Question

Arrange the given rational number in descending order :

$\frac{5}{8},\frac{13}{-16}\text{and}\frac{-7}{12}$

Answer 1

Step 1 : Finding LCM of denominators of given numbers

Given, rational numbers are $\frac{5}{8},\frac{13}{-16}and\frac{-7}{12}$

Where, $\frac{13}{-16}=\frac{-13}{16}$

Now,

Factors of $8=2\times 2\times 2.$

Factors of $16=2\times 2\times 2\times 2.$

Factors of $12=2\times 2\times 3.$

$\therefore$ LCM of 8,16,12 = $4\times 2\times 2\times 3=48.$

Step 2 : Making denominators of rational numbers equal to LCM i.e., 48

$\frac{5}{8}=\frac{5\times 6}{8\times 6}=\frac{30}{48}$ and

$\frac{-13}{16}=\frac{-13\times 3}{16\times 3}=\frac{-39}{48}$ and

$\frac{-7}{12}=\frac{-7\times 4}{12\times 4}=\frac{-28}{48}$

Step 3 : Comparing $\frac{30}{48},\frac{-39}{48}and\frac{-28}{48}$

$\because$ For the same denominator, the rational number with the greater numerator is greater.

$\therefore \frac{30}{48}>\frac{-28}{48}>\frac{-39}{48}[\because \text{denominator are same and}$
$30>-28>-39]$

$\Rightarrow \frac{5}{8}>\frac{-7}{12}>\frac{-13}{16}$

$\Rightarrow \frac{5}{8}>\frac{-7}{12}>\frac{13}{-16}$

Hence, the descending order is $\frac{5}{8}>\frac{-7}{12}>\frac{13}{-16}.$