`(2c^2d)/(10c) -: (5d)/(3c^2)`  I'm confused on this problem.

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lemjay | High School Teacher | (Level 3) Senior Educator

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`(2c^2d)/(10c) -: (5d)/(3c^2)`

When we divide two fractions, the steps are:

> Flip the second fraction and change the operation from division to multiplication.

`=(2c^2d)/(10c) * (3c^2)/(5d)`

> Multiply the numerator of the first fraction with the numerator of the second fraction. Also, multiply the denominator of the first fraction with the denominator of the other.

`=(6c^2c^2d)/(50cd)`

> To multiply same variable, add the exponents ( `a^m*a^n=a^(m+n)` ).

`=(6c^(2+2)d)/(50cd)=(6c^4d)/(50cd)`

> To divide same variable, subtract the exponents (` a^m/a^n=a^(m-n)` ). 

`=(6c^(4-1)d^(1-1))/50=(6c^3d^0)/50=(6c^3)/50`

Then, reduce the fraction 6/50 to its lowest term.

`=(3c^3)/25`

Hence,  `(2c^2d)/(10c)-:(5d)/(3c^2) = (3c^3)/25` .

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