Question

What is the opposite and reciprocal of \[\dfrac{19}{56}\]?

Answer 1

Hint: We are given a fraction consisting of a numerator and a denominator and we are asked to find the opposite and the reciprocal of the given fraction. Opposite refers to the sign of the fraction, if the given fraction is positive then its opposite becomes negative and if the given fraction is negative the opposite becomes positive. Then, we have the reciprocal. Reciprocal refers to the ratio of 1 and the given number, that is, \[\dfrac{1}{n}\]. Doing the above mentioned steps, we will have the required values as per what question demands.

Complete step-by-step answer:
According to the given question, we are given a fraction and we are asked to write the opposite of the given fraction and also the reciprocal of the fraction.
Opposite of a fraction would mean change in the sign of the fraction, that is, if the fraction would have been positive then its opposite would be negative and if the fraction had been negative then the opposite would be positive.
Reciprocal of a number or a fraction just refers to the ratio of 1 and the given number or the given fraction, that is, \[\dfrac{1}{n}\].
The given fraction that we have is, \[\dfrac{19}{56}\].
As we can see that the given fraction is positive, so the opposite would be the negative of it, so the opposite of the give fraction is, \[-\dfrac{19}{56}\].
Next, the reciprocal of the given fraction is,
\[\dfrac{1}{n}=\dfrac{1}{\dfrac{19}{56}}=\dfrac{56}{19}\]
Therefore, the opposite of the given fraction is \[-\dfrac{19}{56}\] and the reciprocal of the given fraction is \[\dfrac{56}{19}\].

Note: The terms asked in the questions should be first understood properly and only then proceed to solve it. A common mistake which is observed is, interpreting the word opposite for reciprocal of a number and vice versa. Though answer is correct but the very logic is disturbed and the question as a whole gets wrong.