Question

Choose the correct word and fill in the blank:

$\frac{-27}{45}$ and $\frac{-3}{5}$ represent the ………. rational number(s).

• A. same
• B. different

Answer 1

Given rational numbers are $\frac{-27}{45}$ and $\frac{-3}{5}$.

Step $1.$ Finding standard form of $\frac{-27}{45}$

HCF of $27$ and $45$ is $9$.

On dividing the numerator and denominator of $\frac{-27}{45}$ by their HCF $9$. We get:

$\frac{-27÷9}{45÷9}=\frac{-3}{5}$

Step $2.$ Finding standard form of $\frac{-3}{5}$

HCF of $3$ and $5$ is $1$.

$\frac{-3}{5}$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 the same. Hence $\frac{-27}{45}$ and $\frac{-3}{5}$ are the same.