### MAT 336 Stony Brook University Spring 2004

## 15-minute Quiz, February 20 , 2004

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

- (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.
- Use this method to multiply 43 times 51.

- Explain why this method always works.

- (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*