Question

Out of the following rational numbers, find the largest and the smallest rational numbers.
$\frac{1}{2},\frac{6}{3},\frac{4}{5},\frac{3}{2},\frac{3}{4}$

• A. Largest number = $\frac{4}{5}$, Smallest number = $\frac{3}{2}$
• B. Largest number = $\frac{6}{3}$, Smallest number = $\frac{1}{2}$
• C. Largest number = $\frac{4}{5}$, Smallest number = $\frac{3}{4}$
• D. Largest number = $\frac{6}{3}$, Smallest number = $\frac{3}{4}$

Answer 1

The correct option is B Largest number = $\frac{6}{3}$, Smallest number = $\frac{1}{2}$

$\frac{6}{3}=2=\frac{2}{1}$

$\therefore$ LCM for the rational numbers$\frac{1}{2},\frac{2}{1},\frac{4}{5},\frac{3}{2},\frac{3}{4}$ is 20

$\Rightarrow$$\frac{1}{2}=\frac{10}{20}$

$\Rightarrow$$\frac{2}{1}=\frac{40}{20}$

$\Rightarrow$$\frac{4}{5}=\frac{16}{20}$

$\Rightarrow$$\frac{3}{2}=\frac{30}{20}$

$\Rightarrow$$\frac{3}{4}=\frac{15}{20}$

Now that the denominators are equal, we can compare the rational numbers. The numerator 40 is the largest and 10 is the least. Hence, the corresponding original rational numbers will be the largest and the least.
$\therefore$ Largest number = $\frac{6}{3}$ = 2 and the smallest number = $\frac{1}{2}$