MAT 336 Stony Brook University Spring 2004

15-minute Quiz, February 20 , 2004

Total score = 10 points. Show all your work on this page.

  1. (6 points) Egyptian multiplication of integers works by repeated doubling of the second factor by factors 1, 2, 4, 8, ... until enough powers of 2 are generated to add up to the first factor. Then the corresponding multiples of the second factor are added up to make the product.
    1. Use this method to multiply 43 times 51.

    2. Explain why this method always works.

  2. (4 points) Use the 2/3k algorithm, or the 2/5k algorithm, or another method of your choice, to write 2/108 as a sum of different fractions with numerator 1. The algorithms are: 2/n = 1/2n + 3/2n and 2/n = 1/3n + 5/3n