Question

Choose the correct word and fill in the blank:

$\frac{-16}{24}$ and $\frac{20}{-16}$ represent the ………. rational number(s).

• A. same
• B. different

Answer 1

Given rational numbers are $\frac{-16}{24}$ and $\frac{20}{-16}$.

Step $1.$ Finding standard form of $\frac{-16}{24}$

HCF of $16$ and $24$ is $8$.

On dividing the numerator and denominator of $\frac{-16}{24}$ by their HCF $8$. We get:

$\frac{-16÷8}{24÷8}=\frac{-2}{3}$

Step $2.$ Finding standard form of $\frac{20}{-16}$

HCF of $20$ and $16$ is $4$.

On dividing the numerator and denominator of $\frac{20}{-16}$ by their HCF $4$. We get:

$\frac{20÷4}{-16÷4}=\frac{5}{-4}$

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

Step $3.$ Compare standard forms:

Since the standard form of given rational numbers is not same. Hence $\frac{-16}{24}$ and $\frac{20}{-16}$ are different.