Separate an integer into two (nearly) equal parts

Let javascript do Math for you.

var x = 7;
var p1 = Math.ceil(x / 2);
var p2 = Math.floor(x / 2);
console.log(p1, p2);

Your code can be simplified a bit:

var num = 7;
var p1 = Math.floor(num / 2);
var p2 = p1;

if (num % 2 != 0) {
   p1++;
}
console.log(p1, p2);

Just find the first part and subtract it from the original number.

var x = 7;

var p1 = Math.floor(x / 2);
var p2 = x - p1;

console.log(p1, p2);

In the case of x being odd, p1 will receive the smaller of the two addends. You can switch this around by calling Math.ceil instead.