Question

Arrange the following fractions in ascending order:
$\frac{2}{5},\frac{7}{10},\frac{11}{15}\mathrm{and}\frac{17}{30}$

Answer 1

The given fractions are $\frac{2}{5},\frac{7}{10},\frac{11}{15}\mathrm{and}\frac{17}{30}.$
L.C.M. of 5, 10, 15 and 30 = (2 $\times$ 5 $\times$ 3) = 30


So, we convert each of the fractions whose denominator is not equal to 30 into an equivalent fraction with denominator 30.
Now, we have:
$\frac{2}{5}=\frac{2\times 6}{5\times 6}=\frac{12}{30};\frac{7}{10}=\frac{7\times 3}{10\times 3}=\frac{21}{30};\frac{11}{15}=\frac{11\times 2}{15\times 2}=\frac{22}{30}$
Clearly, $\frac{12}{30}<\frac{17}{30}<\frac{21}{30}<\frac{22}{30}$
∴ ​$\frac{2}{5}<\frac{17}{30}<\frac{7}{10}<\frac{11}{15}$

Hence, the given fractions can be arranged in the ascending order as follows:
$\frac{2}{5},\frac{17}{30},\frac{7}{10},\frac{11}{15}$