Question

What is the average of $\dfrac{1}{{20}}$ and $\dfrac{1}{{30}}$?

Answer 1

Hint: Average is defined as the sum of given numbers divided by the total number of numbers being averaged.
So, $Average = \dfrac{\text{Sum of given number}}{\text{Total number to be averaged}}$
In this question we have two numbers so first we add both the numbers and then divide the result by $2$.

Complete step by step answer:
In the question we have to calculate the average of the two numbers $\dfrac{1}{{20}}$ and $\dfrac{1}{{30}}$
First, we add both the numbers. We get,
$ \Rightarrow \dfrac{1}{{20}} + \dfrac{1}{{30}}$
Take L.C.M of the numbers which are in denominators.
We get,
$ \Rightarrow \dfrac{{3 + 2}}{{60}}$$ = \dfrac{5}{{60}} = \dfrac{1}{{12}}$
Now, divide $\dfrac{1}{{12}}$ by 2. We get,
$ \Rightarrow \dfrac{1}{2} \times \dfrac{1}{{12}} = \dfrac{1}{{24}}$
Hence, the average of $\dfrac{1}{{20}}$ and $\dfrac{1}{{30}}$ is $\dfrac{1}{{24}}$.

Note:
Average and mean are the two terms which are often used interchangeably. Mean is the average of values present in the data set. The central value which is called as average in mathematics the same value is called as mean in statistics.
We must know the formula for the mean and average of some given numbers to solve the problem. Average of n numbers can be computed using the formula: ${\text{Average}}\,{\text{ = }}\dfrac{{{\text{Sum of n numbers}}}}{{\text{n}}}$ . The value of any of the parameters in the formula can be obtained by substituting the values of remaining ones.