1. ## order of operations

For some reason I have lost all orientation in my head apparently with Order of Operations. Everyone knows PEMDAS. Parenthesis , Exponents, Multiplying, Division, Addition, then Subtraction. YET when I do the following problem in that manner I get the wrong answer.

I am really not understanding this so using this exact problem could someone write out exactly what they do first and as they solve the problem every single step you use. Thank you very very much

$\displaystyle 9 + 16 / (-4) * 8 + 3 * 5$

I'm really at a loss for why I am getting this wrong.

I first did multiplication obviously being the first we see here in PEMDAS.

Multiplied -4 and 8 .. then 3 and 5. Then when those two answers pulled down I divided using the divisor sign, then finished up with the addition then subtraction but -4 is not the right answer

$\displaystyle (x + 3)^2 ..$

In that would the answer be

$\displaystyle x^2 + 6$ or $\displaystyle x^2 + 9$

I don't know if the rule for multiplying stands true for whole numbers too (Constants)

Just which one of those is right anyone?
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2. $\displaystyle 9 + \frac{16}{-4} \cdot 8 + 3 \cdot 5$

$\displaystyle 9 + (-4) \cdot 8 + 15$

$\displaystyle 9 - 32 + 15 = -8$

$\displaystyle (x + 3)^2 = x^2 + 6x + 9$

3. Originally Posted by CyberClaw

$\displaystyle 9 + 16 / (-4) * 8 + 3 * 5$
The problem is this:

When the '/' symbol is used for division, it only affects the first thing it touches to the left and the right. In other words, the equation above means this:

$\displaystyle 9 + \frac{16}{-4} \times 8 + 3 \times 5$

What you have done is interpret the '/' as affecting both the -4 and the 8:

$\displaystyle 9 + \frac{16}{-4 \times 8} + 3 \times 5$

That would only be correct if your original equation had been written like this:

$\displaystyle 9 + 16 / (-4 * 8) + 3 * 5$

4. With order of operations, it is important to note that multiplication and division are to be completed from left to right... in other words, multiplication is not to be done before division... they are supposed to be done from left to right. It is the same with addition and subtraction.

5. Originally Posted by CyberClaw
$\displaystyle (x + 3)^2 ..$

In that would the answer be

$\displaystyle x^2 + 6$ or $\displaystyle x^2 + 9$

I don't know if the rule for multiplying stands true for whole numbers too (Constants)

Just which one of those is right anyone?
[EDITED END]
Here's another acronym you might remember . . . FOIL. Multiply it out using "First, Outer, Inner, Last."

$\displaystyle (x + 3)(x + 3)$

first + outer + inner + last

$\displaystyle x \cdot x + 3 \cdot x + 3 \cdot x + 3 \cdot 3$

$\displaystyle x^2 + 6x + 9$

A lot of us remember squares of the form $\displaystyle (a + b)^2$ as $\displaystyle a^2 + 2ab + b^2$

6. Originally Posted by bluejay
With order of operations, it is important to note that multiplication and division are to be completed from left to right... in other words, multiplication is not to be done before division... they are supposed to be done from left to right. It is the same with addition and subtraction.

This is the awesome thing. Nobody not even a single teacher made that apparent. What is going on with them. I never was taught DIVISION OR MULTIPLICATION as long as it is going from left to right. , I failed a test because I didn't know that. So stupid.

Anyway thanks man this has been a great help.

I have more questions so I will post when some time has passed so Im not looked at as a spammer.

7. Originally Posted by CyberClaw
This is the awesome thing. Nobody not even a single teacher made that apparent. What the is going on with them. I never was taught DIVISION OR MULTIPLICATION as long as it is going from left to right. , I failed a test because I didn't know that. So stupid.

Anyway thanks man this has been a great help.

I have more questions so I will post when some time has passed so Im not looked at as a spammer.
Post away, that's what we're here for. If you're worried about spamming, we appreciate it when you show your attempts, so that way we can see you're trying to do the work