Question

What is the reciprocal of $ \dfrac{1}{3} $ of half a dozen?

Answer 1

Hint: Start by using the fact that one dozen of an object is equivalent to 12 objects. So, half a dozen will be equivalent to 6. Then multiply 6 to $ \dfrac{1}{3} $ to get the exact value of the number of which we are asked to find the reciprocal of. Finally, use the property that $ xy=1 $ , where y is the reciprocal of x to get the answer.

Complete step-by-step answer:
Before moving to the question, let us talk about the multiplicative inverse.
The reciprocal of a number is defined as the multiplicative inverse of the number. In other words, an expression is said to be the ratio of the other if on multiplying the number and the reciprocal, their product is 1.
For example: if $ xy=1 $ , then, x and y are the reciprocals of each other.
Now, moving to the solution to the question mentioned above.
Let the given number be x. So, let us find the exact value of x.
 $ x=\dfrac{1}{3}\text{ of half dozen} $
We know one dozen of an object is equivalent to 12 objects. So, half a dozen will be equivalent to 6.
 $ x=\dfrac{1}{3}\times 6=2 $
Let the reciprocal of x be y.
Now, according to the definition of the reciprocal:
 $ xy=1 $
 $ \Rightarrow y=\dfrac{1}{x} $
 $ \Rightarrow y=\dfrac{1}{2} $
Therefore, the answer to the above question is $ \dfrac{1}{2} $ .

Note: The reciprocal of a number, in general, refers to multiplicative inverse, so don’t confuse it with additive inverse. It is also important that you know the number of objects contained in one Dozen is twelve, in one score is 20 and other number related quantities for a given object.