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5-2 Rules for Adding Positive and Negative Numbers Objective: 1 Add positive and negative numbers 2 Calculate absolute value 3 Recognize uses of the commutative and associative properties of addition and the addition property of equality 4 Calculate magnitude of turns given angle measures or revolutions Review: Rules for Adding Positive and Negative Numbers. If the signs are the same – add the numbers together and keep the same sign. EX: -8 + -14 = 8 + 14 = 22 so the answer would be -22 because both numbers are negative. If the signs are different – subtract the number with the larger absolute value by the smaller absolute value and take the sign of the number with the larger absolute value. EX: -4 + 19 = 19 – 4 = 15, so the answer would be 15 because 19 has the larger absolute value and it is positive. EX: -35 + 11 = 35 – 11 = 24 so the answer would be -24 because -35 has the larger absolute value and it is negative. Absolute value – written |n| is the distance between 0 and n on a number line. Since distance is never negative, absolute values are never negative. Absolute value bars act like parentheses, everything inside must be worked out down to a single number before the absolute value can be taken. Ex: |-5 + 2| = |-3| = 3 2 + |5 – 8| = 2 + |-3| = 2 + 3 = 5 Associative Property of Addition – for any numbers a, b and c, (a + b) + c = a + (b + c) = a + b + c If problem is all adding, changing the grouping does not change the result. Ex: (3 + 5) + 8 = 3 + (5 + 8) Rotation – the turn of a figure in a plane around a point called its center. Magnitude – measures how much a figure has turned and in what direction. Clockwise - negative magnitude Counterclockwise – positive magnitude Revolution – one full turn (360) around the center. Fundamental Property of Rotations – if a rotation of measure x is followed by a rotation of measure y, the result is a rotation of measure x + y. Ex: Karen turned the Lazy Susan in her kitchen 80 clockwise and then 35 counterclockwise, what was the net result? -80 + 35 = -45 or 45 clockwise.