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**frostysmom****Member**- Registered: 2005-08-26
- Posts: 4

Hi, this is my first post here. Let me give everyone a little background. My son is in 7th grade and is just beginning algebra. It's been a while since I've been in school and I'm trying to help my son. While checking his homework I cam across a problem that I thought he'd done wrong. We worked it together and came up with the answer. He went to school the next day and the teacher told him the answer he had was wrong. I disagreed and sent a note to the teacher asking her where we'd gone wrong. She sent home an answer that I'm still not satisfied with. My son (being the smart kid he is) went into Excel, typed in the expression (he simply entered the numbers instead of the letters) and Excel evaluated it with the answer that we got.

So...here's the equation.

w=2, x=6, y=4

(2w + 2y) / 2x

Could someone please help? The answer that we got (and that Excel got) is 36. The teacher says the answer is 1. We know that what's in parentheses gets evaluated first. The question I have is what get's evaluated next - the division or the multiplication? Based on the math textbook I say it's the division and obviously the teacher says it's the multiplication.

Anyway, thanks for any and all help.

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**im really bored****Member**- Registered: 2005-05-12
- Posts: 76

I think the teachers answer is right, in the order of operations it goes: parentheses, exponets, multiplication, division, addition, then subtraction. So in the problem first you would put in the given variables, (2(2) + 2(4) / 2(6), then (4 + 8) / 12, then 12 / 12, which simplifys to 1.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

Welcome to the forum, frostysmom !

You can see a page about this here: PEMDAS

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**frostysmom****Member**- Registered: 2005-08-26
- Posts: 4

Thanks alot - I looked at the PEMDAS web page and I understand it to be like I said. In other words, multiplication and division, working from left to right whichever comes first. And in my mind, it supports my answer.

Then again, could be I'm still being blinded by my need to be right .

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

I think I see the problem, it is what order to do "/2x". Do you divide by 2 **then** multiply by x? In other words:

You could have ((2w + 2y) / 2) × x = ((4 + 8) / 2) × 6 = 6×6 = 36

Or: ((2w + 2y) / (2 × x) = ((4 + 8) / (2 × 6) = 12/12 = 1

When we see something like "2x" we *automatically* think to multiply it first (unless there were brackets and exponents), so we are blinded to the possibility of it behaving the other way.

But if it were written: (2w + 2y) / 2 × x, then we would look at it and go "hmmm... maybe you should multiply by x last"

Maybe that is a little sub-rule that should go on the PEMDAS page!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**frostysmom****Member**- Registered: 2005-08-26
- Posts: 4

So the correct answer is 36. (right?)

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

No, it would be 1 because we would mulitiply "2x" first.

Just like we would if it were:

2w + 2y

---------

2x

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**frostysmom****Member**- Registered: 2005-08-26
- Posts: 4

I'm sorry but I don't understand why you would multiply 2x first? That's what's really getting me...There aren't parentheses around the 2x so why wouldn't you divide then multiply?

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**Flowers4Carlos****Member**- Registered: 2005-08-25
- Posts: 106

when it comes to division or multiplication, it doesn't matter which one u do first. u can either divide right away:

(12/2)/x= 6/x and 6/6=1

or u can simply the denominator first:

12/[2(6)]= 12/12=1

either way u get the same answer!

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