Start from zero — the basic math you need before everything else
Multiplying fractions is straightforward: multiply the tops together and the bottoms together, straight across. 2/3 × 4/5 = (2×4)/(3×5) = 8/15. And the word "of" means multiply, so "half of a half" is 1/2 × 1/2 = 1/4.
Dividing by a fraction means flip and multiply: turn the second fraction upside down (its reciprocal) and multiply instead. 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. This works because dividing asks "how many quarters fit into a half?", and the answer is 2.
Multiplying fractions makes a piece of a piece. Half of a chocolate bar is 1/2; half of that is 1/2 × 1/2 = 1/4 — a quarter of the whole bar. Dividing by a fraction asks 'how many fit?': how many 1/4-bars fit into 1/2 a bar? Two, so 1/2 ÷ 1/4 = 2.
▶ Multiplying & Dividing Fractions