Question

Arrange the following fractions in descending order:
$\frac{3}{4},\frac{5}{8},\frac{11}{12}\mathrm{and}\frac{17}{24}$

Answer 1

The given fractions are $\frac{3}{4},\frac{5}{8},\frac{11}{12}\mathrm{and}\frac{17}{24}.$
L.C.M. of 4, 8, 12 and 24 = (2 ⨯ 2 ⨯ 2 ⨯ 3) = 24


So, we convert each of the fractions whose denominator is not equal to 24 into an equivalent fraction with denominator 24.
Thus, we have;
$\frac{3}{4}=\frac{3\times 6}{4\times 6}=\frac{18}{24};\frac{5}{8}=\frac{5\times 3}{8\times 3}=\frac{15}{24};\frac{11}{12}=\frac{11\times 2}{12\times 2}=\frac{22}{24}$
Clearly, $\frac{22}{24}>\frac{18}{24}>\frac{17}{24}>\frac{15}{24}$

∴ ​$\frac{11}{12}>\frac{3}{4}>\frac{17}{24}>\frac{5}{8}$

Hence, the given fractions can be arranged in the descending order as follows:
$\frac{11}{12},\frac{3}{4},\frac{17}{24},\frac{5}{8}$