# I really need help!!!

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48÷2y

=24y or 24/y?

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Place the equation this way and it will be easier to see:

$\frac{48}{2y}=\frac{24}{y}$

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So that means i need to treat 2y as 1 term?

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I'm afraid no one can answer that for you, except the person who gave you the ambiguous term. I would interpret it the way Spyman did (as $\frac{48}{2y}$), but that's just from my taste of aesthetics, not because I'd know some rule that this surely cannot mean $\frac{48}{2}y$.

Edited by timo

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So that means i need to treat 2y as 1 term?

Otherwise it should have been:

(48/2)y = 24y

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Do you know that or do you just assume that because it is intuitive, Spyman?

Edited by timo

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Well...Thx for ur help

I've also got a question which i guess almost everyone knows lol

is that

48÷2(9+3) = ?

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Do you know that or do you just assume that because it is intuitive, Spyman?

Assume, I am no math expert and don't know any rule for this either.

I guess for this cind of question the math is of such level that multiplication of 2 and y should have precedence.

48÷2(9+3) = ?

Well, I don't think the answer is 24×12, do you?

[EDIT]

Actually I think the general rules are to first perform any calculations inside parentheses and then multiplications/divisions take precedence before additions/subractions and priority is from left to right.

However 48/2(9+3) is different than 48/2×(9+3) since the multiplication sign is significantly missing in the first equation. When it is removed I always intuitive put an extra parentheses around that part making it 48/(2×(9+3)) or 48/(2×y).

Edited by Spyman

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well I guess it should be 2 at first but later i asked my classmates and they had different answers

Some are 2 and some are 288

That's why i am confused

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I usually take 2(9+3) to mean (2(9+3)) and not 2 * (9+3) so I think that 48÷2(9+3) is asking for 48÷(2(9+3)) and the answer is 2. This is also the more logical answer given the context and the numbers.

I think in general, oversights like this are avoided at all costs in literature and they generally constitute a mistake. It is usually pretty clear the intention and this isn't something you should dwell on; there are better uses for your time.

lol

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So that means i need to treat 2y as 1 term?

Just ask yourself: Why would you divide 48 by the 2 but not by the y?

If you had $48 billion, and you had to divide it among 2 hundred people, or 2 thousand people, or 2 million people, you would divide the$48 billion by the 2 *and* the hundred, or thousand, or million.

Edited by ewmon

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I usually take 2(9+3) to mean (2(9+3)) and not 2 * (9+3) so I think that 48÷2(9+3) is asking for 48÷(2(9+3)) and the answer is 2. This is also the more logical answer given the context and the numbers.

I think in general, oversights like this are avoided at all costs in literature and they generally constitute a mistake. It is usually pretty clear the intention and this isn't something you should dwell on; there are better uses for your time.

lol

How can you prove that 2(9+3) = (2(9+3))?

I mean the bracket( 2(9+3) ) is added yourself. My primary teacher told me that brackets are at the first priority to solve and there is no rule of precedence of multiplication and division. That means after solving the brackets, we have

48 ÷ 2(9+3)

=48 ÷ 2 x 12

=288

and that's also quite reasonable , i guess.

Well but my first answer is 2. Truely , i thought it is 2 but the ''288 guys'' still have their own reasons which can't be neglected.

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It's not an issue of proof, this is not conventional mathematics and this is why this is ambiguous. It's an accepted way of doing things just as 2x really means 2 * x, it is an ugly thing to do but it happens. It is what is called 'implied' . . . . . . . . . . . . .

If you wish to maintain conventional mathematics than indeed the answer is 288, but I can guarantee you 100% that this was not the intention. There are a number of other ways that this could have been written that are, statistically speaking, far more likely to have been used. Given the statistics if you answer 288, well you would be someone who ignores their own better judgment; I mean you are questioning this!

Edited by Xittenn

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So that means i need to treat 2y as 1 term?

Yes.

Just like you can treat "2 eggs" as one term, or "two bananas", "two dollars", or "two hours". You don't just have "two". You have to specify "two what?".

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well I guess it should be 2 at first but later i asked my classmates and they had different answers

Some are 2 and some are 288

That's why i am confused

Was not this a test you have finished and as of which you now could ask your teacher for the intention and answer of the question?

Or are you trolling and trying to stirr up fuzz?

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well I guess it should be 2 at first but later i asked my classmates and they had different answers

Some are 2 and some are 288

That's why i am confused

The general rule in mathematics is to be clear.

"48÷2(9+3)" is not clear. To make it clear one needs to use parentheses. So one would write either 48÷(2(9+3) or (48÷2)(9+3).

There is no point in arguing over what 48÷2(9+3) is "supposed to mean" as that reqiuires divining the intent of the writer.

The fundamental problem is the symbol "÷" which is not normally used in scientific circles, or polite company, anyway. I have not seen it in regular use since about the third grade (caculators using algebraic notation (ugh!) excepted).

I have been a professional mathematician for over three decades. I understand arithmetic pretty well, but I flunk tests of clairvoyance with regularity. When in doubt ask the author.

Edited by DrRocket

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48÷2y

=24y or 24/y?

nouseforaname do you know that you can actually prove that 48÷2y= 24/y and not 24y??

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nouseforaname do you know that you can actually prove that 48÷2y= 24/y and not 24y??

no, you can't. you can't "prove" (no matter how big a font you use) a convention. You decide on a convention, and stick to it. The question as asked depends on what convention one uses.

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no, you can't. you can't "prove" (no matter how big a font you use) a convention. You decide on a convention, and stick to it. The question as asked depends on what convention one uses.

Well .

Do we not define division in rational and in real Nos a÷b = $\frac{a}{b}= a\frac{1}{b}$??

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Well .

Do we not define division in rational and in real Nos a÷b = $\frac{a}{b}= a\frac{1}{b}$??

How does this "prove" whether the y in the OP's question is in the numerator or denominator?

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How does this "prove" whether the y in the OP's question is in the numerator or denominator?

well ,the proof is high school level and it is the following:

$\frac{48}{2y} = 48.\frac{1}{2y}$=...........................................by using the definition of division: $\frac{a}{b}= a\frac{1}{b}$

=$48(\frac{1}{2}\frac{1}{y})$=..................................................by using the theorem :$\frac{1}{a}\frac{1}{b}=\frac{1}{ab}$ and the axiom : 1a =a

=$(48.\frac{1}{2})\frac{1}{y}$=...................................................by using the axiom : (ab)c =a(bc)

=$[(24.2)\frac{1}{2}]\frac{1}{y}$=..................................................by using the theorem in Natural Nos 48 =24.2

=$[24(2\frac{1}{2})]\frac{1}{y}$=....................................................by using again the axiom : (ab)c = a(bc)

=$24\frac{1}{y}$=............................................................................by using the axiom : $a\neq 0\Longrightarrow a\frac{1}{a}=1$ and also the axiom :1a = a

=$\frac{24}{y}$................................................................................by using again the definition of division

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Umm, you assumed that the OP's ambiguous statement means $\frac{48}{2y}$, and surely there is no argument that if this is the case then it does equal $\frac{24}{y}$, however, the point is that this statement is ambiguous since we are not sure whether it means $\frac{48}{2y}$ or $(\frac{48}{2})y$, and that you cannot prove the convention of how we interoperate the OP's expression.

Edited by DJBruce

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48÷2y

=24y or 24/y?

Umm, you assumed that the OP's ambiguous statement means $\frac{48}{2y}$, and surely there is no argument that if this is the case then it does equal $\frac{24}{y}$, however, the point is that this statement is ambiguous since we are not sure whether it means $\frac{48}{2y}$ or $(\frac{48}{2})y$, and that you cannot prove the convention of how we interoperate the OP's expression.

Well ,what did the OP asked??

Is there any mathematical book in the whole history of mathematics in which 48÷2y can be equal to $(\frac{48}{2})y$???

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Well ,what did the OP asked??

Is there any mathematical book in the whole history of mathematics in which 48÷2y can be equal to $(\frac{48}{2})y$???

As the OP indicated by saying, "=24y or 24/y?" the he was asking how we would interoperate the expression given. As for where has 48÷2y been equal to:

$(\frac{48}{2})y$,

according the standard oder of operations taught in children operations should be evaluated in the following order Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction (PEMDAS), and when operations of equivalent order are next to each other they are evaluated from left to right. Meaning that since division and multiplication of are same order we would evaluate 48÷2y as being (48÷2)y --since division furthest to the left.

http://www.purplemath.com/modules/orderops.htm

http://www.mathsisfun.com/operation-order-pemdas.html

http://www.math.com/school/subject2/lessons/S2U1L2GL.html

Edited by DJBruce

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2y should be treated as one term because when you get a value for the variable y it is to be multiplied with two. Taking y separately would hamper the result. The co-efficient is always taken with the variable to get exact result.

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