MAT 300                                 Homework Sheet 2

Spring 2004

 

 

Assignment 5

1.         Express the following numbers in Babylonian cuneiform notation.

a.         1000

b.         1234

c.         12,345

2.         Translate each of the following numbers into our system.  Note that the answers are not unique due to the deficiencies in the Babylonian positional system.  I will use < for 10 and | for 1.

a.        

<<<	||||	<<	|||
<	|||		||

b.        

<<<	<<	|||||	<  |||
		|||

 

 

 

3.         Our base-60 notation is called sexagesimal notation.  Expressing your answer in sexagesimal notation,
 add  the sexagesimal numbers   30, 22, 16 and  15, 56, 18 .

 

 

Assignment 6

1.                  Use the Egyptian method of doubling to find the following products:

a.                   18 × 25

b.                  26 × 33

c.                   85 × 21

d.                  105 × 59

 

2.                  Use the Egyptian method to find the following quotients.  If the quotient is not exact, express the fractional part in terms of a sum of unit fractions.

a.                   184 ÷ 8

b.                  1059 ÷ 12

c.                   61 ÷ 8

 

3.                  p. 25-26 in the text
3, 11

 

4.                  This problem should be done by everyone, but we will not go over it until Thursday, February 12.  Students in MAT 300-01 should write up a solution for the problem and submit it at the beginning of class on Thursday, February 12.
p. 25 in the text
2     (Hint:  This falls outside the families of fractions that we discussed using in division problems in class.  Near the end, you will need to divide both sides of  the line  1     5   by 10  to get  .)  If  you have trouble, hold off on doing it and I will do it in class after the students in Section 01 turn in the problem.