Question

What is the opposite and reciprocal of $\dfrac{5}{9}$?

Answer 1

Hint: Here, in the given question, we need to find the opposite and reciprocal of $\dfrac{5}{9}$. The terminology opposite stands for additive inverse and reciprocal stands for multiplicative inverse. An additive inverse of a number is defined as the value, which in addition with the real number results in zero value. Additive inverse simply means changing the sign of the number. The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product as $1$.
Formula used:
Additive inverse formula = $ - 1 \times number$.
Multiplicative inverse = reciprocal of number .i.e., for any number $''n''$, multiplicative inverse can be expressed as $\dfrac{1}{n}$ and ${n^{ - 1}}$.

Complete step-by-step answer:
Additive inverse:
Here, we are given a number $\dfrac{5}{9}$ and we need to find the additive inverse of it.
Additive inverse formula = $ - 1 \times number$. Using this, we get
Additive inverse of $\dfrac{5}{9}$ = $ - 1 \times \dfrac{5}{9}$
Additive inverse of $\dfrac{5}{9}$ = $ - \dfrac{5}{9}$

Multiplicative inverse:
Here, we are given, a fractional number $\dfrac{5}{9}$
Let us assume that $\dfrac{a}{b}$ is the given number then the multiplicative inverse of the given number can be given by $\dfrac{b}{a}$.
We are asked to find the multiplicative inverse of $\dfrac{5}{9}$
Now, the multiplicative inverse of the $\dfrac{5}{9}$ can be given as $\dfrac{9}{5}$.

Note: Remember that the additive inverse of a positive number is always negative and the additive inverse of a negative number is always positive. In additive inverse the sum of two integers is equal to zero, so the zero is known as the additive identity. Similarly when the product of two numbers is equal to one then the numbers are called multiplicative inverses and $1$ is known as the multiplicative identity.