Question

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

• A. $\frac{1}{2}<\frac{2}{3}<\frac{3}{4}<\frac{5}{6}$
• B. $\frac{5}{6}<\frac{2}{3}<\frac{3}{4}<\frac{1}{2}$
• C. $\frac{2}{3}<\frac{5}{6}<\frac{3}{4}<\frac{1}{2}$
• D. $\frac{3}{4}<\frac{2}{3}<\frac{1}{2}<\frac{5}{6}$

Answer 1

The correct option is A $\frac{1}{2}<\frac{2}{3}<\frac{3}{4}<\frac{5}{6}$

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. For that, let us find the LCM of the denominators of $\frac{2}{3},\frac{3}{4},\frac{1}{2}$ and $\frac{5}{6}$.

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

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

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

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