Question

(Discrete Mathematics) If m and n are nonzero integers, show that (2m+3n)/5mn is a rational number.

Answer 1

Answer:

$\frac{(2m+3n)}{5mn}=\frac{2}{5n}+\frac{3}{5m}$ is a rational number for any m and n; nonzero integers.

Step-by-step explanation:

We have been given that 'm' and 'n' are nonzero integers. We are asked to show that $\frac{(2m+3n)}{5mn}$ is a rational number.

We can rewrite our given number as:

$\frac{2m}{5mn}+\frac{3n}{5mn}$

Cancelling out common terms:

$\frac{2}{5n}+\frac{3}{5m}$

Since 'm' and 'n' are nonzero integers, so each part will be a rational number.

We know that sum of two rational numbers is always rational, therefore, our given number is a rational number.