Chapter 6.1, Problem 65ES

Egyptian Multiplication, The Rhind papyrus contains problems that show a doubling procedure used by the Egyptians to find the product of two whole numbers. The following examples illustrate this doubling procedure. In the examples, we have used Hindu-Arabic numerals so that you can concentrate on the doubling procedure and not be distracted by the Egyptian hieroglyphics. The first example determines the product $5\times 27$ by computing two successive doublings of 27 and then forming the sum of the blue numbers in the rows marked with a check. Note that the rows marked with a check show that one 27 is 27 and four 27s is 108. Thus five 27s is the sum of 27 and 108, or 135.

In the next example, we use the Egyptian doubling procedure to find the product of 35 and 94. Because the sum of 1, 2, and 32 is 35, we add only the blue numbers in the rows marked with a check to find that $35\times 94=94+188+3008=3290.$

Use the Egyptian doubling procedure to find each product.

$7\times 29$