Question

A student divided a number by 2/3 when he required to multiply by 3/2. Calculate the
percentage of error in his result.

Answer 1

0%

Solution

3x/2 = x /(2/3)


because multiplying and divinding a number is reciprocal.

Answer 2

Percentage error in the result is zero percentage when a student divided a number by $\bold{\frac{2}{3}}$ and multiplied by $\bold{\frac{3}{2}}$  

Solution:

Let us take the base number as N, which is to be divided or multiplied

By dividing N by $\frac{2}{3}=\frac{N}{\frac{2}{3}}=\frac{N}{2}$

By multiplying N by $\frac{3}{2}=N \times \frac{3}{2}=\frac{3 N}{2}$

Thereby if subtracted the multiplied and divided value tends to be zero.

$\frac{N}{2} \times 3-\frac{N}{2} \times 3=0$

The percentage will be zero which is calculated from above steps.