Question

Which one of the following sets of fractions is in the correct sequence of ascending order of their values ?

• A. $-\frac{1}{2},\frac{5}{6},\frac{-4}{9}$
• B. $-\frac{3}{7},\frac{-5}{6},\frac{3}{5}$
• C. $-\frac{1}{2},-\frac{4}{9},\frac{5}{6}$
• D. $-\frac{4}{9},\frac{5}{6},\frac{1}{6}$

Answer 1

The correct option is C $-\frac{1}{2},-\frac{4}{9},\frac{5}{6}$

(a) Let us consider the first set of fraction $-\frac{1}{2},\frac{5}{6},-\frac{4}{9}$

Taking the LCM to make the denominators same of the above fractions, we have

$-\frac{1\times 9}{2\times 9},\frac{5\times 3}{6\times 3},-\frac{4\times 2}{9\times 2}=-\frac{9}{18},\frac{15}{18},-\frac{8}{18}\Rightarrow -\frac{9}{18}<-\frac{8}{18}<\frac{15}{18}\Rightarrow -\frac{1}{2}<-\frac{4}{9}<\frac{5}{6}$

Therefore, the first set of fraction $-\frac{1}{2},\frac{5}{6},-\frac{4}{9}$ is not in ascending order.

(b) Now, consider the set of fraction $-\frac{3}{7},-\frac{5}{6},\frac{3}{5}$

Taking the LCM to make the denominators same of the above fractions, we have

$-\frac{3\times 30}{7\times 30},-\frac{5\times 15}{6\times 15},\frac{3\times 42}{5\times 42}=-\frac{90}{210},-\frac{175}{210},\frac{126}{210}\Rightarrow -\frac{175}{210}<-\frac{90}{210}<\frac{126}{210}\Rightarrow -\frac{5}{6}<-\frac{3}{7}<\frac{3}{5}$

Therefore, the set of fraction $-\frac{3}{7},-\frac{5}{6},\frac{3}{5}$ is not in ascending order.

(c) Now, consider the set of fraction $-\frac{1}{2},-\frac{4}{9},\frac{5}{6}$

Taking the LCM to make the denominators same of the above fractions, we have

$-\frac{1\times 9}{2\times 9},-\frac{4\times 2}{9\times 2},\frac{5\times 3}{6\times 3}=-\frac{9}{18},-\frac{8}{18},\frac{5}{18}\Rightarrow -\frac{9}{18}<-\frac{8}{18}<\frac{5}{18}\Rightarrow -\frac{1}{2}<-\frac{4}{9}<\frac{5}{6}$

Therefore, the set of fraction $-\frac{1}{2},-\frac{4}{9},\frac{5}{6}$ is in ascending order.

(d) Now, consider the set of fraction $-\frac{4}{9},\frac{5}{6},\frac{1}{6}$

Taking the LCM to make the denominators same of the above fractions, we have

$-\frac{4\times 2}{9\times 2},\frac{5\times 3}{6\times 3},\frac{1\times 3}{6\times 3}=-\frac{8}{18},\frac{15}{18},\frac{3}{18}\Rightarrow -\frac{8}{18}<\frac{3}{18}<\frac{15}{18}\Rightarrow -\frac{4}{9}<\frac{1}{6}<\frac{5}{6}$

Therefore, the set of fraction $-\frac{4}{9},\frac{5}{6},\frac{1}{6}$ is not in ascending order.

Hence, the only set of fraction in ascending order is $-\frac{1}{2},-\frac{4}{9},\frac{5}{6}$