Question

Write the following rational numbers in ascending order: $\frac{1}{3},-\frac{2}{9},-\frac{4}{3}$

Answer 1

Ascending orders of rational numbers:

The given rational numbers are $\frac{1}{3},-\frac{2}{9},-\frac{4}{3}$.

To compare rational numbers. first, we have to make denominators of all the rational numbers to be equal.

$\therefore \frac{1}{3}\times \frac{3}{3}=\frac{3}{9}\mathrm{and}-\frac{4}{3}\times \frac{3}{3}=-\frac{12}{9}$

The rational numbers with the same denominators are $\frac{3}{9},-\frac{2}{9},-\frac{12}{9}$.

When the denominators of the rational numbers are the same. Then, the rational number with a larger numerator will be greater.

$$\begin{gathered} \therefore -\frac{12}{9}<-\frac{2}{9}<\frac{3}{9} \\ \Rightarrow -\frac{4}{3}<-\frac{2}{9}<\frac{1}{3} \end{gathered}$$

Hence,ascending order is $\mathbf{-}\frac{\mathbf{4}}{\mathbf{3}}\mathbf{<}\mathbf{-}\frac{\mathbf{2}}{\mathbf{9}}\mathbf{<}\frac{\mathbf{1}}{\mathbf{3}}$.