The quickest way to measure is not to measure at all.
The board is a rectangle, therefore opposing sides of it are parallel to each other.
Now say you lay your measuring tape across the board like so
wherever the middle of the tape is, it will also be the middle of the board (or half of the board width) You can place the tape however you want. You are basically measuring from one edge to the other at an angle. Now angle the tape in a way that is shows a value that's easy to divide by 2, but longer than the board width, say 10 for example. You can now mark the middle of the tape at 5 and can be sure that this is the middle 0f the board, too.
If you do this two times, you have two points that connect to a line, that is exactly in the middle of the board.
The interesting thing is that this holds true for any fraction and does the math geometrically, which always works, no matter how ugly the numbers are.
Let's say your 8 is a rough cut and is actually something like 8.345 (I made that number up, the unit doesn't even matter)
And you want to divide that evenly by 3.
Ok 8.345 / 3 = ?? phew, not that easy. You could use a calculator...or do what I stated above.
Place the 0 of the tape at one edge of the board and angle it so that 9 is right at the other edge.
To divide the board in thirds, mark 3 and 6.
By choosing a total tape length from edge to edge of the board that you can conveniently divide into the desired fraction, the geometry will do the math for you and probably be done with it a lot quicker.