Write the following fractions in ascending order.$\frac{4}{7}, \frac{7}{5}, \frac{2}{5}, \frac{5}{9}$.
Given :
The given fractions are $\frac{4}{7}, \frac{7}{5}, \frac{2}{5}, \frac{5}{9}$.
To do :
We have to write the given fractions in ascending order.
Solution :
To write the given numbers in increasing order, we have to convert them to like fractions.
First, find the LCM of the denominators.
LCM of 7,5,5 and 9 is $5\times 7\times 9=315$.
Therefore, the denominators of all fractions should be 315.
$\frac{4\times 45}{7\times 45}= \frac{180}{315}$
$\frac{7 \times 63}{5 \times 63}=\frac{441}{315}$
$\frac{2 \times 63}{5 \times 63} = \frac{126}{315}$
$\frac{5 \times 35}{9 \times 35} = \frac{175}{315}$
On comparing the numerators,
$126 < 175 < 180 < 441$
$ \frac{126}{315} < \frac{175}{315} < \frac{180}{315} < \frac{441}{315}$
$ \frac{2}{5} < \frac{5}{9} < \frac{4}{7} < \frac{7}{5}$
Therefore, the given fractions in ascending order is,
$\frac{2}{5}, \frac{5}{9}, \frac{4}{7}, \frac{7}{5}$.
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