Question

Write the following rational numbers in ascending order:
$\dfrac{1}{3}$, $\dfrac{2}{9}$, $\dfrac{4}{3}$.

Answer 1

Hint: In this given question, first of all we must convert all the given rational numbers into numbers having the same denomination by taking the Lowest Common Multiple (LCM) of all the denominators. Then we can know the correct ascending order of the numbers by comparing their numerators.

Complete step-by-step answer:

In this given question, we are asked to write $\dfrac{1}{3}$, $\dfrac{2}{9}$, $\dfrac{4}{3}$ rational numbers in ascending order.
Ascending order in the arrangement which starts from the smallest number and ends at the largest one.
Now, in order to compare the given numbers in order to find the correct ascending order, we must first convert all the rational numbers into numbers having the same denomination by taking the Lowest Common Multiple (LCM) of all the denominators.
The denominators are 3, 9 and 3. So, their Lowest Common Multiple (LCM) is 9.
\[\dfrac{1}{3}=\dfrac{1\times 3}{3\times 3}=\dfrac{3}{9}\]……………… (1.1)
$\dfrac{2}{9}=\dfrac{2\times 1}{9\times 1}=\dfrac{2}{9}$……………… (1.2)
$\dfrac{4}{3}=\dfrac{4\times 3}{3\times 3}=\dfrac{12}{9}$……………. (1.3)
Now, we have to find the correct ascending order of \[\dfrac{3}{9}\], $\dfrac{2}{9}$ and $\dfrac{12}{9}$.
This can all be done by comparing the numerators of the above numbers and then in order of their ascending order.
So, we get the correct ascending order as $\dfrac{2}{9}<\dfrac{3}{9}<\dfrac{12}{9}$……………….(1.4).
Now, From 1.1, 1.2, 1.3 and 1.4, we get $\dfrac{2}{9}<\dfrac{1}{3}<\dfrac{4}{3}$ as the correct ascending order of the given rational numbers.
Therefore, we have got the solution to this question.

Note: In this type of questions of ascending and descending order, we must first convert all the numbers into the form of having the same denominator and then we must arrange them as required.