<P> The method works because multiplication is distributive, so: </P> <Dl> <Dd> 3 × 11 = 3 × (1 × 2 0 + 1 × 2 1 + 0 × 2 2 + 1 × 2 3) = 3 × (1 + 2 + 8) = 3 + 6 + 24 = 33 . (\ displaystyle (\ begin (aligned) 3 \ times 11& = 3 \ times (1 \ times 2 ^ (0) + 1 \ times 2 ^ (1) + 0 \ times 2 ^ (2) + 1 \ times 2 ^ (3)) \ \ & = 3 \ times (1 + 2 + 8) \ \ & = 3 + 6 + 24 \ \ & = 33. \ end (aligned))) </Dd> </Dl> <Dd> 3 × 11 = 3 × (1 × 2 0 + 1 × 2 1 + 0 × 2 2 + 1 × 2 3) = 3 × (1 + 2 + 8) = 3 + 6 + 24 = 33 . (\ displaystyle (\ begin (aligned) 3 \ times 11& = 3 \ times (1 \ times 2 ^ (0) + 1 \ times 2 ^ (1) + 0 \ times 2 ^ (2) + 1 \ times 2 ^ (3)) \ \ & = 3 \ times (1 + 2 + 8) \ \ & = 3 + 6 + 24 \ \ & = 33. \ end (aligned))) </Dd> <P> A more complicated example, using the figures from the earlier examples (23,958,233 and 5,830): </P>

What is the algorithm for multiplying rational numbers