Questions About How To Divide Fractions With Different Denominators

Susan asks…

When dividing complex fractions with the same denominator, how do you go about doing it?

I know when you divide complex fractions with different denominators you have to find an LCD, but I'm not sure about ones with the same denominator. The problem is:
24
___
x-3
_______
36
___
x-3

The problem in words is 24 divided by (x-3), divided by 36 divided by (x-3)
Thanks guys, all your answers helped a lot.

admin answers:

(24/x-3) / (36/x-3)

*Rule - you can't divide fractions...

First: you have to multiply the 1st fraction with the reciprocal of the 2nd fraction >>> (x-3)/36 >>> flip the 2nd fraction.

(24/x-3) * (x-3/36)

SEc: cross cancel the same terms & combine the rest.

(24/1) * (1/36)
24/36

Third: simplify the fraction into lowest terms...

24/36 = 2/3

Daniel asks…

how do i divide radicals with different index if they're written in equations?

so i'm trying to solve this math problem which is in a fraction form...(its saying that i should divide it)

for the numerator.. there are 3 terms which are all radicals with different index

and for the denominator it has 1 term which has a different index also..

thank you for the help.. =)

admin answers:

It would help if you actually gave the problem.

But, the best way to go about would be to split all numbers into their prime factors. That way, you will be able to cancel out common terms in the numerator and denominator. Cancel as many terms as possible, the rest is your answer.

Jenny asks…

I need to learn fractions really badly, do you know any sites to explain?

Okay I need to know how to multiply,divide,add,subtract, you know all that. Not with the shapes though.
For example 4/9+6/32=? stuff like that no shapes and different denominators. Videos, sites, free tutors online anything will work. Just something that will thoroughly explain in SIMPLE TERMS. Thanks!

admin answers:

If you visit http://www.gcflearnfree.org/fractions there are tutorials for how to read and write fractions and how to work with common denominators, reducing and improper fractions. It's free and they use videos and interactives to help you learn.

Maria asks…

Dividing a fraction by a whole number in a word problem.?

my son has to show his work for his 5th grade math word problems. I have come up with the answer and can show him how to do it but I don't understand why the process is different and I would like to explain to him the difference.

The math problem says that out of 96 singers 3/8 of them are tenors. How many are tenors?
The answer is 36 according to his math book.- which is correct of course. To get to the answer I simply divided 96 by 8 and multiplied it by 3 which gives me 36.

BUT- in other sections of his math book it tells him to use the reciprocal method to find the answer for dividing a whole number by a fraction.

When should he simply divide the denominator into the whole number and then multiply it by the numerator versus using the reciprocal method (ie flip the fraction and multiply instead of divide by the whole number) to divide a whole number by a fraction?


What is the difference and any suggestions for explaining this to a 5th grader

admin answers:

In this case you are not dividing by a fraction, you are multiplying:

(3/8) * 96 = (3/8) * (96/1) = (3*96) / (8*1)

The reciprocal method would apply is you had this kind of problem:

96 / (3/8) = 96 * (8/3)

=====================

The first answer is very good - too many kids don't understand ratios. (but it doesn't really answer your question)

Sandra asks…

Please could someone help me with this math question?

I'm not asking you to do the work for me, but could someone give me a few pointers as to how to approach this question?

"Delia is cooking. She has a 1 1/2 KG bag of flour and needs 3/8 of it in a recipe. What fraction of a kilogram does she need and what is this in grams?"

Fraid to say I'm completely bewildered as to what I'm meant to do on this. Do I have to make them have common denominators and divide? Or is it completely different? Thanks for any help in advance.

admin answers:

It's actually very easy. To find a fraction OF a fraction, just multiply the fraction by the fraction! :)

Do this : 3/8 X 1 1/2

To multiply, you have to make all the fractions improper..

So 3/8 is ok, and for 1 1/2:


1 X 2 + 1 = 3

Leave the denominator as is (2) so 1 1/2 becomes 3/2

now do 3/8 X 3/2

Once you get the product, that is KG and convert it to G. (multiply product by 1000 and you can just leave the denominators as is and simplify later)

No, you do not need to make common denominators to divide. You need to make it improper fractions though, and hope you understood what I meant before.

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Questions About How To Divide Fractions With Radicals

Sandy asks…

how do you divide fractions with a radical?

such as (1/2) divided by √3/2, the answer i see is √ 3/3 but idont know how to get it

admin answers:

1/2 divided by √3/2 is the same as
1/2 multiplied by 2/√3 which equals 1/√3
u multiply 1/√3 by √3/√3 because u can't have a root as a denominator
the answer would be √3/(√3*√3)=√3/3

Lizzie asks…

How to divide a fraction by a fraction with radicals?

Please explain what I do and why. Don't just show your work with an answer. For example, in the problem (1/2) ÷ (√3/2)

What would the first step be and why?
Would I multiply by the reciprocal?
EX:
(1/2)∙(2√3)= 2/2√3 ? And if so how would I solve this from there?

I have also heard that the first step is to multiply the whole problem by the conjugate. If so what is the conjugate and how do I do this? If incorrect what should ?I do?

Will vote best answer. I am looking to understand how to solve all problems with fractions and radicals, not this particular problem. I'm just using it as an example. So if you just solve it and don't explain, it's pretty much useless for me. Thanks.
Does it make a difference if you multiply by the conjugate first versus reciprocal? If so, how? Also can a final answer have a radical in the denominator. I have heard yes and no. Why or why not?

admin answers:

(1/2) / (√3/2) --- Problem Stated

(2/1)* (1/2) / (√3/2) * (2/1) --- Multiplied each side by 2/1 (reciprocal)

1 / (√3/1) --- Simplified multiplication

(1/√3) --- Simplified √3/1 to √3

(1/√3) * (√3/√3) = (1√3)/3 --- Simplified further to get the √ out of the Denominator

= √3/3. --- Simplified 1 * √3 to get final solution

Edit:

"Also can a final answer have a radical in the denominator"

Yes a final answer can have a radical in the denominator, though if this is for school I'm almost positive your teachers will make you move it to the top as its not considered completely simplified.

Ruth asks…

How to divide this radicals?

2√6
------
4√5

The dashed line is a fraction/ division symbol. We are suppose to reduce them completely and with no decimals. I'm completely clueless with this paper and I need a little help! Thank you so, so, so much!

admin answers:

We need to rationalize the denominator.

No radicals in denominator so..

It is a fraction so to get rid of the radical in denom multiply by sqrt(5) in both numerator and denom.

Result is 2 sqrt(30)/ ((4)(5))

reduce the 2 and 4 by 2

sqrt(30)/10

Donald asks…

Trouble Dividing Radicals?

I am trying to do the problem "The square root of 15 divided by 3 times the square root of 80 in fraction form it is square root of 15 / 3*square root of 80. After attempting to look up how to divide radicals on the internet, i came up with the answer 5*sq. root of 3/50. Is this correct? If not, could someone link me a good source to learn about this, or explain where i might have gone wrong?

admin answers:

(√15)/(3√80) = (1/3)√(15/80) = (1/3)√(3/16) = (1/3)(√3)/(√16) = (1/3)(1/4)√3 = (1/12)√3

Chris asks…

How To Divide Radical Expressions?

I DO NOT need confusing answers. Please. Help me out---include rules and easy-to-follow examples. I will be choosing the best answer!

Now, I know how to simplify this:

8(roots)6
------------
2(roots)3 = 4(roots)2

And the like. As long as they divide evenly into each other, I'm good.

What I get confused on is when the denominators are larger than the numerators, or they don't go into the numerators easily, etc.. Such as:


9(roots)3
------------
(roots)5 = ? (I'm thinking the answer is 9(roots)3/5, but why? Explain this.)

Also:

(roots)40
------------
(roots)90 = ? (Do you simplify this to:

(roots)4
----------
(roots)9

and solve it from there...

...or do you simplify it to:

2/3

by simply dividing each number by 10?)

I got 2/3 because (root)40 turns to 2(root)10, and (roots)90 turns to 3(root)10, and when divided this equals 2/3...or so I got.

And then there's this:

16
----------
(roots)8 = ? Would it be 8(root)2? By finding the factors of 8, and getting (root)2 x (root)4, which would turn to 2(root)2, and then you would divide 16 and 2, and get 8(roots)2?

Basically, I really need to know this:

Do you simplify first? Like (root)40 over (root)90 would be (root)4/9? And would you simplify (root)4/9 to 2/3 from there? And like (root)2 over (root)6? Would that turn to (root)1/3, or (root)2/6, or what?

Or do you NOT simplify like you usually would with fractions, and simply get the factors of (root)40 and (root)90, and work it from there?

Please, tell me how to do this!

PLEASE.

admin answers:

Either way works, and all of your answers seem correct except the

16
----------
(roots)8

one. (I'll explain that one in a minute.) For example,
(root)1/3
is the same as
(root)2/6.
In any problem, you can feel free to simplify a root before dividing, or you can divide first and then simplify, or any combination of the above.

As for

16
----------
(roots)8

you must first simplify the denominator to become 2(root)2. Then you can divide out the 2 to get

8
----------
(root)2

From here, you can either leave the answer as is or recall that

1
----------
(root)2

=

(root)2
----------
2

This would simplify the above expression to

8(root)2
----------
2

or

4(root)2.

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Questions About How To Divide Fractions With Variables

Nancy asks…

Multiplying and dividing fractions with variables?

Can you help me explain how to do these two problems to my child?

5- x/8 = 10 and
z+3/5 - 1/4 = 3/4
It's hard to write this bu it is 5-x over 8 and z+3 over 5. Like:

5-x
----
8

and

z+3
-----
5

admin answers:

Simply rearrange the terms to get...

1. (5 - x)/8 = 10
5 - x = 80
-x = 75
x = -75

2. Multiply both sides by 20 and then, rearrange the terms...

Good luck!

Ruth asks…

I need more math help please.. dividing fractions with variables?

3x^2/5 * 30/x^3

please explain step by step.. so i know how to do the rest of these problems :)

thank you!!

admin answers:

3x^2/5 * 30/x^3

multiply top by top and bottom by bottom
(3x^2*30) / (5*x^3)
90x^2 / 5x^3

divide like factors
90/5 * x^2/x^3
18/1 * 1/x
18*1 / 1*x
18 / x

Mandy asks…

Intermediate algebra problems..dividing fractions with variables??

Im having so much trouble with this stuff. I know in class he said to find the common denominator and multiply everything else to get that. But how would I do this?? Oh and those long lines are supposed to be division --> ____

1. 36a^2 + 24 -3
_____ ____ ___
b^2c bc^3 7bc


2. 1 - 1
__ __
x 5
___________
1 + 1
__ __
x+3 x
(thats supposed to be 1/x - 1/5 divided by 1/x+3 + 1/x)

3. This one i cant figure out..i thought move x to one side?
Solve ax+b=cx+ d for x
That first problem got messed up but is supposed to be 36a^2/b^2c + 24?bc^3 - 3/7bc

admin answers:

(1)
36a^2/b^2c + 24/bc^3 - 3/7bc

I guess the lowest common denominator is 7b^2c^3
cos you have a b^2c and a bc^3 and a 7bc

So... The first one you need to multiply by 7bc^2, the next one gets multiplied by 7b and the last one needs an extra c^2

((36a^2.7bc^2) + (24.7b) - (3c^2)) / 7b^2c^3

(2)
(1/x - 1/5) / (1/(x+3) + 1/x)
Okay - so you work out what the top fraction is going to be and then you work out what the bottom fraction is going to be, and then you turn the bottom fraction upside down and multiply by it (like how dividing by 1/2 is the same as multiplying by 2)

((5-x)/5x) / ((x+x+3)/(x(x+3))

= (5-x)/5x X x(x+3)/(2x + 3)

= (x(x+3)(5-x)) / (5x(2x+3))

(3)
ax + b = cx + d

Then
ax = cx + d - b if you subtract b from both sides

Likewise
ax - cx = d - b if you now subtract cx from both sides

and to go further
x(a-c) = d-b

And so now you can get x all by itself by dividing both sides by (a-c)

Daniel asks…

how to divide fractions with a variable?

like x/4=12

admin answers:

The key to these is to have a method of getting rid of the fraction and how you do it is to do the opposite
x/4 = 12 ..... X is being divided by 4 and the opposite of dividing by 4 is multiplying by 4 but what you do to one side of the equation you must do to the other
4x/4 = 12 x 4
x = 48
the other way of thinking about it is to ask yourself: what number (x) divided by 4 gives an answer of 12? Answer: 48

Lisa asks…

Dividing a variable fraction by a regular fraction?

I'm sorry, i'm having trouble with fraction variables...here:

-x/6 = 3/6

I don't know how to solve this

admin answers:

Since both are over the same number, 6, you know that -x = 3
so x must be -3

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