2021/058) FInd integers a and b such that $5\frac{3}{a} * b\frac{1}{2} = 19$

it is easier to work for b rather than a  as the term $b\frac{1}{2}$ is between 2 integers

Now $5 < 5\frac{3}{a} < 6$ 

Now $5 * 4 = 20 > 19$ and $6 * 3= 18 < 19$ so $b\frac{1}{2}$ is between 3 and 4 and hence b = 3

$b\frac{1}{2} = \frac{7}{2}$

So  $5\frac{3}{a} = 19 * \frac{2}{7} = \frac{38}{7}= 5 \frac{3}{7}$

Or a = 3