Question

What is the reciprocal of \[\dfrac{6}{3}\]?

Answer 1

Hint: Here in this question, we need to find the reciprocal of the given number. The reciprocal of a number is another word for its multiplicative inverse. To find the reciprocal of any number, simply take 1 and divide it by that number or it is also found by interchanging the numerator and denominator.

Complete step by step solution:
In Mathematics, reciprocal means an expression which when multiplied by another expression, gives unity (1) as a result. The reciprocal of any quantity is, one divided by that quantity, It is also called the multiplicative inverse.
For any number ‘$a$’, the reciprocal will be \[\dfrac{1}{a}\].
Consider the given question: we need to find the reciprocal of \[\dfrac{6}{3}\].
 simply take 1 and divide it by that number \[\dfrac{6}{3}\], then
The reciprocal of \[\dfrac{6}{3}\] is \[\dfrac{1}{{\dfrac{6}{3}}}\]
in the denominator the term is in the fraction, so this is written as
\[ \Rightarrow 1 \times \dfrac{3}{6}\]
This can be written as \[\dfrac{3}{6}\]
We can check that this is the multiplicative inverse of \[\dfrac{6}{3}\] by multiplying those two numbers together and seeing if we get 1:
\[ \Rightarrow \,\dfrac{6}{3}.\dfrac{3}{6}\]
\[ \Rightarrow \,1\]
Therefore, the reciprocal of \[\dfrac{6}{3}\] is \[\dfrac{3}{6}\].

Note:
> As a side note for future or further reciprocal problems, you may want to remember that the number 0 does not have a reciprocal. This is because there isn't any number you can multiply by zero to get 1.
> Usually in the fraction the denominator term will be replaced by the numerator and vice versa. The reciprocal is sometimes called inverse.