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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