Question

Out of the following fractions which is the smallest and which the greatest?
$\frac{1}{2},\frac{6}{3},\frac{4}{5},\frac{3}{2},\frac{3}{4}$

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

Answer 1

The correct option is C

Greatest fraction = $\frac{6}{3}$, Smallest fraction = $\frac{1}{2}$

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

$\therefore$ LCM for the fractions $\frac{1}{2},\frac{2}{1},\frac{4}{5},\frac{3}{2},\frac{3}{4}$ 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 denominator is equal, we can compare the fractions. The numerator 40 is the greatest and 10 is the least. Hence, the corresponding original fractions will be the greatest and the least.
$\therefore$ Greatest fraction = $\frac{6}{3}$ = 2 and the smallest fraction = $\frac{1}{2}$