Operations on Real Numbers
Double Negative Signs
A negative of a negative is a positive, for example
(7) = 7
and in general
Addition Involving Positive and Negative Numbers
To add two negative numbers add then without the negatives and placing a
negative in front of the answer. To subtract two numbers when one is
positive and the other is negative, subtract the smaller from the larger and
if the larger is negative, the result is also negative. To subtract
two negative numbers, just recall that minus a negative is the same as a
plus.
Some Useful Rules of Addition and
Subtraction
 a + (b) = (a + b)
 a  b = (b  a)
 a  (b) = a + b

Algebraic Examples

3 + 2 : 3  2 = 1
since 3 > 2 the answer is
1.

4 + 10: 10  4 = 6
since 10 > 4 the answer is
6.

3  2: same sign so that 3 + 2 =
5, since they are both negative the
answer is 5.

1  10 = 11.

4  6 : 6  4 = 2 since
6 > 4 the answer is
2.
Multiplication and Division
Multiplication and Division Rules:

An even number of negatives gives a positive.

An odd number of negatives gives a negative.

We can never divide by
0.

0/(non zero) = 0.

(a)/b = a/(b) = (a/b) (The negative sign can be
placed on the numerator, the denominator or to the left.)

Examples
(3)(6) =
18, (4)(8) = 32
12
0
7
= 3
= 0
=
undefined
4
10
0
Exercises: Simplify (Hold the mouse on the yellow rectangle
for the solution).

3 + 4
2

5  (3)
+
4
2

3  4  4

2(4  3)

1 1
+
2
3

2/5  1/3
1/3  1/5

6x
3

(5)(5z)

4(3x + 2)

(x  y)
Applications
Example:
Suppose that you own a casino and want to monitor the average winnings of
your patrons. The four players at your table had the following results:
player 1 won $4, player 2 lost $2, player 3 lost $7
and player 4 broke
even. What was the average earnings?
Solution:
To find the average, we add up all the numbers and divide by 4:
4 + (2) + (7) +
0 2 +
(7) 5
=
=
or $1.25
4
4
4
The average winnings of your patrons was $1.25, hence they lost an average
of $1.25.
Exercise
Suppose your bank balance is $250 and your Visa balance
is $750. What is your net worth?
Back to
Math 152A Home Page
email
Questions and Suggestions
