Positive lntegers

• $\text{odd} \times \text{odd} = \text{odd}$
• The largest even integer less than $ab$ is: $ab-1$ because $ab$ is odd
• Since half of the numbers in that range will odd, the number of even integers will be half that $= \dfrac{ab-1}{2}$

Since $a$ and $b$ are both odd, then $ab$ is odd.

Therefore, the largest even integer less than $ab$ is $ab - 1$ .

Since every other positive integer less than or equal to $ab - 1$ is even, then the number of even positive integers less than or equal to $ab - 1$ (thus, less than ab) is $\frac{ab - 1}{2}$