Question

Arrange the following in ascending order.

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

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

Answer 1

The correct option is A $\frac{1}{3}<\frac{1}{2}<\frac{2}{3}<\frac{2}{2}$

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 only the numerators we get $2<3<4<6$.

Now we can write,

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

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