Question

If we multiply a fraction by itself and divide the product by its reciprocal,then the fraction thus obtained is 1 integer 217/512.What is the original fraction?

Answer 1

Answer:

Answer:

\frac{x}{y}=\frac{8}{3}

y

x

=

3

8

Step-by-step explanation:

Let the numerator be x

Let the denominator be y

Fraction : \frac{x}{y}

y

x

Product of fraction with itself = \frac{x}{y} \times \frac{x}{y} =\frac{x^2}{y^2}

y

x

×

y

x

=

y

2

x

2

Reciprocal of fraction : \frac{y}{x}

x

y

Now divide the product by its reciprocal

So, \frac{\frac{x^2}{y^2}}{\frac{y}{x}}

x

y

y

2

x

2

\frac{x^2}{y^2}\times \frac{x}{y}

y

2

x

2

×

y

x

\frac{x^3}{y^3}

y

3

x

3

Now we are given that we get the fraction 512/27.

So, \frac{x^3}{y^3}=\frac{512}{27}

y

3

x

3

=

27

512

\frac{x}{y}=\sqrt[3]{\frac{512}{27}}

y

x

=

3

27

512

\frac{x}{y}=\frac{8}{3}

y

x

=

3

8

Hence the original fraction is \frac{x}{y}=\frac{8}{3}

y

x

=

3

8