What is a fraction? A fraction a/b says: the whole is cut into b equal parts and we take a of them. The bottom number is the size of the part, the top number is how many parts.
Equal slices. Cutting a round pizza into n equal slices means every slice has the same angle at the middle:
slice angle = 360° / n (n=8 gives 45°)
A slice is 1/n of the pizza, so n slices put together make exactly 1 whole pizza.
Equal fractions. Cut each slice again and the amount stays the same: a/b = (a×k)/(b×k). So 2/4 = 1/2 = 3/6 = 4/8. Two fractions are equal when a×d = c×b.
Adding. With the same slice size just add the counts: 1/4 + 2/4 = 3/4. With different sizes, first cut into the same size (common denominator): 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2.
Comparing. Put both on the same denominator or cross-multiply: 2/3 vs 3/4 gives 2×4 = 8 and 3×3 = 9, so 3/4 is bigger.
Simplifications. The pizza is a flat disc and every slice has the same toppings; real slices are never perfectly equal. All the maths in this game uses whole numbers only, so there are no rounding errors.