Question

Arrange the following in ascending order.

$\frac{1}{11},$ $\frac{13}{11},$ $\frac{1}{3},$ $\frac{4}{3}$

• A. $\frac{1}{3}<\frac{13}{11}<\frac{1}{11}<\frac{4}{3}$
• B. $\frac{1}{3}<\frac{1}{11}<\frac{13}{11}<\frac{4}{3}$
• C. $\frac{1}{11}<\frac{13}{11}<\frac{1}{3}<\frac{4}{3}$
• D. $\frac{1}{11}<\frac{1}{3}<\frac{13}{11}<\frac{4}{3}$

Answer 1

The correct option is D $\frac{1}{11}<\frac{1}{3}<\frac{13}{11}<\frac{4}{3}$

At first we convert the given fractions into like fractions.

$\frac{1}{11}=\frac{1\times 3}{11\times 3}=\frac{3}{33}$

$\frac{13}{11}=\frac{13\times 3}{11\times 3}=\frac{39}{33}$

$\frac{1}{3}=\frac{1\times 11}{3\times 11}=\frac{11}{33}$

$\frac{4}{3}=\frac{4\times 11}{3\times 11}=\frac{44}{33}$

If we compare only the numerators we get,
$3<11<39<44$.

Now we can write,

$\frac{3}{33}<\frac{11}{33}<\frac{39}{33}<\frac{44}{33}$

$\therefore \frac{1}{11}<\frac{1}{3}<\frac{13}{11}<\frac{4}{3}$