Question

Arrange the following in ascending order:

$\frac{-7}{8},\frac{5}{6},\frac{6}{-7}$

Answer 1

Step 1: Converting given fraction into equivalent fractions.

To convert them in equivalent fraction we have to make $\frac{6}{-7}$ in standard form.

$\frac{6}{-7}=\frac{-6}{7}$ (Multiplying numerator and denominator by $-1$)

So, LCM of $8,6$ and $7$ is $168$.

Now convert the given rational numbers in equivalent fraction with denominator $168$.

$\frac{-7\times 21}{8\times 21}=\frac{-147}{168},\frac{5\times 28}{6\times 28}=\frac{140}{168}$ and

$\frac{-6\times 24}{7\times 24}=\frac{-144}{168}$

Step 2: Arranging the fractions in ascending order.

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, $-147<-144<140$

So, $\frac{-147}{168}<\frac{-144}{168}<\frac{140}{168}$

Hence, arrangement of given fractions in ascending order is $\frac{-7}{8}<\frac{6}{-7}<\frac{5}{6}$.