Question

Choose the correct word and fill in the blank:

$\frac{38}{49}$ and $\frac{-2}{-7}$ represent the ………. rational number(s).

• A. same
• B. different

Answer 1

Given rational numbers are $\frac{38}{49}$ and $\frac{-2}{-7}$.

Step $1.$ Finding standard form of $\frac{38}{49}$

HCF of $38$ and $49$ is $1$.

$\frac{38}{49}$is in standard form because both the numerator and denominator have no common factor other than $1$.

Step $2.$ Finding standard form of $\frac{-2}{-7}$

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

$\frac{-2\times \left(-1\right)}{-7\times \left(-1\right)}=\frac{2}{7}$

HCF of $2$ and $7$ is $1$.

$\frac{2}{7}$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 different. Hence $\frac{38}{49}$ and $\frac{-2}{-7}$ are different.