#### • Class 11 Physics Demo

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# Dividing Fractions with Variables and Exponents

Dividing Fractions with Variables and Exponents

Division is a simple process in mathematical calculations, but it will befuddle sometimes when there are more number of fractions and exponents involved.

Hence to divide the fractions with the other variables and exponents, it should be simplified as much it can be and then the basic algebraic actions can be done.
In dividing the fractions, there are three terms involved and these terms can be said as the parameters.

The first number which we have in our hand is called as Dividend; the number with what we are going to divide the dividend is called as the Divisor.

Finally the result we get after division is known as the Quotient.

Now for dividing the fractions with other fractions or fractional variables, we can follow basic simple three steps as follows:

•    Turn the fraction with which the fractional number is to be divided as upside down, i.e. it’s reciprocal.
•    Now multiply the reciprocal number with the Dividend or the first number which is needed to be divided.
•    After this, doing basic simplification of the terms derived will yield the final value needed.

This process lies with all normal algebraic numbers and even for other variables such as unknowns.
Eventually, the case involves some more steps when the division involves some exponential numbers.
In that case, the exponential multiplication and division rule has to be followed while doing the mathematical operations.

For divisions involving the exponential variables or numbers, there are two main points to be considered, which are given below:

•    If there are both numerical coefficients and variables with exponents, then first the numerical coefficients should be divided.
After that, the exponent rule should be applied for dividing the variables.

•    For dividing the variables having exponentials or powers, the variables should be kept constant and only the exponents should be subtracted, which represents the exponential rule.

Herewith we shall take an example to show the division of fractions with variables and exponents.

Let us consider a problem of 20*a5 *b3 divided by b5, should be divided by 4*a2 divided by b4
Now to divide this equation, first we have to invert the divisor and hence we will get, ‘b’ power 4 divided by multiplication of 4 and ‘a’ square. Now we have to multiply this with the dividend.
First, dividing the numerical coefficients we will get a value of 5 and it is kept separate.
Now considering, ‘a’ variable it has power 5 on numerator and power 2 on denominator.
Subtracting these two will yield ‘a’ power 3.
Similarly considering for b, it will give finally b power 2 or simply b square.
Hence, finally we will get the answer as 4*a3 * b2

Question:(b^7)/(b^-2) No explanation needed, unless you feel so inclined. Thanks :D it says "Simplify. write your answer with a positive exponent only"

Question:3x-6 * 8y^-1 -------- -------- (2y)^3 10-5x Thats the problem, im having trouble with it for a few reasons: -it has negative exponents, and -it hass a monomial that has a exponent Thanks so much! (please no "use your brain" answers)

Answers:((3x - 6) / (2y)^3) * (8y^-1 / (10 - 5x)) (3(x - 2) / 8y^3) * (8 / y(10 - 5x)) 24(x - 2) / (8y^4 * -5(x - 2)) 3 / -5y^4

Question:2x^5y^2 - 4xy^2 / 2xy^2 = ?? Please Provide Explanation :)

Answers:Hi, 2x^5y^2 - 4xy^2 ----------------------- = . . . . 2xy^2 2x^5y^2 . 4xy^2 ----------- - --------- = 2xy^2 . . .2xy^2 Divide coefficients. Subtract exponents on each variable. 2x^5y^2 . 4xy^2 ----------- - --------- = x^4 - 2 <==ANSWER 2xy^2 . . .2xy^2 I hope that helps!! :-)

Question:I am befuddled by how to go about simplifing this. (-2m^2n^-4)^3 ----------------------- (4m^-5n^3)^0 Please include all steps invovled and the correct answer.

Answers:(-2m^2n^-4)^3 / (4m^-5n^3)^0 Remember: x^0 = 1 (-2m^2n^-4)^3 / (4m^-5n^3)^0 = (-2m^2n^-4)^3 / 1 = Remember (xy)^a = x^a*y^a (-2)^3 *(m^2)^3 * (n^-4)^3 = Remember: (x^a)^b = x^(a*b) (-2)^3 *(m^2)^3 * (n^-4)^3 = -8 * m^6 * n^-12 = Remember: x^-a = 1/x^a -8m^6 / n^12