Doubling and Halving

Multiplying by doubling one factor and halving the other preserves the product. So 25 x 16 becomes 50 x 8 = 400. Keep going: 14 x 35 becomes 7 x 70 = 490. The trick is to double until one factor lands on a round, easy number. This turns an awkward multiplication into one you can read straight off.

Doubling and halving works because you are really multiplying by 2/2 = 1, which changes nothing about the answer. The ancient Egyptians built their entire multiplication system on this idea, combining only doubling and addition to multiply any two numbers. To multiply 13 x 21, they doubled 21 repeatedly, then added the doublings that summed to 13.