if we multiply a fraction by itself and divide the product by its reciprocal,the fraction thus obtained is 512/27.the original fraction is?
Let the fraction be x.
x^2/(1/x) = x^3 = 512/27 = (8/3)^3
Therefore the fraction is 8/3
FRACTION
To find the original fraction, let's start by setting up the equation based on the given information.
Let's assume the original fraction is represented by "x/y".
According to the given information, if we multiply the fraction by itself (x/y * x/y) and divide the product by its reciprocal ((x/y * x/y) / (y/x)), we obtain the fraction 512/27.
So we have the equation:
(x/y * x/y) / (y/x) = 512/27
Next, let's simplify this equation.
(x^2/y^2) / (y/x) = 512/27
Multiplying x^2/y^2 with x/y, we get:
(x^3/y^3) = 512/27
Now, let's cross-multiply to eliminate the denominator:
512 * y^3 = 27 * x^3
Rearranging the equation, we have:
x^3/y^3 = 512/27
Now, take the cube root of both sides of the equation:
∛(x^3/y^3) = ∛(512/27)
Simplifying further, we get:
x/y = 8/3
So, the original fraction is 8/3.