A student wrote an algebraic expression for " \[5\] less than a number \[n\] divided by \[3\] " as \[\dfrac{n}{3} - 5\]. What error did the student make?

Question

A student wrote an algebraic expression for " $$5$$ less than a number $$n$$ divided by $$3$$ " as $$\dfrac{n}{3} - 5$$. What error did the student make?

Vedantu Content Team · Accepted Answer

Hint: In the above question, we are given an error which is written by a student. He was asked to write an expression such that it is “ $$5$$ less than a number $$n$$ divided by $$3$$ " but his answer was $$\dfrac{n}{3} - 5$$. This answer has a small error. We have to point out the mistake that the student made and determine the error in the answer given by him. In order to approach the solution, first we have to write the correct expression of the given problem.Complete step by step answer:In the given problem, one has to write the correct expression for the following statement,“ $$5$$ less than a number $$n$$ divided by $$3$$ "For the above problem, one student has answered the expression as $$\dfrac{n}{3} - 5$$ .That is an incorrect answer given by the student.We have to determine what error he has in his answer.To find the error, let's find the correct answer first.Let a number be $$n$$ .Now, “ $$5$$ less than a number $$n$$ “ is written as$$ \Rightarrow n - 5$$Therefore, “ $$5$$ less than a number $$n$$ divided by $$3$$ " is written as$$ \Rightarrow \dfrac{{n - 5}}{3}$$That is the required expression.Therefore, “ $$5$$ less than a number $$n$$ divided by $$3$$ " is expressed as $$\dfrac{{n - 5}}{3}$$ .Whereas, the error in the student's answer was that he had written $$\dfrac{n}{3} - 5$$ , where he divided only the number $$n$$ instead of $$n - 5$$ .Note: In the converse method of the above solution, we can also write the statement for the student’s incorrect answer which is $$\dfrac{n}{3} - 5$$ .Again, let a number $$n$$ .Now, “one-third of a number $$n$$ “ is written as$$ \Rightarrow \dfrac{n}{3}$$Therefore, “$$5$$ less than one-third of a number $$n$$ “ is written as$$ \Rightarrow \dfrac{n}{3} - 5$$That is the correct statement for the student’s answer.Therefore, $$\dfrac{n}{3} - 5$$ is written as “$$5$$ less than one-third of a number $$n$$ “.