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

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

Write an equivalent expression without using absolute value bars

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

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

Rational Exponents

Perform each operation mentally

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.

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.

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.