Question

Arrange the following fractions in descending order:
$\frac{5}{7},\frac{9}{14},\frac{17}{21}\mathrm{and}\frac{31}{42}$

Answer 1

The given fractions are $\frac{5}{7},\frac{9}{14},\frac{17}{21}\mathrm{and}\frac{31}{42}.$
L.C.M. of 7, 14, 21 and 42 = (2 ⨯ 3 ⨯ 7) = 42


We convert each one of the fractions whose denominator is not equal to 42 into an equivalent fraction with denominator 42.
Thus, we have:
$\frac{5}{7}=\frac{5\times 6}{7\times 6}=\frac{30}{42};\frac{9}{14}=\frac{9\times 3}{14\times 3}=\frac{27}{42};\frac{17}{21}=\frac{17\times 2}{21\times 2}=\frac{34}{42}$
Clearly, $\frac{34}{42}>\frac{31}{42}>\frac{30}{42}>\frac{27}{42}$
∴ ​$\frac{17}{21}>\frac{31}{42}>\frac{5}{7}>\frac{9}{14}$
Hence, the given fractions can be arranged in the descending order as follows:
$\frac{17}{21},\frac{31}{42},\frac{5}{7},\frac{9}{14}$