Directions:  Answers should be neatly handwritten or typed, on one side of the page only.  Please cut off any messy edges and staple the pages together.  Show your work in detail--answers that are unsupported by work will not receive credit.  The essay should be typed and double-spaced.

1. Find the product 135 x 209
1. using Egyptian multiplication
2. using gelosia multiplication
3. using vedic multiplication
2. What do the diagonals in gelosia multiplication represent?
3. In your own words, state the distributive law.
1. Explain how the distributive law is used in Egyptian multiplication.  Give an example.
2. Explain how the distributive law is used in vedic multiplication.  Give an example.
4. In order to learn multiplication, children in our culture have to memorize the times table from 1x1 through 9x9 and understand how to multiply by 0 and powers of 10.  Once you have done that, the distributive law does the rest.
1. If you were living in a culture that used a base 20 positional system (like the Mayans did), how large a times table would you have to memorize?
2. If you were living in a culture that used a base 60 positional system (like the Babylonians did), how large a times table would you (theoretically) have to memorize?  Do you think the Babylonians really did this?  (Hint:  think about the archaeological evidence we have seen on Babylonian multiplication.)
5. Divisors
1. Write all the divisors of 6.
2. Find the greatest common divisor (GCD) of 18 and 12.
3. Write all the numbers that divide both 18 and 12.
4. Two numbers are called relatively prime if their GCD is 1.  Which of the following pairs of numbers are relatively prime?
1. 9 and 21
2. 4 and 17
3. 1 and 100
4. 1 and any number
5. any even number and any odd number
5. A number is called prime if it is greater than 1 and its only divisors are itself and 1.  For example, 5 is prime because its only divisors and 5 and 1, but 6 is not prime because 2 divides 6.
1. Explain why 11 is prime.
2. Explain why 24 is not prime.
3. Explain why 2 is prime.
4. Explain why every even number except 2 is not prime.
6. Essay Type your answer double-spaced.  This should be 2-3 pages.

We have seen several examples of how religion and superstition have influenced developments in mathematics in many (and, indeed, most) cultures.  Using examples from the course packet (p. 32-181), class discussions and handouts, and, if you wish, from outside sources, develop several examples of this phenomenon. You can either choose one culture and discuss mathematical ideas in that culture's religion, or choose a mathematical topic and trace it through several cultures and religions.