Question

What is the opposite and reciprocal of $\dfrac{7}{9}$?

Answer 1

Hint: In mathematics, the multiplicative inverse means the reciprocal. Let us suppose that “x” be any number then its multiplicative inverse can be expressed as $\dfrac{1}{x}{\text{ and }}{{{x}}^{ - 1}}$. The opposite means the additive inverse.

Complete step-by-step answer:
Opposite of the given term is the additive inverse of the number. Additive inverse can be defined as the number which when added to the original number gives zero as the resultant value. For example; Additive inverse of
Opposite of the number $\dfrac{7}{9}$is $ - \dfrac{7}{9}$ …. (A)
We know that multiplicative inverse of any fraction can be expressed for –
Let us assume that $\dfrac{a}{b}$ is the given number then the multiplicative inverse of the given number can be given by - $\dfrac{b}{a}$
Now, we are asked to find the inverse of
It can be written as \[\dfrac{1}{{\dfrac{7}{9}}}\]
Now, the multiplicative inverse of the above fraction can be given as $\dfrac{9}{7}$

Note: Always remember that when the number zero is multiplied with any number gives resultant value as the zero. Also, when any number is divided by zero gives the resultant value as undefined or the infinity.