Question

Express $\dfrac{{ - 11}}{9}$ as a rational number with denominator -99.

Answer 1

Hint: We are given a fraction and we need to express it with -99 as the new denominator. So, for expressing this fraction in this form, we need to carry out mathematical operations. Here, we can see that -99 can be obtained if we multiply 9 with -11. So, on multiplying the numerator and denominator of the given fraction with -11, we will get our answer.

Complete step-by-step answer:
In this question, we are given a fraction and we need to find the new fraction if we change its denominator with 99.
The given fraction is $\dfrac{{ - 11}}{9}$.
Here, the numerator is -11 and the denominator is 9.
We need to express this fraction with denominator as -99.
So, we need to carry out some mathematical operations to make these changes.
Here note that we can get -99 by multiplying 9 with -11.
So, now we have to multiply both numerator and denominator with -11 to get -99 in denominator.
So, therefore multiplying the given fraction $\dfrac{{ - 11}}{9}$ with -11 in both numerator and denominator, we get
$ \Rightarrow \dfrac{{ - 11}}{9} = \dfrac{{ - 11}}{9} \times \dfrac{{ - 11}}{{ - 11}} = \dfrac{{121}}{{ - 99}}$
Hence, we have expressed $\dfrac{{ - 11}}{9}$ as a rational number with -99 as a denominator.

Note: In the question, a word rational number is used. Let us see what a rational number is.
A rational number is nothing but a number of the form $\dfrac{a}{b}$ where the value of a can be zero but the value of b can never be zero.