**Positive and Negative Numbers ***((Reference))*

*((Reference))*

A number is denoted as *positive* if it is directly preceded by a "

**Opposites ***((Reference))*

*((Reference))*

Opposites are numbers that are the same distance from zero on the number line but have opposite signs.

**Double-Negative Property ***((Reference)) *

*((Reference))*

**Absolute Value (Geometric) ***((Reference))*

*((Reference))*

The absolute value of a number

**Absolute Value (Algebraic) ((Reference))**

**Addition of Signed Numbers ***((Reference))*

*((Reference))*

To add two numbers with*like signs*, add the absolute values of the numbers and associate the common sign with the sum.*unlike signs*, subtract the smaller absolute value from the larger absolute value and associate the sign of the larger absolute value with the difference.

**Addition with 0 ***((Reference))*

*((Reference))*

**Additive Identity ***((Reference))*

*((Reference))*

Since adding 0 to a real number leaves that number unchanged, 0 is called the additive identity.

**Definition of Subtraction ***((Reference)) *

*((Reference))*

**Subtraction of Signed Numbers ***((Reference))*

*((Reference))*

To perform the subtraction

**Multiplication and Division of Signed Numbers ***((Reference))*

*((Reference))*

**Reciprocals ***((Reference))*

*((Reference))*

Two numbers are reciprocals of each other if their product is 1. The numbers 4 and

**Negative Exponents ***((Reference))*

*((Reference))*

If

**Writing a Number in Scientific Notation ***((Reference)) *

*((Reference))*

To write a number in scientific notation:

- Move the decimal point so that there is one nonzero digit to its left.
- Multiply the result by a power of 10 using an exponent whose absolute value is the number of places the decimal point was moved. Make the exponent positive if the decimal point was moved to the left and negative if the decimal point was moved to the right.

**Converting from Scientific Notation:**

positive exponent *((Reference))*

positive exponent

*((Reference))*

To convert a number written in scientific notation to a number in standard form when there is a *positive* exponent as the power of 10, move the decimal point to the *right* the number of places prescribed by the exponent on the 10.

**Negative Exponent ***((Reference))*

*((Reference))*

To convert a number written in scientific notation to a number in standard form when there is a *negative* exponent as the power of 10, move the decimal point to the *left* the number of places prescribed by the exponent on the 10.

Comments:"Reviewer's Comments: 'I recommend this book for courses in elementary algebra. The chapters are fairly clear and comprehensible, making them quite readable. The authors do a particularly nice job […]"