Multiply by halving and doubling — no times tables needed
Even difficult products like 19×23 can be calculated without multiplication tables. Keep halving one number (discarding the remainder) and doubling the other; then add only the right-hand values on rows where the left-hand number is odd.
Why does it work? It uses the same principle as expressing the left-hand number in binary. The remainders produced by halving (whether the number is odd) become the binary digits, and adding the corresponding right-hand values (which double each time) gives exactly the original product.
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💡 This method got its name because it was passed down among farmers in ancient Russia and Egypt. The way computers perform multiplication internally is based on a similar principle (they calculate everything in binary).