Question

Choose the correct word and fill in the blank:

$\frac{-9}{81}$ and $\frac{1}{9}$ represent the ………. rational number(s).

• A. same
• B. different

Answer 1

Given rational numbers are $\frac{-9}{81}$ and $\frac{1}{9}$.

Step $1.$ Finding standard form of $\frac{-9}{81}$

HCF of $9$ and $81$ is $9$.

On dividing the numerator and denominator of $\frac{-9}{81}$ by their HCF $9$. We get:

$\frac{-9÷9}{81÷9}=\frac{-1}{9}$

Step $2.$ Finding standard form of $\frac{1}{9}$

HCF of $1$ and $9$ is $1$.

$\frac{1}{9}$ is in standard form because both the numerator and denominator have no common factor other than $1$.

Step $3.$ Compare standard forms:

Since the standard form of given rational numbers is not same. Hence $\frac{-9}{81}$ and $\frac{1}{9}$ are different.