Question

How do you solve $\dfrac{{6 + n}}{{60}} = \dfrac{{15}}{{90}}$?

Answer 1

Hint: In this question, we are given an equation and we have been asked to find the value of $n$. Start by multiplying the denominator with the numerator of the other side. This is called cross multiplication. Then, open the brackets and multiply the number outside the bracket with the terms inside the bracket. Simplify by shifting numbers to the other side and find the value of $n$.
You can also use another method. In this method, make the denominator on both the sides equal. Then, compare the numerator on both the sides. You will get your answer.

Complete step-by-step solution:
We are given an equation in terms of $n$ and we have to find the value of $n$.
$ \Rightarrow \dfrac{{6 + n}}{{60}} = \dfrac{{15}}{{90}}$ …. (given)
Simplifying the RHS first. (You can skip this step but we would recommend it as it will make the calculations simpler.)
$ \Rightarrow \dfrac{{6 + n}}{{60}} = \dfrac{1}{6}$
Now, we will cross multiply. See below how it is done.
$ \Rightarrow 6\left( {6 + n} \right) = 60$
This equation can be further solved by two methods:
Method 1:
Simply open the brackets and multiply.
$ \Rightarrow 36 + 6n = 60$
Shifting to find the desired values,
$ \Rightarrow 6n = 60 - 36 = 24$
$ \Rightarrow n = \dfrac{{24}}{6} = 4$
Method 2:
We can write the RHS as –
$ \Rightarrow 6\left( {6 + n} \right) = 6 \times 10$
On comparing, we can say that,
$ \Rightarrow 6 + n = 10$
$ \Rightarrow n = 10 - 6 = 4$
Hence, $n = 4$.

Therefore the value of n is equal to 4.

Note: We can solve the question by another method also.
I will rewrite the step where we simplified the RHS of the equation. We got –
$ \Rightarrow \dfrac{{6 + n}}{{60}} = \dfrac{1}{6}$
Multiplying the numerator and the denominator of the RHS by $10$,
$ \Rightarrow \dfrac{{6 + n}}{{60}} = \dfrac{1}{6} \times \dfrac{{10}}{{10}}$
$ \Rightarrow \dfrac{{6 + n}}{{60}} = \dfrac{{10}}{{60}}$
Next step is to compare the numerator of both sides. (We can do this because the denominator of both sides is the same and there is a sign of equals in between.)
$ \Rightarrow 6 + n = 10$
$ \Rightarrow n = 10 - 6 = 4$
Hence, $n = 4$.