Question

What is the product of the biggest and the smallest fraction among $\frac{2}{3},\frac{3}{4},\frac{4}{5}and\frac{5}{6}$?

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is B

For comparison, we have to convert the given fraction in like fractions.
$\frac{2}{3},\frac{4}{5},\frac{3}{4},\frac{5}{6}$
The L.C.M of denominator of given fraction is 60.
So, $\frac{2}{3}\times \frac{20}{20}=\frac{40}{60}$
$\frac{3}{4}\times \frac{15}{15}=\frac{45}{60}$
$\frac{4}{8}\times \frac{12}{12}=\frac{48}{60}$
$\frac{5}{6}\times \frac{10}{10}=\frac{50}{60}$
The biggest fraction is $\frac{50}{60}$.
Smallest fraction is $\frac{40}{60}$.
Now, their difference = $\frac{50}{60}\times \frac{40}{60}=\frac{2000}{3600}=\frac{20}{36}=\frac{5}{9}$