Question

Out of the following rational numbers, which one is the greatest : $\frac{-4}{5}$, $\frac{-2}{3}$, $\frac{-7}{8}$ and $\frac{-5}{6}$

• A. $\frac{-7}{8}$
• B. $\frac{-5}{6}$
• C. $\frac{-2}{3}$
• D. $\frac{-4}{5}$

Answer 1

The correct option is C

$\frac{-2}{3}$

To compare the given numbers, we first have to make the denominator same by finding the LCM.

LCM of 5, 3, 8 and 6 is 120

When we rewrite the numbers with denominator as 120 we get :

$\frac{-4\times 24}{5\times 24}$ , $\frac{-2\times 40}{3\times 40}$ , $\frac{-7\times 15}{8\times 15}$, $\frac{-5\times 20}{6\times 20}$

$\Rightarrow$ $\frac{-96}{120}$ , $\frac{-80}{120}$, $\frac{-105}{120}$, $\frac{-100}{120}$

Comparing these numbers we get : $\frac{-105}{120}$ < $\frac{-100}{120}$< $\frac{-96}{120}$< $\frac{-80}{120}$

$\therefore$ $\frac{-80}{120}$ = $\frac{-2}{3}$ is the Greatest Rational number out of the given numbers.