Question

Arrange the following in descending order.

$\frac{1}{2}$, $\frac{2}{2}$, $\frac{1}{3}$, $\frac{2}{3}$

• A. $\frac{2}{2}>\frac{1}{2}>\frac{2}{3}>\frac{1}{3}$
• B. $\frac{2}{2}>\frac{2}{3}>\frac{1}{2}>\frac{1}{3}$
• C. $\frac{2}{3}>\frac{1}{2}>\frac{1}{3}>\frac{2}{2}$
• D. $\frac{2}{3}>\frac{2}{2}>\frac{1}{2}>\frac{1}{3}$

Answer 1

The correct option is B $\frac{2}{2}>\frac{2}{3}>\frac{1}{2}>\frac{1}{3}$

At first we convert the given fractions into like fractions.

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

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

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

$\frac{2}{3}=\frac{2\times 2}{3\times 2}=\frac{4}{6}$

If we compare the numerators we get, $6>4>3>2$.

Now we can write,

$\frac{6}{6}>\frac{4}{6}>\frac{3}{6}>\frac{2}{6}$

$\therefore \frac{2}{2}>\frac{2}{3}>\frac{1}{2}>\frac{1}{3}$