Full solution

Q. Find five rational numbers between

\frac{3}{5} \& \frac{4}{5}

Understand Difference: To find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ , we first need to understand that the difference between these two numbers is $\frac{1}{5}$ . We can divide this difference into more parts to find numbers in between.
Divide Interval Equally: We can divide the interval from $\frac{3}{5}$ to $\frac{4}{5}$ into six equal parts to ensure we find five numbers in between. To do this, we divide $\frac{1}{5}$ by $6$ .
Calculate Parts: $\frac{1}{5}$ divided by $6$ is $\frac{1}{30}$ . This means that each part between $\frac{3}{5}$ and $\frac{4}{5}$ is $\frac{1}{30}$ apart.
Find First Number: Now, we can add $\frac{1}{30}$ to $\frac{3}{5}$ to find the first rational number. $\frac{3}{5}$ is the same as $\frac{18}{30}$ , so adding $\frac{1}{30}$ gives us $\frac{19}{30}$ .
Simplify Second Number: Continuing this process, we add $\frac{1}{30}$ to $\frac{19}{30}$ to get the second number, which is $\frac{20}{30}$ . However, $\frac{20}{30}$ can be simplified to $\frac{2}{3}$ .
Calculate Third Number: Adding another $\frac{1}{30}$ to $\frac{20}{30}$ gives us $\frac{21}{30}$ , which simplifies to $\frac{7}{10}$ .
Determine Fourth Number: The next number is found by adding $\frac{1}{30}$ to $\frac{21}{30}$ , resulting in $\frac{22}{30}$ , which simplifies to $\frac{11}{15}$ .
Find Fifth Number: Finally, adding $\frac{1}{30}$ to $\frac{22}{30}$ gives us $\frac{23}{30}$ , which cannot be simplified further.
Find Fifth Number: Finally, adding $\frac{1}{30}$ to $\frac{22}{30}$ gives us $\frac{23}{30}$ , which cannot be simplified further.We have now found five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ : $\frac{19}{30}$ , $\frac{2}{3}$ , $\frac{7}{10}$ , $\frac{11}{15}$ , and $\frac{23}{30}$ .