Question

What is $\left( {\dfrac{1}{5}} \right)$ of $30$?

Answer 1

Hint: The given expression deals with operations on fractions. Fraction represents equal parts of a whole or a collection. Basic operations like addition, subtraction, multiplication and division can be done on fractions with ease. The given problem deals with multiplication of a fraction and a whole number and finding the product. We must know that when we are doing operations on fractions, ‘of’ means multiplication.

Complete step-by-step solution:
In the given problem, we are required to multiply a fraction with a whole number. Multiplication of fractions is an extremely easy task. In other words, we need to find the product of a fraction and whole number.
We know that every whole number can be represented as a fraction having a denominator as one.
To multiply with fraction, we just need to multiply their numerators and denominators separately and we can get the required product.
So, $\left( {\dfrac{1}{5}} \right)$ of $30$ means that $\left( {\dfrac{1}{5}} \right)$ is to be multiplied with $30$.
So, we have, $\left( {\dfrac{1}{5}} \right) \times 30$
We can represent the whole number $30$ as a fraction with a denominator equal to one as $\dfrac{{30}}{1}$.
$ = $$\dfrac{1}{5} \times \dfrac{{30}}{1}$
Cancelling the common factors in numerator and denominator, we get,
$ = 6$
Thus, $\left( {\dfrac{1}{5}} \right)$ of $30$ is equal to $6$.

Note: After multiplication of fractions, we generally reduce the resultant product into its lowest form by cancelling the common divisors between numerator and denominator. But in the given problem, the resultant product $6$is already in its lowest form as it has a denominator equal to one. Hence, there is no need to reduce it in its lowest term. Also, we should keep in mind that division of a fraction by another fraction is equivalent to multiplication of the first fraction by the multiplicative inverse of the second fraction.