Question

Find and correct errors of the following mathematical expression $\dfrac{{3{x^2}}}{{3{x^2}}} = 0$

Answer 1

Hint: According to the basics of the arithmetic in mathematics, when a number is divided by itself then, it will always result in 1. Here, in the question we need to determine the error in the given expression and correct that error as well by following the arithmetic rules.

Complete step-by-step answer:
According to the basics of the arithmetic in mathematics, when a number is divided by itself then, it will always result in 1
The given expression is $\dfrac{{3{x^2}}}{{3{x^2}}} = 0$ in which we can see that the numerator as well as the denominator are both same i.e., $3{x^2}$. Following the basic theory of arithmetic that if the number is divided by itself then, the result will always be 1. But here, in the expression it is given as 0 which is an error.
So, the error in the expression is 0
And, the correct result for the given expression is $\dfrac{{3{x^2}}}{{3{x^2}}} = 1$.

Note: Alternatively, we can also detect the error by cross-multiplying the terms present in the terms in the expression $\dfrac{{3{x^2}}}{{3{x^2}}} = 0$ such that
$
  3{x^2} = 0 \times 3{x^2} \\
   = 0 \\
 $
The above equation cannot be true under any circumstances and for any value of $x$ as it is raised to the power of 2 which results in positive and we know that the product of two positive terms can never be equal to zero. Hence, 0 is the error in the given expression.