Let’s get the numbers out of the way so we can move on to the fun stuff. Half of ¾ is ⅜ (three-eighths). That’s the clean, dry answer, and it’s been true since your grandmother’s first pie.
How did we get there? Multiply the denominator (the bottom number, 4) by 2, and you get 8. Then you keep the numerator (3) the same. So ¾ becomes 6/8, and half of that is 3/8. See? Easy math, no sweat.