Maths-
General
Easy

Question

A Student divided the rational expression as follows :
fraction numerator 4 x over denominator 5 y end fraction divided by fraction numerator 20 x squared over denominator 25 y squared end fraction equals fraction numerator 16 x cubed over denominator 25 y cubed end fraction
Describe and correct the errors the student made ?

hintHint:

The mathematical operation of dividing one rational number with other rational number is called division of rational numbers.
We are asked to describe and correct the error made by the student while dividing the expression.

The correct answer is: = y/x


    Step 1 of 2:
    The given expression is: fraction numerator 4 x over denominator 5 y end fraction divided by fraction numerator 20 x squared over denominator 25 y squared end fraction equals fraction numerator 16 x cubed over denominator 25 y cubed end fraction
    Rewrite the division as the product of the first rational expression and the reciprocal of the second.
    Thus, we get:
    fraction numerator 4 x over denominator 5 y end fraction cross times fraction numerator 25 y squared over denominator 20 x squared end fraction
    Now, multiply them:
    fraction numerator 4 x over denominator 5 y end fraction cross times fraction numerator 25 y squared over denominator 20 x squared end fraction equals fraction numerator 5 y over denominator 5 x end fraction
    equals y over x
    Step 2 of 2:
    The error that the student made was not taking the reciprocal of the second expression for multiplication. If it was done, they would have gotten the correct answer.

    Whenever you divide two expressions, make sure to take the reciprocal of the second and then multiply to get the answer.

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