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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.
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