Question

Choose the correct word and fill in the blank:

$\frac{-5}{9}$ and $\frac{5}{-9}$ represent the ………. rational number(s).

• A. same
• B. different

Answer 1

Given rational numbers are $\frac{-5}{9}$ and $\frac{5}{-9}$.

Step $1.$ Finding standard form of $\frac{-5}{9}$

HCF of $5$ and $9$ is $1$.

$\frac{-5}{9}$is in standard form because both the numerator and denominator have no common factor other than $1$.

Step $2.$ Finding standard form of $\frac{5}{-9}$

Here denominator is negative so we have to multiply both numerator and denominator by $-1$.

$\frac{5\times \left(-1\right)}{-9\times \left(-1\right)}=\frac{-5}{9}$

$\frac{-5}{9}$is in standard form as mentioned above.

Step $3.$ Compare standard forms:

Since the standard form of given rational numbers is the same. Hence $\frac{-5}{9}$ and $\frac{5}{-9}$ are the same.