Question

How do you solve $\dfrac{3}{7}n = 6$?

Answer 1

Hint: When we are given an expression with an ‘equals to’ sign which is also called an equation and an unknown variable whose value we need to find, what we have to do is try to shift everything else except the variable itself to the right-hand side of the ‘equals to’ sign by manipulating the equation in such a way that the equilibrium or the balance of the equation doesn’t get affected.

Complete step by step answer:
(i)
We are given
$\dfrac{3}{7}n = 6$
In order to obtain the value of $n$, we need to shift everything else except $n$ to the right-hand side of the ‘equals to’ sign without harming the equilibrium or the balance of the equation. Therefore, whatever we will do to LHS, we will also do to RHS.
So, firstly we will multiply both the sides by $7$. We will get
$\dfrac{3}{7} \times n \times 7 = 6 \times 7$
Since, we have a common factor in the numerator and the denominator of the LHS i.e., $7$ we can directly cancel them out. So, we will get
$3n = 6 \times 7$
(ii)
Now, we will divide both the sides by $3$. So, we will get
$\dfrac{{3n}}{3} = \dfrac{{6 \times 7}}{3}$
Since, again we have got a common factor between the numerator and the denominator in the LHS i.e., $3$ we will directly cancel it out. So, we will get:
$n = \dfrac{{6 \times 7}}{3}$
(iii)
Again, here we can see a common factor $3$ in both numerator and the denominator, we will cancel it out and solve it further to obtain the final value of $n$.
$
  n = \dfrac{{6 \times 7}}{3} \\
  n = 2 \times 7 \\
  n = 14 \\
 $
Hence for $\dfrac{3}{7}n = 6$, $n = 14$

Note: We could also solve this question by taking $n$ on the other side and cross multiplying the numerators and denominators across the ‘equals to’ sign with each other. We would have got, $\dfrac{3}{7} = \dfrac{6}{n}$ and then after cross multiplication, $3 \times n = 7 \times 6$ which is the same as we got in the end of first step so we can see, we would have got the same answer by this approach also.