Question

How do you find the reciprocal of $ -\dfrac{14}{23} $ ?

Answer 1

Hint: We know that if a and b are reciprocal of each other the product of a and b is equal to 1 so $ ab=1 $ reciprocal of a is $ \dfrac{1}{a} $ and reciprocal of b is equal to $ \dfrac{1}{b} $ . if we have to find the reciprocal of a number then we have to divide 1 by that number.

Complete step by step answer:
We have to find the reciprocal of $ -\dfrac{14}{23} $ . we know that reciprocal of any number x is $ \dfrac{1}{x} $
To find the reciprocal of $ -\dfrac{14}{23} $ we have divide 1 by $ -\dfrac{14}{23} $
So reciprocal of $ -\dfrac{14}{23} $ = $ 1\div \left( -\dfrac{14}{23} \right) $
We know that while dividing any number by a fraction we can multiply the fraction by alternating the value of denominator and numerator
So we can write = $ 1\div \left( -\dfrac{14}{23} \right)=1\times \left( -\dfrac{23}{14} \right) $
So the reciprocal of $ -\dfrac{14}{23} $ is equal to $ -\dfrac{23}{14} $
In this way, we can find the reciprocal of any number.

Note:
To simplify we can find the reciprocal of any number just by alternating the value of numerator and denominator for example reciprocal of $ \dfrac{3}{8} $ is $ \dfrac{8}{3} $ , reciprocal of $ \dfrac{2}{3} $ is $ \dfrac{3}{2} $ . Whenever an integer is given we can assume the denominator is 1 except for 0, for example, the reciprocal of 5 is equal to $ \dfrac{1}{5} $ . We can write reciprocal of any number except for 0 because the reciprocal of 0 tends to infinity. One point to observe is that the reciprocal of a negative real number is always a negative real number and the reciprocal of a positive number is always positive.