## Simple problem, I think

order of operations

Discuss the language of the universe.

### Simple problem, I think

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

Here's the problem:

2x2 + 3x + 4

Let x = -2

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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The_Metatron
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### Re: Simple problem, I think

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

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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Check out Hack's blog, too. He writes good.

The_Metatron
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### Re: Simple problem, I think

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
A man who carries a cat by the tail learns something he can learn in no other way. - Mark Twain
The sky is falling! The sky is falling! - Chicken Little
I never go without my dinner. No one ever does, except vegetarians and people like that - Oscar Wilde

laklak
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### Re: Simple problem, I think

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

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### Re: Simple problem, I think

Because (-2)2 is (-2) * (-2) = 4.
A man who carries a cat by the tail learns something he can learn in no other way. - Mark Twain
The sky is falling! The sky is falling! - Chicken Little
I never go without my dinner. No one ever does, except vegetarians and people like that - Oscar Wilde

laklak
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### Re: Simple problem, I think

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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ElDiablo

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### Re: Simple problem, I think

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.
God is silly putty.

ElDiablo

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### Re: Simple problem, I think

I understand that but I see two positives and one negative. Where the second negative?
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felltoearth

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### Re: Simple problem, I think

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
"Walla Walla Bonga!" — Witticism

felltoearth

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### Re: Simple problem, I think

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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felltoearth

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### Re: Simple problem, I think

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.

Thommo

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### Simple problem, I think

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.
"Walla Walla Bonga!" — Witticism

felltoearth

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### Re: Simple problem, I think

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!

Thommo

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### Re: Simple problem, I think

"Walla Walla Bonga!" — Witticism

felltoearth

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### Re: Simple problem, I think

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

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
"And, isn't sanity really just a one-trick pony anyway? I mean all you get is one trick, rational thinking, but when you're good and crazy, oooh, oooh, oooh, the sky is the limit." - T. Tick.

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### Re: Simple problem, I think

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.
"Walla Walla Bonga!" — Witticism

felltoearth

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### Re: Simple problem, I think

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.

Retired AiF

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### Re: Simple problem, I think

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.
I AM Skepdickus!

Check out Hack's blog, too. He writes good.

The_Metatron
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