Number and Operations Session 1: What Is a Number System?

Session 1, Part A:
A Simpler Number System

In This Part: Addition in Units Digit Arithmetic | Inverse, Identity, and Closure
Multiplication in Units Digit Arithmetic | Multiplicative Inverse and Identity

Once more, we can look for the identity and inverse elements for multiplication. Remember, we are interested in these elements in order to have a better understanding of the behavior of numbers in a particular number system.

The multiplicative identity element is a number that, when multiplied by any other number in the table, doesn't change its value.

The multiplicative inverse element is a number that, when multiplied by any other number in the table, gives back the identity element.

Problem A10

a.	Find the multiplicative identity element for the multiplication table you created.
b.	Is there one number that works for every number in your table?

Problem A11

a.	Find the multiplicative inverse element for the number 3 in the multiplication table you created.
b.	Find the multiplicative inverse for as many of the numbers in your table as you can.
c.	Separate the elements into two sets -- those with and those without inverses. What similarities and differences can you observe between the two sets?

Video Segment
In this video segment, Kristen and Nancy contemplate the inverse and identity elements for the multiplication table in the finite number system. They notice some interesting patterns, which the whole class then discusses. Watch this segment after you've completed Problems A8-A11.

Can you think of any other sets that are dense?

If you are using a VCR, you can find this segment on the session video approximately 10 minutes and 9 seconds after the Annenberg Media logo.

Next > Part B: Comparing Number Systems

Session 1: Index | Notes | Solutions | Video