Question

Match the following with the numbers that lie between them.

• A. 1
• B. $\frac{15}{56}$
• C. $\frac{3}{16}$
• D. $\frac{11}{60}$

Answer 1

To find the rational number between $\frac{1}{6}$ and $\frac{1}{5}$, make the denominators same.

LCM of 5 and 6 is 30, so,
$\frac{1}{6}=\frac{1\times 5}{6\times 5}=\frac{5}{30}$

$\frac{1}{5}=\frac{1\times 6}{5\times 6}=\frac{6}{30}$

A rational number between $\frac{5}{30}$ and $\frac{6}{30}$ is $\frac{5.5}{30}=\frac{55}{300}=\frac{11}{60}$.

Similarly, LCM of 7 and 8 is 56, so,
$\frac{2}{8}=\frac{2\times 7}{8\times 7}=\frac{14}{56}$

$\frac{2}{7}=\frac{2\times 8}{7\times 8}=\frac{16}{56}$

One of the rational numbers between $\frac{14}{56}$ and $\frac{16}{56}$ is $\frac{15}{56}$.

In the case of $\frac{1}{8}$ and $\frac{2}{8}$, denominators are already same.

So, a rational number between $\frac{1}{8}$ and $\frac{2}{8}$ is $\frac{1.5}{8}=\frac{15}{80}=\frac{3}{16}$ .

In the case of $\frac{3}{5}$ and $\frac{6}{5}$ also, denominators are already same.
So, some of the rational numbers between them are $\frac{4}{5}$ and $\frac{5}{5}$.