Question

Choose the correct word and fill in the blank:

$\frac{20}{-25}$ and $\frac{32}{40}$ represent the ………. rational number(s).

• A. same
• B. different

Answer 1

Given rational numbers are $\frac{20}{-25}$ and $\frac{32}{40}$.

Step $1.$ Finding standard form of $\frac{20}{-25}$

HCF of $20$ and $25$ is $5$.

On dividing the numerator and denominator of $\frac{20}{-25}$ by their HCF $5$. We get:

$\frac{20÷5}{-25÷5}=\frac{4}{-5}$

Now $\frac{4}{-5}=\frac{4\times \left(-1\right)}{-5\times \left(-1\right)}=\frac{-4}{5}$ (In the standard form of any rational number, the denominator is positive)

Step $2.$ Finding standard form of $\frac{32}{40}$

HCF of $32$ and $40$ is $8$.

On dividing the numerator and denominator of $\frac{32}{40}$ by their HCF $8$. We get:

$\frac{32÷8}{40÷8}=\frac{4}{5}$

Step $3.$ Compare standard forms:

Since the standard form of given rational numbers is not the same. Hence $\frac{20}{-25}$ and $\frac{32}{40}$ are different.