Question

The fraction $\frac{3}{5}$ is found between which pair of fractions on a number line?

• A. $\frac{7}{10}$ and $\frac{3}{4}$
• B. $\frac{2}{5}$ and $\frac{1}{2}$
• C. $\frac{1}{3}$ and $\frac{5}{13}$
• D. $\frac{2}{7}$ and $\frac{8}{11}$

Answer 1

The correct option is D $\frac{2}{7}$ and $\frac{8}{11}$

(a) Let us consider the first set of fraction $\frac{7}{10},\frac{3}{4}$ and another given fraction $\frac{3}{5}$

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

$\frac{7\times 2}{10\times 2},\frac{3\times 4}{5\times 4},\frac{3\times 5}{4\times 5}=\frac{14}{20},\frac{12}{20},\frac{15}{20}\Rightarrow \frac{12}{20}<\frac{14}{20}<\frac{15}{20}\Rightarrow \frac{3}{5}<\frac{7}{10}<\frac{3}{4}$

Therefore, $\frac{3}{5}$ does not lie between the first set of fraction $\frac{7}{10},\frac{3}{4}$.

(b) Now, consider the set of fraction $\frac{2}{5},\frac{1}{2}$ and another given fraction $\frac{3}{5}$

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

$\frac{2\times 2}{5\times 2},\frac{3\times 2}{5\times 2},\frac{1\times 5}{2\times 5}=\frac{4}{10},\frac{6}{10},\frac{5}{10}\Rightarrow \frac{4}{10}<\frac{5}{10}<\frac{6}{10}\Rightarrow \frac{2}{5}<\frac{1}{2}<\frac{3}{5}$

Therefore, $\frac{3}{5}$ does not lie between the set of fraction $\frac{2}{5},\frac{1}{2}$.

(c) Now, consider the set of fraction $\frac{1}{3},\frac{5}{13}$ and another given fraction $\frac{3}{5}$

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

$\frac{1\times 65}{3\times 2},\frac{3\times 39}{5\times 39},\frac{5\times 15}{13\times 15}=\frac{65}{195},\frac{108}{195},\frac{75}{195}\Rightarrow \frac{65}{195}<\frac{75}{195}<\frac{108}{195}\Rightarrow \frac{1}{3}<\frac{5}{13}<\frac{3}{5}$

Therefore, $\frac{3}{5}$ does not lie between the set of fraction $\frac{1}{3},\frac{5}{13}$.

(d) Now, consider the set of fraction $\frac{2}{7},\frac{8}{11}$ and another given fraction $\frac{3}{5}$

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

$\frac{2\times 55}{7\times 55},\frac{3\times 77}{5\times 77},\frac{8\times 35}{11\times 35}=\frac{110}{385},\frac{221}{385},\frac{280}{385}\Rightarrow \frac{110}{385}<\frac{221}{385}<\frac{280}{385}\Rightarrow \frac{2}{7}<\frac{3}{5}<\frac{8}{11}$

Therefore, $\frac{3}{5}$ lies between the set of fraction $\frac{2}{7},\frac{8}{11}$.

Hence, the fraction $\frac{3}{5}$ is found between $\frac{2}{7}$ and $\frac{8}{11}$ on a number line.