Not sure what the purpose is here, as I cannot see the difference with the normal table - is it just to make the calculations easier?

Dividing integers (or half-integers) is a tricky thing to do without pen-and-paper or a calculator, but multiplications are a lot easier. So the "trick" is to multiply the defender's FP by the ratio, and this gives you the minimum FP of the attacker to reach that ratio. With this in mind, only the 3:2 ratio is not completely obvious, and then you do it the other way: halve the defender (halving is reasonably easy) and add that result to the defender's original FP, this gives you the minimum FP the attacker needs to reach 3:2.

For ratios under 1:1, do it the other way around. Multiply the attacker's FP by the inverse of the ratio, and this gives you the maximum FP of a defender to reach this ratio. So if an attacker has only 2 FP, and you are facing a larger force, and you hesitate between 1:4 and 1:6 (usually you should have at least that feeling), just multiply 2 (the attacker's FP) by 4 (the inverse of 1:4): if the defender has at most 8 FP, you're at 1:4 (or better); if he has more than 8 FP, you're at 1:6 (or worse).