Question

Arrange the rational numbers $\frac{-7}{10},\frac{5}{-8},\frac{3}{-4}$ in ascending order.

Answer 1

The given rational numbers are:
$\frac{-7}{10},\frac{5}{-8},\frac{3}{-4}$
The given rational numbers with positive denominators are
$\frac{-7}{10},\frac{-5}{8},\frac{-3}{4}$
We now convert the given fractions into like fractions.
For this, we take the LCM of $10,8$ and $4$. The LCM is $40$.
Therefore, we have
$\frac{-7}{10}=\frac{-7\times 4}{10\times 4}=\frac{-28}{40}$
$\frac{-5}{8}=\frac{-5\times 5}{8\times 5}=\frac{-25}{40}$
$\frac{-3}{4}=\frac{-3\times 10}{4\times 10}=\frac{-30}{40}$
Comparing the numerators of these numbers, we find that
$-30<-28<-25$
Therefore, the ascending order is: $\frac{-30}{40}<\frac{-28}{40}<\frac{-25}{40}$ or $\frac{-3}{4}<\frac{-7}{10}<\frac{-5}{8}$ or $\frac{3}{-4}<\frac{-7}{10}<\frac{5}{-8}$