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Adding Real Numbers (2.2)

Adding Real Numbers (2.2). Properties of Addition. Commutative Property – changing the order of numbers being added does not change the sum. EX. 3 + (-2) = (-2) + 3 Associative Property – Grouping does not change the sum when adding. EX. (-5 + 6) + 2 = -5 + (6 + 2).

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Adding Real Numbers (2.2)

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  1. Adding Real Numbers (2.2)

  2. Properties of Addition • Commutative Property – changing the order of numbers being added does not change the sum. • EX. 3 + (-2) = (-2) + 3 • Associative Property – Grouping does not change the sum when adding. • EX. (-5 + 6) + 2 = -5 + (6 + 2)

  3. Properties of Addition (cont.) • Identity Property – The sum of a number and 0 is the number. • EX. - 4 + 0 = - 4 • Inverse Property – The sum of a number and its opposite is zero. • EX. 5 + (-5) = 0

  4. What are Opposites? • Two integers the same distance from the origin, but on different sides of zero • Every positive integer has a negative integer an equal distance from the origin • Example: The opposite of 6 is -6 • Example: The opposite of -2 is 2

  5. Practice With Opposites Opposite of -13 Opposite of 6 Opposite of -67 Opposite of 52

  6. What is Absolute Value? • Distance a number is from zero on a number line (always a positive number) • Indicated by two vertical lines | | • Every number has an absolute value • Opposites have the same absolute values since they are the same distance from zero • Example: |-8| = 8 and |8| = 8 • Example: |50| = 50 and |-50| = 50

  7. Practice With Absolute Value |12| = |-95| = |-17| = |1/2| = |10| = |0| =

  8. Adding Rules – Same Signs • If the numbers have the SAMEsigns: ADD the numbers & keep the same sign! • Positive + Positive = Positive Answer • Negative + Negative = Negative Answer • Examples: -3 + (-10) = -13 • 6 + (8) = 14

  9. Adding (Same Signs) - Examples • - 15 + (-12) = • -8 + (-9) + (-2) =

  10. Adding (Same Signs) - Examples • 3) (-3.5) + (-2) = • 4) -2 + (-3.4) + (-2.1) =

  11. Adding Rules – Different Signs • If the numbers have the DIFFERENT signs: SUBTRACT the numbers & use sign of the BIGGERnumber! • Bigger # is Positive = Positive Answer • Bigger # is Negative = Negative Answer • Examples: -13 + (7) = -6 • 23 + (-8) = 15

  12. Adding (Different Signs) - Examples • 25 + (-17) • 4 + (-8) + 2

  13. Adding (Different Signs) - Examples • 3) (-18.5) + 12 • 4) (-9.2) + 10

  14. Adding (Different Signs) - Examples • -4 + 10 + (-6) • 6) 6.8 + 3.3 + (-4.1)

  15. Notecard Check -10 + 12 9 + (-1.7) 1.5 + (-5.6) + 1

  16. Homework • Pg. 75 • Numbers: 1, 11, 21 – 36.

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