M326K
Sample Writeups for Select Problems:
Class Activities Handout 1
Problem 1
Make sure you are ready to explain how you determined each entry in the table. (“I did
the same thing as in the example. ” is not sufficient explanation although I have to admit
that sometimes, “Just follow the example.” seems to have the desired effect on a student.)
For example, you might say
To find 6
⊕
8, I first find 6 + 8 using the usual addition, then find the units digit
of 6 + 8.
Since 6 + 8 = 14 and the units digit of 14 is 4, I can conclude that
6
⊕
8 = 4.
If that seems a bit too wordy, another option might be:
6 + 8 = 14
The units digit of 14 is 4.
Therefore, 6
⊕
8 = 4.
Problem 3
a.) This problem asked for an algebraic definition of an
additive identity
of a number number.
In class, we have concluded that:
•
We need an equation that expresses the idea that an additive identity of a number
system is a number in the number system that when any other number is added to
that number, it does not change the value of that other number.
•
All the variables must be properly declared.
(That is, clearly explain exactly what
each of the variables represent.)
•
In this particular case, we need to make clear that an additive identity is a num
ber/object in the given number system, and the other number we are adding it to is
another (possibly same) number/object in the same number system.
Here are some sample definitions:
(Definition 1) A number
b
in a number system is an
additive identity
if
a
+
b
=
a
for every
number
a
in the same number system. (Note: you need to explain for which number(s)
a
is
the equation supposed to hold.)
(Definition 2) If
x
is an object in the number system such that
x
+
y
=
y
for all objects
y
in
the same number system, then
x
is an
additive identity
in the number system.
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 Spring '08
 Harper
 Addition, Additive Identity

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