Question

Question 87

Arrange the fractions $\frac{2}{3},\frac{3}{4},\frac{1}{2}and\frac{5}{6}$ in ascending order.

Answer 1

As per the question

We have to arrange the fractions $\frac{2}{3},\frac{3}{4},\frac{1}{2}$ and $\frac{5}{6}$ in ascending order.

In order to arrange the given fractions in ascending order, we have to first convert them into like fractions, that is fractions having the same denominator.

$\begin{array}{cc}2& 3,4,2,6\\ 2& 3,2,1,3\\ 3& 3,1,1,3\\ & 1,1,1,1\end{array}$

So, LCM of the denominators, i.e. 3, 4, 2 and 6 = 2 $\times$ 2 $\times$ 3 = 12.

Now, we convert the given fractions to equivalent fractions with denominator 12.

$\frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12},\frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12}$

$\frac{1}{2}=\frac{1\times 6}{2\times 6}=\frac{6}{12},\frac{5}{6}=\frac{5\times 2}{6\times 2}=\frac{10}{12}$

When we compare like fractions, the fraction having greater numerator will be greater.

Now, 6 < 8 < 9 < 10

$\therefore \frac{6}{12}<\frac{8}{12}<\frac{9}{12}<\frac{10}{12}$

$\therefore \frac{1}{2}<\frac{2}{3}<\frac{3}{4}<\frac{5}{6}$