Question

ORDER OF OPERATIONS WITH INTEGERS PLZ HELP OMG

Answer 1

PEDMAS, OMG!

Answer 2

\[\large \frac{-5^2+10^2}{(2\times(-5)\times3)+3^2}\]

Ok I just wanted to repost it a sec, so everyone can see it :)

Answer 3

So if we're doing this in the correct order, we would start with P right?
Anything in Parenthesis we should deal with first.

Answer 4

\[\large \frac{-5^2+10^2}{(2\times\color{orangered}{(-5)}\times3)+3^2}\]This set of brackets doesn't mean anything, it's just to clarify that the negative sign is not subtraction.
So we'll start with these brackets,\[\large \frac{-5^2+10^2}{\color{orangered}{(2\times(-5)\times3)}+3^2}\]

With multiplication we want to execute it from left to right.
So start by multiplying 2 and -5, then multiply that result by 3.
What do you get so far? :)

Answer 5

2*-5=-10*3=-30 @zepdrix

Answer 6

\[\large \frac{-5^2+10^2}{\color{orangered}{-30}+3^2}\]Ok good job! :) Looks correct so far.

Answer 7

What's the next letter we're suppose to execute? E I guess? Hmm

So let's deal with those pesky `Exponents`.

Answer 8

side note

\[\frac{-5^2 +10^2}{(2 \times (-5) \times 3)+3^2}\]

can be considered as
\[[-5^2+10^2] \div [(2 \times (-5) \times 3) +3^2]\]

Answer 9

One important thing to consider Cassie, see how the -5 on top is NOT in brackets?
That's telling us that we're suppose to square the 5, but not square the negative.

Answer 10

Confused at all?
What do you get for each of those squared values?

Answer 11

Wait what do I have to do for the exponents?

Answer 12

We'll use the 10 as an example.

\(\large 10^2\) is the same as \(\large 10 \times 10\).

Answer 13

\[\large \frac{-5^2+\color{green}{10}^2}{-30+3^2} \qquad =\qquad\frac{-5^2+\color{green}{100}}{-30+3^2}\]Understand what I did there?
The 2 exponent is telling us to take two 10's and multiply them together.

Answer 14

Yeah, I get that one, so I multiplied 10x10 and I got 100, what do I do next.?

Answer 15

We need to do the same with the \(\large 3^2\) and the \(\large -5^2\).
Can you figure those two values out using the same idea? :)

Answer 16

3*3=9... what do I do with the negative 5? I don't use the negative right?

Answer 17

Correct :) Don't use the negative.
There will end up being a negative in front. But for now, we can think of the square being only applied to the 5 like this \(\large 5^2\).

Answer 18

okay so \[3^{2}=3\times3=9\] and \[5^{2}=5\times5=25\] am I right?

Answer 19

Yes good!\[\large \frac{-5^2+10^2}{-30+3^2} \qquad = \qquad \frac{-25+100}{-30+9}\]Is it somewhat clear, based on what I explained before, why I left the negative in front of the 25?

Answer 20

because the answer will be negative?

Answer 21

It's because this \(\large -5^2\) is NOT the same as this \(\large (-5)^2\).

\(\large \color{royalblue}{-5^2 \qquad = \qquad -5\times5}\)
\(\large (-5)^2 \qquad = \qquad -5\times -5\)

We were dealing with the blue one. So we don't have 2 negatives being multiplied together.

I dunno, it's a little tricky to explain :) lol

Answer 22

I get that part now :)

Answer 23

The next step is pretty straight forward.. I'm having trouble justifying it with the order of operations though.

We want to separately add the top terms together, and then add the bottom terms together, to form a simpler fraction.

Answer 24

If you want to be able to justify it using the order of operations, we might want to use Complete's hint.\[\large \frac{-25+100}{-30+9} \qquad = \qquad (-25+100)\div(-30+9)\]The fraction bar means `divide`, so we're allowed to write it this way if we want.
The reason we might want to, is so we can see that we have brackets, and need to deal with that before we deal with the division.
I "magically" made brackets appear... i know i know :\ hmm

Answer 25

Order of Operations is so annoying :P This stuff gets easier I promose...
but then it gets harder later on lol

Answer 26

I got 25 over 7

Answer 27

Oh so you added the stuff and did some stuff.. then simplified the fraction I guess? :)

Answer 28

I don't know aha I used the scientific calculator website my teacher gave us to use online

Answer 29

oh lol XD

Answer 30

Try to be careful with your addition. See how the negative value is LARGER on the bottom of the fraction? We should get a -21 on bottom.
\[\large \frac{75}{-21}\]

Answer 31

oh see I first added it up by myself on paper, and that's what I got so the calculator lied oooh

Answer 32

That rotten calculator +_+

Answer 33

so wait is that the answer?

Answer 34

It is the answer, but not in the `simplest form`.
We still have another step we can do.

The fraction can be simplified since both the top and bottom are divisible by 3.

Answer 35

\[\large \frac{75}{-21} \qquad = \qquad \frac{25\times3}{-7\times3}\]

Answer 36

-32?

Answer 37

The reason I factored a 3 out of the top and bottom is so we can "cancel" them out.\[\large \frac{25\times\cancel{3}}{-7\times\cancel{3}} \qquad = \qquad \frac{25}{-7}\]Is that step a lil confusing? :o

Answer 38

yeah it is

Answer 39

was that the last step is that the answer?

Answer 40

Yes. As a final step, we could bring the negative in front of the fraction instead of leaving it in the bottom.

\[\large \frac{25}{-7}\qquad =\qquad -\frac{25}{7}\]

Answer 41

So there is our answer.
It's not too bad of a problem, it's just a lot of steps.

You have some stuff you can look at here though if you get confused :o

Answer 42

can you please help me with a few others?

Answer 43

btw thank you :)

Answer 44

wait it said it was wrong

Answer 45

Did it say it was wrong? Ok try this answer.

\(\large -\dfrac{125}{21}\)

Answer 46

nope that didnt work i dont think it can be in fraction form :O

Answer 47

Ah interesting :o hmm

Answer 48

The fraction bar, as we said before, means `divide`.
So as a final step, divide 25 and -7.

You'll get a number with an ugly decimal.. but maybe that's what they want you to enter.

Answer 49

nope ):

Answer 50

ok lemme look back at the original problem a sec, to make sure we didn't make a boo boo anywhere.

Answer 51

Ah I see what's going on :( I pasted the problem incorrectly...\[\huge \frac{-5^2+10^2}{(2\times(-5)\times3)+3^{\color{red}{3}}}\]

Answer 52

It should have been 3 to the 3rd power on the bottom.

\(\large 3^3 \qquad = \qquad 3\times3\times3\)

Answer 53

27

Answer 54

Everything else looked ok though, so we only need to fix this one part,\[\large \frac{-25+100}{-30+\color{red}{9}}\]27? Ok that sounds about right,\[\large \frac{-25+100}{-30+\color{green}{27}}\]

Answer 55

So what do you get this time? :)
It should give us a nice clean number.

Answer 56

-25

Answer 57

YAY IT WORKED ... can you help me with a few others please :)

Answer 58

This thread is getting a little too long D:
Close it down and start a new one with your new problem.

You can type @zepdrix somewhere in the description and it will help me get to your problem easier. I might hop off for a little bit D: But I'll try to come help if noone else does.
I'm sure someone can help ya though!! c: