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Learning Math Home
Patterns, Functions, and Algebra
 
Session 1 Part A Part B Part C Homework
 
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Session 1 Materials:
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Session 1:
Homework

Think back to the finite system of units digits that you explored in Part A and answer the following questions about that system.

Problem H1

Solution  

a. 

The commutative law for multiplication states that (a • b) = (b • a). Does this law hold for the finite number system in your table? Why or why not?

b. 

The associative law for multiplication states that (a • b) • c = a • (b • c). Does this law hold for the finite number system in your table? Why or why not?


 

Problem H2

Solution  

a. 

How could you use the multiplication table you created to divide?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Think of division as a way of undoing multiplication. For example, to find y divided by x, think, "x times what number equals y?"    Close Tip

 
 

b. 

Does this finite system allow you to divide any two numbers in the system, or are there limits?


 

Problem H3

Solution  

Is this finite set closed under the operation of multiplication?


 

Problem H4

Solution  

The distributive law of multiplication over addition says that a • (b + c) = (a • b) + (a • c). Does the distributive law work for the finite system? Why or why not?


 

Problem H5

Solution  

Is it possible to categorize numbers as even or odd in the finite system? Why or why not?


 

Problem H6

Solution  

In the finite system, which numbers are multiples of 3? Which are multiples of 4? Of 5? How do you know?


 

Problem H7

Solution  

Which numbers are perfect squares (i.e., a product of a number multiplied by itself) in the finite system? How do you know?


 

Problem H8

Solution  

In the real number system, if you multiply two numbers and you get 0, what can you conclude about these two numbers? Does the same apply in the finite number system?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Think about a • b = 0, with, for example, a = 5.   Close Tip

Take it Further

Problem H9

Solution

You have determined the length of on the number line. Can you determine the length of on the number line?


 

Suggested Readings:

Read these excerpts from the following book:
Seife, Charles (2000). Zero: The Biography of a Dangerous Idea (pp. 6, 12-21).
Reproduced with permission from Viking Penguin. © 2000 by Charles Seife. All rights reserved.

Download PDF File:
Zero: The Biography of a Dangerous Idea


Next > Session 2: Number Sets, Infinity, and Zero

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