Question:
Find 10 rational numbers between $\frac{-3}{4}$ and $\frac{5}{6}$.
Solution:
LCM of 4 and 6 is 12 .
Now,
$\frac{-3}{4}=\frac{-3 \times 3}{4 \times 3}=\frac{-9}{12}$
And,
$\frac{5}{6}=\frac{5 \times 2}{6 \times 2}=\frac{10}{12}$
Rational numbers lying between $\frac{-3}{4}$ and $\frac{5}{6}$ :
$\frac{-8}{12}, \frac{-7}{12}, \frac{-6}{12}, \frac{-5}{12}, \frac{-4}{12}, \ldots \frac{1}{12}, \frac{2}{12}, \frac{3}{12}, \frac{4}{12}, \frac{5}{12}, \frac{6}{12}, \frac{7}{12}, \frac{8}{12}, \frac{9}{12}$
We can take any 10 out of these.