Question

Which of the following is the greatest rational number?
(A) $\frac{-17}{24}$
(B) $\frac{-13}{16}$
(C) $\frac{-7}{8}$
(D) $\frac{-31}{48}$

Answer 1

Making all the fractions equivalent,
$\frac{-17}{24}=\frac{-17\times 2}{24\times 2}=\frac{-34}{48}$
$\frac{-13}{16}=\frac{-13\times 3}{16\times 3}=\frac{-39}{48}$
$\frac{-7}{8}=\frac{-7\times 6}{8\times 6}=\frac{-42}{48}$
$\frac{-31}{48}=\frac{-31}{48}$
$\frac{-31}{48}>\frac{-34}{48}>\frac{-39}{48}>\frac{-42}{48}$
$\frac{-31}{48}$ is the greatest.