Question

Among the given rational numbers, find the second largest number.
$\frac{-4}{3},\frac{-7}{8},\frac{-9}{12},\frac{-19}{24}$

• A. $\frac{-9}{12}$
• B. $\frac{-19}{24}$
• C. $\frac{-7}{8}$
• D. $\frac{-4}{3}$

Answer 1

The correct option is B $\frac{-19}{24}$

Taking the LCM of the denominators, we first convert the given rational numbers into rational numbers having the same denominator.
LCM of 24, 12, 8 and 3 is 24.

$\frac{-4}{3}=\frac{-4\times 8}{3\times 8}$ = $\frac{-32}{24}$

$\frac{-7}{8}=\frac{-7\times 3}{8\times 3}$ = $\frac{-21}{24}$

$\frac{-9}{12}=\frac{-9\times 2}{12\times 2}$ = $\frac{-18}{24}$

Now, $-18>-19>-21>-32$
So, the second largest number is $\frac{-19}{24}$