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

Also, find the difference between the largest and the smallest of these rational numbers. Express this difference as a decimal fraction correct to one decimal place.

L.C.M. of 9, 12, 3 and 18 is 36.

So, converting denominator of each fraction $-\dfrac{5}{9}, \dfrac{7}{12}, -\dfrac{2}{3} \text{ and } \dfrac{11}{18}$ into 36.

$\Rightarrow -\dfrac{5}{9} \times \dfrac{4}{4} = -\dfrac{20}{36} \\[1em] \Rightarrow \dfrac{7}{12} \times \dfrac{3}{3} = \dfrac{21}{36} \\[1em] \Rightarrow -\dfrac{2}{3} \times \dfrac{12}{12} = -\dfrac{24}{36} \\[1em] \Rightarrow \dfrac{11}{18} \times \dfrac{2}{2} = \dfrac{22}{36}.$

Since, -24 < -20 < 21 < 22

∴ -$\dfrac{24}{36} \lt -\dfrac{20}{36} \lt \dfrac{21}{36} \lt \dfrac{22}{36}$

$\Rightarrow -\dfrac{2}{3} \lt -\dfrac{5}{9} \lt \dfrac{7}{12} \lt \dfrac{11}{18}$

Difference between largest and smallest fraction :

$\Rightarrow \dfrac{11}{18} - \Big(-\dfrac{2}{3}\Big) \\[1em] \Rightarrow \dfrac{11}{18} + \dfrac{2}{3} \\[1em] \Rightarrow \dfrac{11}{18} + \dfrac{12}{18} \\[1em] \Rightarrow \dfrac{23}{18} \\[1em] \Rightarrow 1.3$

Hence, fractions in ascending order are $-\dfrac{2}{3} \lt -\dfrac{5}{9} \lt \dfrac{7}{12} \lt \dfrac{11}{18}$ and required difference = 1.3