Question

How do you find the reciprocal of \[6\]?

Answer 1

Hint: Here, we will assume a number \[n\] to be equal to the reciprocal of \[6\] and form a mathematical equation by using the definition of the reciprocal of a number mathematically. On solving the equation formed, we will obtain the required value of the reciprocal of \[6\].

Complete step-by-step solution:
Let us assume the reciprocal of the given number, which is \[6\], to be equal to \[n\].
The reciprocal of a number is defined as the multiplicative inverse of the number. And the multiplicative inverse of a number is a number, with which when the number is multiplied, the multiplication is equal to one. That is, the product of a number with its reciprocal is equal to one.
According to the definition of the reciprocal of a number, the product of the numbers \[6\] and \[n\] must be equal to one. On writing this statement in the form of a mathematical equation, we get
\[6n = 1\]
On dividing both sides of the above equation by \[6\], we get
\[n = \dfrac{1}{6}\]

Hence, the reciprocal of \[6\] is equal to \[\dfrac{1}{6}\].

Note:
There is no need to determine the quotient of the fraction \[\dfrac{1}{6}\] by using the long division method. This is because on dividing one by six, we will get a decimal number in the form of non-terminating repeating digits. So only the approximate value will be expressed by the quotient of \[\dfrac{1}{6}\] and not the exact value of the reciprocal. When we find the reciprocal of any number then we will convert the number into fraction form. Then we will interchange the value of numerator and denominator i.e. numerator becomes denominator and the denominator becomes the numerator.