Question

Simplify this expression 5a/11a?
I don't know if it's in correct format but it's 5a over 11a. I don't know how to do this, I take online classes and I don't hardly get help.

Answer 1

5/11
The a's divide out.

Answer 2

Is it really as simple as that? o-o Well, I feel dumb now. Thank you.

Answer 3

It's not as simple as that if you think about why \(a\)'s must kill each other out

Answer 4

They can't just kill eachother with swords and call it the results?
(I'm sorry I attempt to create funny comments.)

Answer 5

Imagine you have 12 cookies,
and you want to distribute them equally to your 4 friends

Answer 6

How many cookies each friend gets ?

Answer 7

3?

Answer 8

How ?

Answer 9

12 divided by 4 equals 3?

Answer 10

Exactly! So you can think of the "division operation" intuitively as distributing cookies to friends :
\[\dfrac{12}{4}\]

top is number of cookies you have
bottom is number of friends you want to distribute the cookies to

Answer 11

The result "3" tells you the number of cookies EACH friend gets

Answer 12

Unless I kill a friend and share their cookies right?

Answer 13

Unless you're partial to one of your friends.. it won't be an equal distribution anymore

Answer 14

Let me ask you a difficult question now

Answer 15

(5a/a)/(11a/a) = 5/11

Answer 16

Imagine you have killed half of your friends and ate half of your cookies.

Answer 17

Then, how many cookies and friends you're left with ?

Answer 18

I don't like this idea of killing, maybe let me rephrase the question.. one moment

Answer 19

Should we say they half of the friends are allergic to the cookies then?

Answer 20

Suppose you don't want to give cookies to half of your friends as you don't like them.

So you ate half the cookies yourself and want to distribute the remaining half of cookies to the the remaining half of friends that you love so much.

Answer 21

I want you think about above situation.
Now, after eating half of the cookies, if you distribute the remaining cookies equally to half of your friends, how many cookies does EACH of your friend get ?

Answer 22

Lets see 12 cookies to start, 5 people(including myself) 2.4 cookies for everyone? o.o Okay, Let's take it to 2 cookies for everyone, I ate 2 cookies leaving 10, 2 friends are allergic and 2 friends ate their 2, that would would leave 6 cookies left and since only three could eat them that would give them three 2 more cookies meaning there would be 0 cookies, but 3 people got 4 cookies each. Right?

Answer 23

don't include yourself

Answer 24

your friends are the guests, you're just happy watching them eat

Answer 25

Okay, so only 2 friends get to eat since the other 2 cannot?
But in the questions you said I ate half of the cookies and that there were 12, so 2 people get 3 each and the other 2 don't get any due to allergies?

Answer 26

Right, so each of your loving friends are getting just 3 cookies again.
recall that earlier also they got the same 3 cookies

Answer 27

Distributing 12 cookies to 4 friends

is same as

distributing 6 cookies to 2 friends

Answer 28

I mean, each friend gets the same number of cookies in both situations

Answer 29

Could you explain why they get the same number of cookies ?

Answer 30

I mean, I don't get how 4 friends sharing 12 cookies and 2 friends sharing 6 cookies is even, but I am going to say because there is 12 cookies in both situations. I don't even know, It's 2:30AM and I have alot more "homework" to do...

Answer 31

It's okay, you're doing great and you know enough to complete your homework. Just think about this when you have lots of time :

\[\dfrac{12}{4} = 3\]
\[\dfrac{6}{2} = 3\]

Why they both give the same answer ?

Answer 32

Ah, I get that. I wasn't thinking of the part I ate half of the cookies leaving 6 between 2 friends. XD

Answer 33

More generally, think about why below "rule" is true:
\[\dfrac{a}{b} = \dfrac{a/c}{b/c}\]

The answer doesn't change if you divide top and bottom by the same number \(c\)

Answer 34

Awesome! I see you have nailed this division thingy! keep going with the rest of problems :)

Answer 35

Well, I ran into another road block. It's asking me for the simplest form of 4(-m-1)-5. I am terrible at math as you can tell.

Answer 36

Could you take a screenshot of that expression and attach here if psble ?

Answer 37

Sure. One second.

Answer 38

It won't let me send once I attach a photo.

Answer 39

This is it though.
http://prntscr.com/b0gbc0

Answer 40

That's okay, so is it like this ?
\[ \LARGE 4(-m-1)-5\]

Answer 41

Familiar with PEMDAS ?

Answer 42

I am.

Answer 43

Good. So first look for any parenthesis in the expression and simplify the stuff inside them

Answer 44

\[ \LARGE 4(\color{red}{-m-1})-5\]

Answer 45

So when you do that would inside the parenthesis equal -1m or 1m by a chance?

Answer 46

There is nothing to simplify inside the parenthesis

Answer 47

Get out of parenthesis and distribute 4

Answer 48

\[ \LARGE \color{red}{4(-m-1)}-5\]

Answer 49

Meaning something like -4m -4 -5?

Answer 50

\[ \LARGE \color{red}{4(-m) + 4(-1)}-5\]

Answer 51

\[ \LARGE \color{red}{-4m - 4}-5\]

Answer 52

Yes, next combine the numbers -4 and -5

Answer 53

(-4) + (-5) = ?

Answer 54

So -4m -9

Answer 55

Perfect!

Answer 56

Awesome.

Answer 57

As you can see, these are simple if you understand few rules and follow them

Answer 58

\[n(-4n^3-8)+7n^4\]

Answer 59

So here I would distribute the n?

Answer 60

Yes

Answer 61

\[-4n^4 -8n + 7n^4\]

Answer 62

Looks good, but it simplifies further

Answer 63

I know I was taking it step by step.
\[3n^4 - 8n\]
Final?

Answer 64

Yep! can't mess with it further

Answer 65

Always look for "similar" terms :-)

That is two monomials that are exactly alike or are the same except for their numerical coefficients.

Answer 66

Alright, Thank you all. :D

Answer 67

Thanks for trying to learn and understand :D

Answer 68

Np :) You did a great job in understanding these tricky things ! keep up the good work !

Answer 69

@ganeshie8 I just quoted you on my facebook profile

"Exactly! So you can think of the "division operation" intuitively as distributing cookies to friends : "-ganeshie8

Answer 70

Great quote, may I add if you have no friends the question of "distributing cookies to friends" has no meaning.

Answer 71

omg xD one could always distribute to imaginary friends and eat their share too ;)

Answer 72

o-o Okay, so I got another one, I am just going to ask this just to completely know. When distributing you multiply the outside number to the inside the parenthesis number right? I was looking at the problems we were doing and it they were just the letter and/or 1.

Answer 73

Yes, distribute to each term: $$\Huge a(b+c)=ab+ac$$

Answer 74

Alright, thank you for the clarification.

Answer 75

Thanks for asking :-)

Answer 76

I distribute the 3 to the other parenthesis correct?
\[-2(-x-3)+3(-x-1)\]

Answer 77

yes, also the -2

Answer 78

Yeah, wow, you all are truly amazing! :D

Answer 79

Btw in your ordinal question be sure to note a is not equal to 0.

Answer 80

For that equation I got -1x+5.

Answer 81

Well, I was incorrect.

Answer 82

Which one?

Answer 83

My most recent equation I sent.

Answer 84

it should be -x + 3

Answer 85

I forgot... 1x =x correct?

Answer 86

Darn, I failed the quiz due to that one mistake.

Answer 87

:( try to learn from your mistakes as well as your successes :)

Answer 88

I just want to clarify this answer before I miss it if that is okay.
8a/10(a+b) (8a over 10(a+b)) would that simplify to 4/ 5+5b

Answer 89

You are missing the variables :-/

Answer 90

I figured the A's would cancel out.

Answer 91

Nope. Try again :-)

Answer 92

So then it'd be 4a/5a+5b?

Answer 93

yes, write it as $$\huge (4a)/(5a+5B)$$

Answer 94

Correct :D

Answer 95

Can there be a decimal in a fraction?
\[\frac{ 7a }{ 14(a+b) }\]

Answer 96

Sure, why not? But we normally eliminate them by multiplying the numerator and the denominator by a suitable power of 10.

Answer 97

o.o? So would this not equal something like
\[\frac{ 3.5a }{ 7a+7b }\]

Answer 98

Just cancel the 7 in the numerator and the denominator in the original expression by writing 14 as 7 X 2