1. Real Numbers and Their Properties
Unit #1
Real Numbers and Their Properties

2. Properties of Order Trichotomy Property Transitive Property
For all real numbers a, b, and c
Trichotomy Property
Either a < b, a > b, or a = b
Transitive Property
If a < b and b < c, then a < c
Addition Property
If a < b, then a + c < b + c
Multiplication Property
If a < b, and if, c > 0, then ac < bc
If a < b, and if, c < 0, then ac > bc

3. Write an equivalent expression without using absolute value bars

4. Properties of Absolute Value
For all real numbers a and b
Triangle Inequality Property

5. Properties of Exponents
Let m and n be rational numbers.
The results are valid for all positive numbers a and b.

6. Rational Exponents

7. Perform each operation mentally

8. Perform the indicated operations
Perform the indicated operations. Write the answer using only positive exponents. Assume that all variables represent positive real numbers and that variables used as exponents represent rational numbers.

9. Perform the indicated operations
Perform the indicated operations. Write the answer using only positive exponents. Assume that all variables represent positive real numbers and that variables used as exponents represent rational numbers.

10. Perform the indicated operations
Perform the indicated operations. Write the answer using only positive exponents. Assume that all variables represent positive real numbers and that variables used as exponents represent rational numbers.