Question

What is \[\dfrac{1}{5}\] of \[30\]?

Answer 1

Hint: A fraction is a part of the whole number it consists of two parts numerator and a denominator. Here we have multiplication of a fraction and a whole number (or rational number). Multiplication of fraction is as simple as the multiplication of numbers in the number system.

Complete step-by-step solutions:
Given \[\dfrac{1}{5}\] of \[30\]
Or
\[\dfrac{1}{5} \times 30\]
That is we have a multiplication of fraction with whole number, meaning that it is equal to whole number times the fraction added.
\[\dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5} + ........30 times\].
But we don’t add this 30 times.
Instead of that we can see write the given problem as
\[ \Rightarrow \dfrac{1}{5} \times \dfrac{{30}}{1}\]
Now multiplying the numerators and the denominators we ,
\[ \Rightarrow \dfrac{{30}}{5}\]
\[ \Rightarrow 6\].

Thus \[\dfrac{1}{5}\] of \[30\] is 6.

Additional information:
Suppose we have a division of two fractions. That is \[\dfrac{a}{b} \div \dfrac{c}{d}\], then reciprocate the second fraction by interchanging its numerator with the denominator. Multiply the second fraction with the first one by multiplying the numerator and denominator with each other.
\[ \Rightarrow \dfrac{a}{b} \times \dfrac{d}{c}\]
\[ \Rightarrow \dfrac{{a \times d}}{{b \times c}}\]. This is the required result.

Note: We have different types of fractions. Proper fraction: A fraction in which the numerator is less than the denominator is known as a proper fraction. Example \[\dfrac{1}{7}\]. Improper fraction: A fraction where the numerator is greater than the denominator then it is known as an improper fraction. Example \[\dfrac{7}{5}\]. Mixed fraction: A mixed fraction refers to the combination of the natural number and the fraction. Example \[1\dfrac{1}{4}\].