Question

What is the half of \[\dfrac{1}{7}\]?

Answer 1

Hint: Here in this question we have to find the half of the given quantity. The half means the two equal parts. Usually half is represented as \[\dfrac{1}{2}\],here 1 is the whole complete quantity and it is divided into two parts. So here to find the solution of the given question we have to divide the given quantity by 2.

Complete step by step answer:
The given quantity is in the form of fraction. There are three different kinds of fraction namely, proper fraction, improper fraction and mixed fraction.
Proper fraction: The numerator value is smaller than the denominator value.
Improper fraction: The numerator value is greater than the denominator value.
Mixed fraction: The fraction is a combination of whole number and fraction number.
On considering the given question
\[ \Rightarrow \dfrac{1}{7}\]
Now we have to find the half of the above quantity, so we have to divide the given quantity by 2.
 \[ \Rightarrow \dfrac{{\dfrac{1}{7}}}{2}\]
Since the numerator of the above fraction is also a fraction, to simplify it we use the concept of reciprocal. So on taking the reciprocal for the above quantity we have
 \[ \Rightarrow \dfrac{1}{7} \times \dfrac{1}{2}\]
On multiplying we get
\[ \Rightarrow \dfrac{1}{{14}}\]
Therefore the half of \[\dfrac{1}{7}\] is \[\dfrac{1}{{14}}\].

Note:
The reciprocal of a given number when multiplied by that number gives one as a product. Thus, it is also called the multiplicative inverse. In math, reciprocal can simply be defined as the inverse of a number or a value. For a real number n, the reciprocal is \[\dfrac{1}{n}\]. While multiplying the fractions the numerator value of one fraction is multiplied to the numerator value of another fraction.