Question

Insert three rational numbers between 2/3 and 3/5.

Answer 1

2\3 +3\5÷2
now take the LCM of 3 & 5 
10 + 9 \15 \ 2
now multiply 15 × 2=30
1st no= 19\30
2nd no= 2\3 + 19\30 ÷ 2
20 + 19 \30\2
39\60
3rd no= 19\30 + 3\5 ÷2
19 +18\30\2
37\60

Answer 2

The three rational numbers between $\frac{2}{3}\ and\ \frac{3}{5}$ are $\bold{\frac{91}{150}, \frac{92}{150}, \frac{93}{150}}$.

Since the denominators are not in same value, first we have to make the denominators are the same, such that  

$\frac{2}{3} \times \frac{5}{5}=\frac{10}{15}$  

$\frac{3}{5} \times \frac{3}{3}=\frac{9}{15}$  

The rational numbers between $\frac{9}{15}\ and\ \frac{10}{15}$ are not the proper rational number values such that the value, we should go rationalization again.

$\frac{10}{15} \times \frac{10}{10}=\frac{100}{150}$

$\frac{9}{15} \times \frac{10}{10}=\frac{90}{150}$

There could have a chance of proper rational values between $\frac{90}{150}\ and\ \frac{100}{150}$, such that $\bold{\frac{91}{150}, \frac{92}{150}, \frac{93}{150}, \frac{94}{150}, \frac{95}{150}}$ etc.