Question

Arrange the following in ascending order:

$\frac{-4}{-5},\frac{3}{10},\frac{-7}{15}$

Answer 1

Step 1: Converting given fraction into equivalent fractions.

To convert them in equivalent fraction we have to make $\frac{-4}{-5}$ in standard form.

$\frac{-4}{-5}=\frac{4}{5}$ (minus-minus sine get canceled)

So, LCM of $5,10$ and $15$ is $30$.

Now convert the given rational numbers in equivalent fraction with denominator $30$.

$\frac{4\times 6}{5\times 6}=\frac{24}{30},\frac{3\times 3}{10\times 3}=\frac{9}{30}$ and

$\frac{-7\times 2}{15\times 2}=\frac{-14}{30}$

Step 2: Comparing the numerator of $\frac{24}{30},\frac{9}{30}$ and $\frac{-14}{30}$.

We know ascending order means to arrange numbers in increasing order, that is, from smallest to largest.

Here, $-14<9<24$ so, $\frac{-14}{30}<\frac{9}{30}<\frac{24}{30}$

Hence, arrangement of given fractions in ascending order is $\frac{-7}{15}<\frac{3}{10}<\frac{4}{5}$.