Question

Arrange $ - \dfrac{5}{9}$, $\dfrac{7}{{12}}$, $ - \dfrac{2}{3}$ and $\dfrac{{11}}{{18}}$ in ascending order of their magnitudes. Identify the smallest.

Answer 1

Hint: Fractions are numerical quantities that are a part of a whole number. When a number or an object is split into equal parts, each part becomes a fraction of the whole. A fraction is a term that comes from the Latin language. “Fractus” means “broken” in Latin. To compare the given fractions, we first make the denominators of all the fractions equal and then compare the numerators of all the fractions. Arranging in ascending order means to arrange the fractions from smallest to largest order.

Complete step by step answer:
The magnitude of fractions may be grouped in either ascending or descending order.Ascending order is the arrangement of numbers from lowest to highest, while descending order is the arrangement of numbers from highest to lowest.Consider the numbers given :
$ - \dfrac{5}{9}$, $\dfrac{7}{{12}}$, $ - \dfrac{2}{3}$ and $\dfrac{{11}}{{18}}$

To arrange the above numbers in the increasing order of the magnitude we have to equalise the denominator. To equalise the denominator of each fraction we find the LCM of all the denominators of the above numbers. The Least Common Multiple (LCM) of the denominators $9$, $12$, $3$ and $18$ is $36$.

Now, we multiply the numerator and denominator by the same number in such a way that the denominator of all the fractions becomes equal to the LCM. So, we get,
\[ - \dfrac{5}{9} \times \dfrac{4}{4} = - \dfrac{{20}}{{36}}\]
$\Rightarrow \dfrac{7}{{12}} \times \dfrac{3}{3} = \dfrac{{21}}{{36}}$
$\Rightarrow - \dfrac{2}{3} \times \dfrac{{12}}{{12}} = - \dfrac{{24}}{{36}}$
$\Rightarrow \dfrac{{11}}{{18}} \times \dfrac{2}{2} = \dfrac{{22}}{{36}}$
Now, the denominators of all the fractions are equal. So, we can arrange the fractions in ascending order by comparing the numerators. Now, let us arrange the above fractions in the ascending order as shown below:
$ - \dfrac{{24}}{{36}}$, \[ - \dfrac{{20}}{{36}}\], $\dfrac{{21}}{{36}}$, $\dfrac{{22}}{{36}}$

Hence, the smallest fraction is $ - \dfrac{2}{3}$.

Note: In mathematics, we use fractions to find the fractional part of a number, calculate decimals and percentages, ratio and proportion, probability, and algebraic equations. We should also know how to compare the unlike fractions by taking LCM of the denominators. One should know the method to calculate the equivalent fractions by taking the LCM of the denominators.