Question

Arrange in descending order in each of the following using symbol $ > $:
$\dfrac{8}{{17}},\dfrac{8}{9},\dfrac{8}{5},\dfrac{8}{{13}}$.

Answer 1

Hint: In this problem, the numerators of the given fractions are the same. So we need to check the
denominator of each fraction. Higher the value of the denominator lower will be the result. For
that we can verify the results by converting the given fractions into the decimal form.
The denominators of the given fractions are 17, 9, 5, 13. Since 17 is the biggest denominator of
all thus, $\dfrac{8}{{17}}$ will be the smallest value. Similarly, 5 is the smallest denominator
Thus, $\dfrac{8}{5}$ will give the largest value.

First, converting $\dfrac{8}{{17}}$ into the decimal form.
$\dfrac{8}{{17}} = 0.4705 \ldots $ (1)

Now, converting $\dfrac{8}{5}$ into the decimal form.
$\dfrac{8}{5} = 1.6$ (2)

Similarly, converting $\dfrac{8}{9}$ and $\dfrac{8}{{13}}$ into the decimal form.
$\dfrac{8}{9} = 0.8888 \ldots $ (3)
$\dfrac{8}{{13}} = 0.6153 \ldots $ (4)

From (1), (2), (3) and (4) we can say that $\dfrac{8}{5}$ is the biggest among them and
$\dfrac{8}{{17}}$ is the smallest among them.
Also, $\dfrac{8}{5}$ is followed by $\dfrac{8}{9}$, $\dfrac{8}{{13}}$and $\dfrac{8}{{17}}$.

Now, in descending order we can arrange the numbers as$\dfrac{8}{5} > \dfrac{8}{9} >
\dfrac{8}{{13}} > \dfrac{8}{{17}}$.
Note: Here, we have to arrange the given fractions into the descending order. Since the fractions
are given we convert the fractions into the decimal from. By comparing them we can arrange the
fraction in descending order.