Multiplication by Doubling and Halving (Mediation & Duplation)
To multiply two numbers by doubling and halving:

How the Doubles Are Chosen  The Odd Halves Match the Powers of 2 Expressing a number as the sum of powers of two is important. The idea of multiple is important.
Because 92 may be expressed as the sum of powers of two, the product of 92 and 45671 may be expressed as the sum of the multiples of 45671 which match the required powers of two. 
Division Yes, division may be completed by repeated subtraction. The following algorithm will also complete division. It may be difficult to find the sum of "doubles." To divide:

Unit Fractions and Negative Powers of Two The Egyptians used unit fractions long before calculus teachers taught students Taylor and McLauren and other power series. They use a third and a fifth and any other unit fraction needed and symbolized it by an open mouth written above the number. The most important fractions were those above. The most famous idea was the one below. 
References

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