By the end of this section, you will be able to:
- Locate positive and negative numbers on a number line.
- Compare and order positive and negative numbers using a number line.
- Write the opposite of a given number.
- Use correct notation to indicate the opposite of a number.
- Use correct notation to indicate absolute value and simplify and evaluate expressions that contain absolute value.
- Translate word phrases that contain negative numbers, or opposites.
- Perform arithmetic operations on integers.
- Simplify and evaluate expressions containing integers.
- Use operations on integers in applications.
The focus of this module, graph theory, requires very little prerequisite mathematical understanding. You’ll be expected to be able to perform basic arithmetic operations, but nothing more. Graph theory may seem simple because of this but what it lacks in technical complexity, it makes up for in power, logic, and efficiency. You’ll need to spend a good deal of time working through the examples thoroughly to be able to form new ways of thinking about and visualizing the processes involved. Each page in this module begins with a study tip to help you succeed.
In preparation for this module, you should be familiar with concepts and skills found in previous review sections and with the subject of this review section: the integers, the set of all whole numbers along with their opposites. You’ve seen the rules on how to perform arithmetic operations on signed numbers. In this review sections, you’ll study the integers more deeply. Integers help us to understand the notion of opposition in math and mathematical applications: forward and reverse motion, gains and losses, numbers and their opposites. When we wish to consider something like a loss or a decrease in value as a pure quantity, separate from its negative sign, we use absolute value, which we’ll look briefly at in this review section as well.
Recall for success
Look for red boxes like this one throughout the text. They’ll show up just in time to give helpful reminders of the math you’ll need, right where you’ll need it.