Simple problem, I think

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Simple problem, I think

#1  Postby The_Metatron » Jan 09, 2016 4:42 am

PEMDAS is how I learned it. Parentheses, exponents, multiplication, division, addition, and subtraction.

Here's the problem:

2x2 + 3x + 4

Let x = -2

What's the answer?

My solution went like this:

2(-2)2 + 3(-2) + 4
2 * 4 - 6 + 4
8 - 6 + 4
8 - 10
-2

But, the book disagreed:

2(-2)2 + 3(-2) + 4
2 * 4 - 6 + 4
8 - 6 + 4
2 + 4
6

Well, -2 is not equal to 6.

My answer is wrong. But, I don't clearly see why.
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Re: Simple problem, I think

#2  Postby laklak » Jan 09, 2016 4:45 am

I agree with the book, because addition and subtraction have an equal precedence and are performed left to right.

Try it on an HP Reverse Polish calculator, comes out 2.
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Re: Simple problem, I think

#3  Postby The_Metatron » Jan 09, 2016 5:00 am

I think you're right about that, too. I think my mistakes were applying PEMDAS too literally, and taking a shortcut:

8 - 6 + 4 is actually an addition problem: 8 + (-6) + 4
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Re: Simple problem, I think

#4  Postby laklak » Jan 09, 2016 5:09 am

That's how I look at it, and division as multiplication by the reciprocal.

4 / 2 * 6 =
4 * 1/2 * 3 =
2*3 = 6

not

4 / 2 * 3=
4 / 6 = 0.667
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Re: Simple problem, I think

#5  Postby felltoearth » Jan 09, 2016 5:15 am

How does 2(-2)2 produce 8? Shouldn't it be a minus?
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Re: Simple problem, I think

#6  Postby laklak » Jan 09, 2016 5:20 am

Because (-2)2 is (-2) * (-2) = 4.
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Re: Simple problem, I think

#7  Postby ElDiablo » Jan 09, 2016 6:01 am

I had to dust off a lot of cobwebs...
Here's a calculator I found http://www.mathpapa.com/calc.html?q=2x%5E2+2y%20for%20x%3D5%2C%20y%3D3
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Re: Simple problem, I think

#8  Postby ElDiablo » Jan 09, 2016 6:08 am

felltoearth wrote:How does 2(-2)2 produce 8? Shouldn't it be a minus?

Regarding multiplication...
Two positives equal a positive.
Two negatives equal a positive.
If only one is a negative, then the product will be a negative.
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Re: Simple problem, I think

#9  Postby felltoearth » Jan 09, 2016 4:52 pm

I understand that but I see two positives and one negative. Where the second negative?
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Re: Simple problem, I think

#10  Postby felltoearth » Jan 09, 2016 4:58 pm

laklak wrote:Because (-2)2 is (-2) * (-2) = 4.

So the notation is saying that there are two negatives not 2 times -2. Got it. Thanks
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Re: Simple problem, I think

#11  Postby felltoearth » Jan 09, 2016 4:59 pm

ElDiablo wrote:I had to dust off a lot of cobwebs...
Here's a calculator I found http://www.mathpapa.com/calc.html?q=2x%5E2+2y%20for%20x%3D5%2C%20y%3D3


So when I enter 2(-2) the calculator says -4.
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Re: Simple problem, I think

#12  Postby Thommo » Jan 09, 2016 5:03 pm

The_Metatron wrote:My solution went like this:

2(-2)2 + 3(-2) + 4
2 * 4 - 6 + 4
8 - 6 + 4
8 - 10
-2


-6+4 is not equal to 10.
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Simple problem, I think

#13  Postby felltoearth » Jan 09, 2016 5:03 pm

Oh! The second two is a square! I'm used to seeing this way of noting it 2x^2

ETA: silly me I didn't see it was a quadratic equation.
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Re: Simple problem, I think

#14  Postby Thommo » Jan 09, 2016 5:08 pm

felltoearth wrote:
ElDiablo wrote:I had to dust off a lot of cobwebs...
Here's a calculator I found http://www.mathpapa.com/calc.html?q=2x%5E2+2y%20for%20x%3D5%2C%20y%3D3


So when I enter 2(-2) the calculator says -4.


It will do, 2(-2) is shorthand for 2 x (-2) or "two lots of minus two".

The other part is the superscript 2, the "exponent" or "power", which is written:-

(-2)2

which is (-2)x(-2) or "minus two squared".

I don't know if the original problem using 2s everywhere is potentially confusing. If we consider instead:-

4y2

Then it's saying 4 x y x y ("4 times y times y" or "4 y squared"), which will always be positive, because if y is negative then the sign will cancel with the negative sign from the second appearance of y.

Edit: Oops, by the time I submitted this, you'd already noticed. Never mind, ignore! ;)
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Re: Simple problem, I think

#15  Postby felltoearth » Jan 09, 2016 5:10 pm

:thumbup:
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Re: Simple problem, I think

#16  Postby igorfrankensteen » Jan 09, 2016 6:35 pm

Here's a link that shows how you went wrong with "PEMDAS."

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

The problem with the acronym, is that saying it or memorizing it as though it's a weird word, causes it to BECOME confusing.

It really should be memorized as P E M-D A-S. Even that isn't quite right. Maybe instead, try to remember as a list:

1. P
2. E
3. M and D, left to right
4. A and S, left to right.

They do it with color coding on that link site, and say out loud that Multiplication and Division, like Addition and Subtraction, are actually equal in the order.

Lesson for the day: some memory tricks are better designed than others.

Does make me think of something else though. I wonder of I could design a coat to wear, that would make it appear that I was always INSIDE A SET OF PARENTHESIS. Maybe I could trick the world of standing-in-lines police, into thinking they had to take care of me first, every time.

Is that why old fashioned tuxedos look like that?
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Re: Simple problem, I think

#17  Postby Greyman » Jan 10, 2016 8:48 am

The_Metatron wrote:My solution went like this:

2(-2)2 + 3(-2) + 4
2 * 4 - 6 + 4
8 - 6 + 4
8 - 10
-2

My answer is wrong. But, I don't clearly see why.

-6 + 4 = -2
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Re: Simple problem, I think

#18  Postby felltoearth » Jan 10, 2016 6:02 pm

felltoearth wrote:Oh! The second two is a square! I'm used to seeing this way of noting it 2x^2

ETA: silly me I didn't see it was a quadratic equation.


And looking at this now on a browser. Tapatalk doesn't do superscript it seems.
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Re: Simple problem, I think

#19  Postby Weaver » Jan 11, 2016 7:02 pm

The_Metatron wrote:I think you're right about that, too. I think my mistakes were applying PEMDAS too literally, and taking a shortcut:

8 - 6 + 4 is actually an addition problem: 8 + (-6) + 4

This is it.

Doing it the other way would necessitate writing the equation 8 - (6+4) - introducing a higher function level where none was originally.
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Re: Simple problem, I think

#20  Postby The_Metatron » Jan 11, 2016 7:30 pm

Weaver wrote:
The_Metatron wrote:I think you're right about that, too. I think my mistakes were applying PEMDAS too literally, and taking a shortcut:

8 - 6 + 4 is actually an addition problem: 8 + (-6) + 4

This is it.

Doing it the other way would necessitate writing the equation 8 - (6+4) - introducing a higher function level where none was originally.

Yeah, it sure did trick me.
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