Question

Arrange $\frac{5}{8},\frac{3}{16},-\frac{1}{4}$ and $\frac{17}{32}$ in descending order of their magnitudes.Identify the largest rational number.

Answer 1

Consider the given numbers $\frac{5}{8},\frac{3}{16},-\frac{1}{4}$ and $\frac{17}{32}$.

The LCM of the denominators $8,16,4,32$ is $32$. Therefore, the given numbers will be:

$1]\frac{5\times 4}{8\times 4}=\frac{20}{32}$

$2]\frac{3\times 2}{16\times 2}=\frac{6}{32}$

$3]-\frac{1\times 8}{4\times 8}=-\frac{8}{32}$

$4]\frac{17}{32}$

Thus, the numbers in descending order are shown below:

$\frac{20}{32},\frac{17}{32},\frac{6}{32},-\frac{8}{32}\Rightarrow \frac{5}{8},\frac{17}{32},\frac{3}{16},-\frac{1}{4}$

Thus the largest rational number is $\frac{5}{8}$.