Question

Find five fractions between $\frac{2}{3}$ and $\frac{4}{5}$.

Answer 1

Making equal denominators of both the dfractions.

$\frac{2}{3}=\frac{2}{3}\times \frac{5}{5}$

$=\frac{10}{15}$

And,

$\frac{4}{5}=\frac{4}{5}\times \frac{3}{3}$

$=\frac{12}{15}$

Now, the dfraction between $\frac{10}{15}$ and $\frac{12}{15}$ is,

$\frac{\frac{10}{15}+\frac{12}{15}}{2}=\frac{22}{30}$

So, $\frac{10}{15}<\frac{22}{30}<\frac{12}{15}$

The dfraction between $\frac{10}{15}$ and $\frac{22}{30}$ is,

$\frac{\frac{10}{15}+\frac{22}{30}}{2}=\frac{42}{30\times 2}$

$=\frac{21}{30}$

So, $\frac{10}{15}<\frac{21}{30}<\frac{22}{30}<\frac{12}{15}$

The dfraction between $\frac{22}{30}$ and $\frac{12}{15}$ is,

$\frac{\frac{22}{30}+\frac{12}{15}}{2}=\frac{46}{30\times 2}$

$=\frac{23}{30}$

$\frac{10}{15}<\frac{21}{30}<\frac{22}{30}<\frac{23}{30}<\frac{12}{15}$

The dfraction between $\frac{10}{15}$ and $\frac{21}{30}$ is,

$\frac{\frac{10}{15}+\frac{21}{30}}{2}=\frac{41}{30\times 2}$

$=\frac{41}{60}$

So, $\frac{10}{15}<\frac{41}{60}<\frac{21}{30}<\frac{22}{30}<\frac{23}{30}<\frac{12}{15}$

The dfraction between $\frac{23}{30}$ and $\frac{12}{15}$.

$\frac{\frac{23}{30}+\frac{12}{15}}{2}=\frac{47}{30\times 2}$

$=\frac{47}{60}$

So, $\frac{10}{15}<\frac{41}{60}<\frac{21}{30}<\frac{22}{30}<\frac{23}{30}<\frac{47}{60}<\frac{12}{15}$

Therefore, the five dfractions between the given numbers are $\frac{41}{60},\frac{21}{30},\frac{22}{30},\frac{23}{30},\frac{47}{60}$.