Operations with Signed Numbers
Before using the basic rules of algebra to solve for variables, it is essential to know how to
perform the four operations, addition, subtraction, multiplication, and division, with positive and
negative numbers. Positive numbers are those to the right of zero on the number line. Negative
numbers have values less than zero and are found to the left of zero on the number line.
negative positive
… -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 …
Remember, the number line is a representation of all numbers even though there is not enough
space to write all of the whole numbers, fractions, decimals, etc. They are all theoretically sitting
in their proper place on the number line. Also, the number line is infinite. It extends in both
directions with no end.
Practice this exercise to review your understanding of the number line. Answers are on page 21.
negative positive
… -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 …
On the number line above:
a. circle zero f. draw a triangle around 10
b. draw a box around -8 g. add 7 3/4 in the correct place
c. add 4.5 in the correct place h. add the next whole number to the left and right
d. put a star above -2 i. add - 2 1/2 in the correct place
e. add -1/2 in the correct place j. shade +9
There are special rules to add, subtract, multiply, and divide signed numbers. These rules are not
difficult, but you must be able to perform these operations with confidence in order to succeed in
algebra.
When solving algebraic equations, you must be able to move terms from one side of the equals
sign to the other in order to isolate variables. In order to move terms, you will make use of the
rules for operations with signed numbers. You will also be using inverse operations as well.
Inverse operations are the opposite operations. Addition and subtraction are opposites, and
multiplication and division are opposites. Later you will learn to eliminate terms using inverse
operations.
However, before we follow the basic rules of algebra to solve equations, we must practice using
the rules for operations with positive and negative numbers. Different math books explain the
rules in slightly different ways, but the result is always the same. Read and practice the rules for
each of the four operations, addition, subtraction, multiplication and division. When you find you
are comfortable with these methods, then you will be ready for the basic rules of algebra.