Question

Arrange the following fractions in ascending order:
$\frac{2}{3},\frac{5}{6},\frac{7}{9}\mathrm{and}\frac{11}{18}$

Answer 1

The given fractions are $\frac{2}{3},\frac{5}{6},\frac{7}{9}\mathrm{and}\frac{11}{18}.$


L.C.M. of 3, 6, 9 and 18 = (3 $\times$ 2 $\times$ 3) = 18
So, we convert each of the fractions whose denominator is not equal to 18 into an equivalent fraction with denominator 18.
Now, we have:
$\frac{2}{3}=\frac{2\times 6}{3\times 6}=\frac{12}{18};\frac{5}{6}=\frac{5\times 3}{6\times 3}=\frac{15}{18};\frac{7}{9}=\frac{7\times 2}{9\times 2}=\frac{14}{18}$
Clearly, $\frac{11}{18}<\frac{12}{18}<\frac{14}{18}<\frac{15}{18}$
∴ ​$\frac{11}{18}<\frac{2}{3}<\frac{7}{9}<\frac{5}{6}$

Hence, the given fractions can be arranged in the ascending order as follows:
$\frac{11}{18},\frac{2}{3},\frac{7}{9},\frac{5}{6}$