Question

Arrange the following fractions in ascending order.
$\dfrac{4}{9},\dfrac{1}{5},\dfrac{2}{15}$

Answer 1

Hint: We solve this question by first checking whether the given fractions are like fractions or unlike fractions, that is if their denominators are the same or not. As they are unlike, we find the LCM of the denominators and then multiply the numerator and denominator of fractions to make their denominators equal to LCM obtained. Then we compare the obtained fractions and arrange them in ascending order. Then we replace the fractions with their original value in the order obtained.

Complete step by step answer:
The fractions we are given are $\dfrac{4}{9},\dfrac{1}{5}$ and $\dfrac{2}{15}$.
As we see the denominators of the given fractions are different. So, the given fractions are unlike fractions.
Here we need to arrange them in ascending order, that is we need to compare the fractions. To compare them we need to convert the given unlike fractions to like fractions.
So, to convert them into like fractions let us find the LCM of the denominators of given fractions.
So, let us find the LCM of 9, 5 and 15. Then we get,
$\begin{align}
  & 3\left| \!{\underline {\,
  9,5,15 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3,5,5 \,}} \right. \\
 & 5\left| \!{\underline {\,
  1,5,5 \,}} \right. \\
 & \ \ 1,1,1 \\
\end{align}$
So, LCM of 9, 5 and 15 is equal to,
$LCM=3\times 3\times 5=45$
Now let us multiply the fractions to make their denominator equal to LCM, that is 45.
Now let us consider the first fraction, $\dfrac{4}{9}$. We can convert it as,
$\begin{align}
  & \Rightarrow \dfrac{4}{9}=\dfrac{4}{9}\times \dfrac{5}{5} \\
 & \Rightarrow \dfrac{4}{9}=\dfrac{20}{45}...........\left( 1 \right) \\
\end{align}$
Now let us consider the second fraction, $\dfrac{1}{5}$. We can convert it as,
$\begin{align}
  & \Rightarrow \dfrac{1}{5}=\dfrac{1}{5}\times \dfrac{9}{9} \\
 & \Rightarrow \dfrac{1}{5}=\dfrac{9}{45}...........\left( 2 \right) \\
\end{align}$
Now let us consider the third fraction, $\dfrac{2}{15}$. We can convert it as,
$\begin{align}
  & \Rightarrow \dfrac{2}{15}=\dfrac{2}{15}\times \dfrac{3}{3} \\
 & \Rightarrow \dfrac{2}{15}=\dfrac{6}{45}...........\left( 3 \right) \\
\end{align}$
Now using the equations (1), (2) and (3) we can write the given fractions $\dfrac{4}{9},\dfrac{1}{5},\dfrac{2}{15}$ as $\dfrac{20}{45},\dfrac{9}{45},\dfrac{6}{45}$.
Now we can see that they are like fractions, that is their denominators are the same. So, let us compare the obtained fractions and write them in ascending order.
$\Rightarrow \dfrac{6}{45},\dfrac{9}{45},\dfrac{20}{45}$
From equations (1), (2) and (3) we can write them as,
$\Rightarrow \dfrac{2}{15},\dfrac{1}{5},\dfrac{4}{9}$

So, the correct answer is “$\dfrac{2}{15},\dfrac{1}{5},\dfrac{4}{9}$”.

Note: We can also convert them into the like fractions by multiplying the denominator of each fraction with the denominators of the other two.
$\begin{align}
  & \Rightarrow \dfrac{4}{9}=\dfrac{4}{9}\times \dfrac{5\times 15}{5\times 15} \\
 & \Rightarrow \dfrac{4}{9}=\dfrac{300}{675} \\
\end{align}$
Similarly, we can convert the other two fractions and then compare them and write them in ascending order.