SIGNED NUMBER OPERATIONS & SIMPLIFYING ALGEBRAIC EXPRESSIONS

Positive numbers are the result of any measurement - in length, weight, volume, loudness, etc.
Negative numbers are the result of any measuring process in which a certain zero point is reached. For
example, a temperature of -10 is 10 units below zero. We can record positive and negative numbers
easily by setting up a number line.

Signed numbers are positive (+4 or 4) or negative (-4) and have two parts : magnitude (in this case, 4) and
direction (positive or negative.) All numbers to the right of zero on the number line are positive; all
numbers to the left are negative. Operations with signed numbers can be represented by movement on
the number line.

Objective: to learn how to add, subtract, multiply and divide signed numbers. There are several
different ways to approach calculations using positive and negative numbers . Two, rather different
approaches are presented below. Please feel free to try them both and use the one that works best for
you.

METHOD #1

Use this series of questions to apply computation rules to signed number operations with TWO SIGNED
NUMBERS. (See note above for hints about operations with more than 2 numbers.)

Question: What operation am I being asked to perform?
Go to the rules for that operation.

MULTIPLICATION & DIVISION
Question: First, look at the signs for the numbers. Are the signs alike? If so, your answer will be
positive. In multiplication and division of signed numbers, like signs = a positive result. Are
the signs different? If so, your answer will be negative. Different signs = a negative result.

Rule: Multiply or divide the digits and apply the proper sign to the answer.

ADDITION
Question: First look at the signs for the numbers. Are the signs alike? ...different?

Rule: If signs are alike, add the digits, keep the same sign in your answer. If the signs are
different, subtract the smaller digit from the larger digit, use the sign of the larger for
your answer.

SUBTRACTION
Rule: Rewrite all subtraction problems as equivalent addition problems by adding the opposite.

a - b = a + (-b)

This phrase says "positive a minus positive b equals positive a plus negative b". Then
follow the rules for addition of signed numbers.

Examples:

METHOD #2

ADDITION & SUBTRACTION

STEP 1: Always simplify your work by removing as many "extra" signs as possible. Replace any
number in the form -(-n) with +n or simply n. Replace any number in the form of +(-n) or -(+n)
with -n.

-(-8) = +8 or 8

+(-2) or -(+2) = -2

STEP 2: If two numbers that you are combining (adding or subtracting) have the same sign, find
the sum and apply that same sign to your answer

STEP 3: If the two numbers you are combining have different signs, find the difference between
the two numbers and apply the sign of the larger number to your answer.

+8 - 2 = +6 or 6

-8 -(-2) = -8 + 2 = -6

MULTIPLICATION & DIVISION

RULE: For any two numbers that you are multiplying or dividing with the same sign, the result will
always be positive. For any two numbers that you're multiplying or dividing with opposite signs, the result
will always be negative.

NOTE: Any odd number of negative terms, multiplied or divided, will result in a negative answer. Any
even number of negative terms, multiplied or divided, will result in a positive answer

PRACTICE: Perform the indicated operations.

Multiply or divide the following.

ANSWERS:

SOLVING FOR GIVEN VALUES

Using what you know about operations with signed numbers and order of operations , evaluate the
following algebraic expressions for the given values . Here’s an example to get you started.

If x = -9, z = 3, and c = -2, what is 4x - c ?
 

PRACTICE:

1) If a = 3 and b = -2, what is b² - 3ab ?

2) If a = -4 and b = 6, what is ?

3) If a = -2, b = 6, and c = -4, what is 4a - c ?

4) If a = -2, b = 6, and c = -4, what is 5c² ?

5) If a = -2, b = 6, and c = -4, what is 6 (2b - 3c)?

6) If x = 4 and y = -2, what is 2y - 4?

7) If x = 4 and y = -2, what is 3x² - 2x + 4?

8) If x = 4 and y = -2, what is ?
9) If a = -2, b = 6, and c = -4, what is ?
10) If x = 4 and y = -2, what is ?

Answers:

SIMPLIFYING ALGEBRAIC EXPRESSIONS WITH UNKNOWN VALUES

In the previous exercise you evaluated algebraic expressions for given values. Now you will use what
you know about order of operations, signed numbers and variable terms to practice simplifying algebraic
expressions with unknown values. This is merely a practice page. You should learn about combining
like terms and expanding parentheses in your NovaNET lessons first.

Answers: