move the divisor to the rhs, becomes

48 = 2 * 2(9+3)

solve brackets, becomes

48 = 2 * 2(12)

multiple, becomes

48 = 2 *24

multiple again, becomes

48 = 48

or

48 - 48 = 0 equation solved.

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To further clarify, this problem is a formulae in the form of an equation (anything after the Division symbol is a divisor in an equation).

A

-- = x

B

A is the numerator.....in this case 48.

B is the divisor.....in this case 2(9+3).

The BODMAS is the order of operation, that is applied to the numerator and the divisor separately.

so A = 48

B= 2(9+3) = 2(12) = 24

A/B = 48 / 24 = 2.

So.......... x = 2

Basically once you get to the division mark in an equation, you stay in the divisor unless there is a second division mark.......clear :D

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To further clarify, this problem is a formulae in the form of an equation (anything after the Division symbol is a divisor in an equation).

A

-- = x

B

A is the numerator.....in this case 48.

B is the divisor.....in this case 2(9+3).

The BODMAS is the order of operation, that is applied to the numerator and the divisor separately.

so A = 48

B= 2(9+3) = 2(12) = 24

A/B = 48 / 24 = 2.

So.......... x = 2

Basically once you get to the division mark in an equation, you stay in the divisor unless there is a second division mark.......clear :D

Pretty sure it would look like this if you want to restructure it to put something in the divisor:

48

--- (9+3)

2

The parentheses does not also make it into the divisor.

To put it another way, if the question was

10 ÷ 2 + 6, the anwswer would be 11, as you would divide 10 by 2 first, then add six. You would not put 10 in the numerator, and put 2+6 in the denominator, like you would have to if it was like you described, where anything after the division sign would have to go into the denominator..

To put it another way, if we used your numerator/denominator of

48

---

2(9+3)

the original would have looked like:

48 ÷ (2(9+3))

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Basically once you get to the division mark in an equation, you stay in the divisor unless there is a second division mark.......clear :D

So,

consider a÷(b÷c) = n

this equation in visual form becomes

  a

------ = n

(b÷c)

or

a * c

------ = n

  b

The second ÷ shifts the argument back to the numerator.

Try solving with different valuse of a, b, c without the distractions of other functions.

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Pretty sure it would look like this if you want to restructure it to put something in the divisor:

48

--- (9+3)

2

This ignores basic mathematic principals.......you cannot arbitrarily decide what goes into the numerator and what goes into the denominator....just to suit the argument. :D

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This ignores basic mathematic principals.......you cannot arbitrarily decide what goes into the numerator and what goes into the denominator....just to suit the argument. :D

I thought I was following principles. Could you explain using the other example in my post? If you're correct that the term after the division symbol goes into the divisor, you are arguing that:

10 ÷ 2 + 6

is the equivalent of

10

---

2 + 6

Obviously, this would be incorrect.

Also, are you saying that

48 ÷ 2(9+3)

is the equivalent of

48 ÷ [2(9+3)]

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Clearly the result is 42, as 42 is the Answer to the Ultimate Question of Life, the Universe, and Everything.

:D

And here you had me trying to remember Please Excuse My Dear Aunt Sally, probably one of the stupidest mnemonic I can remember.

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I thought I was following principles. Could you explain using the other example in my post? If you're correct that the term after the division symbol goes into the divisor, you are arguing that:

10 ÷ 2 + 6

is the equivalent of

10

---

2 + 6

Obviously, this would be incorrect.

The equation is 10 ÷ 2 + 6 = x

The +6 does not go into the divisor as the ÷ rankes higher (BODMAS) than the +, therefor the division is done first using only the 6.

In the problem put forward the Brackets are of higher order than the ÷, so must be applied first (puting it in the divisor).

You could also write the equation as 10 ÷ 2 = x - 6 to make clearer.

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Basically any part of an equation with brackets must be applied first. Simply piece by piece and the problem sorts itself out.

BTW

Left or right only relates to entering data in scientific calculators, exception being HP's calculators using Reverse polish Notation which tends to sort things out by itself (up to 4 levels of embedment).

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Basically any part of an equation with brackets must be applied first. Simply piece by piece and the problem sorts itself out.

BTW

Left or right only relates to entering data in scientific calculators, exception being HP's calculators using Reverse polish Notation which tends to sort things out by itself (up to 4 levels of embedment).

But the implied multiplication isn't part of the standard order of operations, BODMAS, or PEMDAS, or whetever people call it.

Using BODMAS,

B brackets

O orders

D division M multiplication

A addition S subtraction

the 2 is not part of the brackets, it is outside of them.

I think the problem is that the question is vague.

If it is read as 48 ÷ 2 x (9+3) it comes out 288, but if it's read as 48 ÷ [2(9+3)], with the implication that the 2(12) multiplication comes before the division, you get 2.

Here's some further discussion. The funny thing is, this has been going around a few forums today, and some of the discussions have been pretty heated. Kind of funny....

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

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I think the problem is that the question is vague.

If it is read as 48 ÷ 2 x (9+3) it comes out 288, but if it's read as 48 ÷ [2(9+3)], with the implication that the 2(12) multiplication comes before the division, you get 2.

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

Agreed...very poor notation

as written.... my brain, google, excel, python, matlab (in order of trustworthiness), all say 288. If written as it should be then it would be 2.

done and done.

David

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the 2 is not part of the brackets, it is outside of them.

yes but 2(9+3) means 2*(9+3)........................anyway, lets agree to differ.

The question would be best written as either:

(48 ÷ 2)(9+3), simplifying to (24)(12), equaling 288

or

48 ÷ (2(9+3)), becoming 48 ÷ (2*12), equalling 2

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By the way.......the reason Google gives 288 is because it interprets the problem as (48 ÷2) * (9 + 3):

post-1158-1302319255.png

So it is not necessarily a correct solution, just Googles interpretion of the problem.

post-1158-1302318902.jpg

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yes but 2(9+3) means 2*(9+3)........................anyway, lets agree to differ.

The question would be best written as either:

(48 ÷ 2)(9+3), simplifying to (24)(12), equaling 288

or

48 ÷ (2(9+3)), becoming 48 ÷ (2*12), equalling 2

I don't think we really differ. I mean, both of us agree that it's not written too well.

And yes, 2(9+3) means 2*(9+3). But the argument is that as it is written, should 2*(9+3) be the equivalent of [2*(9+3)]? According to the order of operations, however people learned it, whether BODMAS or PEMDAS, multiplication and division are equal, and should be done from left to right. So

48 ÷ 2*(12) should be done left to right, which would yield 288. If instead we had 48 ÷ [2*(12)], then we get 2.

I think all this just shows this is why the ÷ symbol isn't used much past very young ages.

"Please Excuse My Dear Aunt Sally".... Multiplication comes first in that so thats what I go with

Technically, it's

P Parentheses

E Exponents

MD Multiplication Division left to right

AS Addition Subtraction left to right

Multiplication doesn't come first. Multiplication and division are equal. You need to go left to right, not pick multiplication over division.

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