Question

Arrange the following in descending order:

$\frac{-2}{3},\frac{3}{4},\frac{5}{-7}$

Answer 1

Step 1: Converting given fraction into equivalent fractions.

To convert them in equivalent fraction we have to make $\frac{5}{-7}$ in standard form.

$\frac{5}{-7}=\frac{-5}{7}$ (Multiplying numerator and denominator by $-1$)

So, LCM of $3,4$ and $7$ is $84$.

Now convert the given rational numbers in equivalent fraction with denominator $84$.

$\frac{-2\times 28}{3\times 28}=\frac{-56}{84},\frac{3\times 21}{4\times 21}=\frac{63}{84}$

and $\frac{-5\times 12}{7\times 12}=\frac{-60}{84}$

Step 2: Arranging the fractions in descending order.

Descending order means to arrange numbers in decreasing order, that is, from largest to smallest and fractions with larger numerators are larger.

Here, $63>-56>-60$

so, $\frac{63}{84}>\frac{-56}{84}>\frac{-60}{84}$

Hence, arrangement of given fractions in descending order is $\frac{3}{4}>\frac{-2}{3}>\frac{5}{-7}$.