Lesson #6Addition, Subtraction, Multiplication and Division of Signed Numbers p Absolute Value -the distance a number is from zero, regardless of the direction. |5| = 5 |-7| = 7 ADDITION OF SIGNED NUMBERS p Addition of Two Positive Numbers Keep the sign and combine Addition of Two Negative Numbers Keep the sign and combine

Addition of a Positive and a Negative Number Take the sign of the number farther from zero (largest absolute valve), and take the difference between the numbers absolute values. SUBTRACTION OF SIGNED NUMBERS p To subtract one sign number from another, add the opposite of the subtrahend to the minuend. Examples: (+9) - (+4) = to (+9) + (-4) = (-8) - (-3) = to (-8) + (+3) = (+7) - (-2) = to (+7) + (+2) = (-6) - (+1) = to (-6) + (-1) = (- x) - (- x) = - x + x = 0 (x) - (x - 5) = x + (- x) + 5 = 5

Uses of the Symbol (-) To indicate that a number is negative: -6 -> negative 6 To indicate the opposite of the number: -(-5) -> opposite of negative 5 -x -> the opposite of x To indicate subtraction: 9 - (-7) -> the difference between 9 and -7

MULTIPLICATION AND DIVISION OF SIGNED NUMBERS p Same Signs if the signs are the same when you multiply or divide two numbers, the answer is always positive. Different Signs - if the signs of two numbers are different when multiplying or dividing them, the sign of the answer is always negative.

Properties of Signed Numbers - Closure - Commutative - Associative - Distributive - Multiplication Property of One - Multiplication Property of Zero - Multiplication Property of Negative One a * (-1) = -a and (-1) * a = -a - Dividing Zero by a Nonzero Number 0/a = 0 -Dividing by Zero is Undefined a/0 = undefined a - Multiplicative Inverse (a)(1/a) = 1