question_answer

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

Answer:

Given fractions are \[\frac{2}{3},\frac{3}{4},\frac{1}{2}\]  and \[\frac{5}{6}\] As we have to arrange fractions in ascending order. So we take L.C.M. of numerator of all fractions

2	13, 4, 2, 6
2	3, 2, 1, 3
3	3, 1, 1, 3
	1, 1, 1, 1

\[\therefore \]      L.C.M. \[=2\times 3\times 3=12\]             \[\frac{2}{3}=\frac{2}{3}\times \frac{4}{4}=\frac{8}{12}\]             \[\frac{3}{4}=\frac{3}{4}\times \frac{3}{3}=\frac{9}{12}\]             \[\frac{1}{2}=\frac{1}{2}\times \frac{6}{6}=\frac{6}{12}\]             \[\frac{5}{6}=\frac{5}{6}\times \frac{2}{2}=\frac{10}{12}\]             \[\frac{6}{12}<\frac{8}{12}<\frac{9}{12}<\frac{10}{12}\]             \[\frac{1}{2}<\frac{2}{3}<\frac{3}{4}<\frac{5}{6}\] (\[\because \] Denominator of fractions are same the fraction having smaller numerator will be smaller) Thus, ascending order is \[\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{5}{6}\]