Question

Arrange the following in ascending order:

$\frac{-5}{-6},\frac{11}{12},\frac{-17}{18},\frac{23}{-24}$

Answer 1

Step 1: Converting given fraction into equivalent fractions.

To convert them in equivalent fraction we have to make $\frac{-5}{-6}$ and $\frac{23}{-24}$ in standard form.

$\frac{23}{-24}=\frac{-23}{24}$ (Multiplying numerator and denominator by -1)

And $\frac{-5}{-6}=\frac{5}{6}$ (minus-minus sine get canceled)

So, LCM of $6,12,18$ and $24$ is $72$.

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

$$\begin{gathered} \Rightarrow \frac{5\times 12}{6\times 12}=\frac{60}{72},\frac{11\times 6}{12\times 6}=\frac{66}{72}, \\ \frac{-17\times 4}{18\times 4}=\frac{-68}{72} \end{gathered}$$

and $\frac{-23\times 3}{24\times 3}=\frac{-69}{72}$

Step 2: Comparing the numerator of $\frac{60}{72},\frac{66}{72},\frac{-68}{72},\frac{-69}{72}$

We know ascending order means to arrange numbers in increasing order, that is, from smallest to largest and fractions with smaller numerators are smaller.

Here, $-69<-68<60<66$

so, $\frac{-69}{72}<\frac{-68}{72}<\frac{60}{72}<\frac{66}{72}$

Hence, arrangement of given fractions in ascending order is $\frac{23}{-24}<\frac{-17}{18}<\frac{-5}{-6}<\frac{11}{12}$.