Question

How do you solve for n in \[h=\dfrac{p}{n}\]?

Answer 1

Hint: We can use the properties of multiplication and division. When the same number is multiplied on both sides of an equality, we get the resultant same result as well. Similarly, is the case for division. So, here, we will begin by multiplying both sides of the equation by n and then proceed further such that we get only n on the LHS.

Complete step by step answer:
According to the given question, we have to solve for n in \[h=\dfrac{p}{n}\] which means we have to write the given expression in terms of n.
The given expression has ‘n’ in the denominator of the RHS (right hand side) of the equality. So we can start by multiplying ‘n’ on both sides of the equality.
Multiplying ‘n’ on both sides we get,
\[\Rightarrow h\times n=\dfrac{p}{n}\times n\]
In RHS of the equality we have ‘n’ both in numerator and denominator so it gets cancelled, but the ‘n’ on LHS (left hand side) stays intact.
\[\Rightarrow h\times n=p\]
\[\Rightarrow hn=p\]
We have to write the equation in terms of ‘n’ alone so we need to separate ‘h’ from ‘n’.
We can carry out this by dividing ‘h’ on both the sides so as to get the expression for ‘n’.
Dividing both sides of the equality by ‘h’ we get
\[\Rightarrow \dfrac{hn}{h}=\dfrac{p}{h}\]
We have ‘h’ in numerator as well as in denominator so it can be cancelled but the ‘h’ on the RHS remains intact. So we left with the equation as follows:
\[\Rightarrow n=\dfrac{p}{h}\]

Note: Multiplication and division operation should be carried out step wise and not in one go. It might result in getting a wrong answer or a reversed answer. Step wise calculation is advised for preventing errors. We can also solve this question by using the method of cross multiplication. So, we can directly cross multiply so that n from the denominator in the RHS is shifted to the numerator in the LHS and h from the numerator in the LHS is shifted to the denominator in the RHS. We will get the result as \[\Rightarrow n=\dfrac{p}{h}\] .