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Agenda • Call Roll • Introduce • Class policies & procedures – Syllabus, textbook form, • Student Handbook • Info sheets • Notes • Icebreaker • Assign HW The Essential 55 by Ron Clark • Rule 1: When responding to any adult, you should answer by saying “Yes ma’am” or “No sir.” Notes 1.1 Addition and Subtraction The Real Number System Reals Rationals (fractions, decimals) Integers (…, -1, -2, 0, 1, 2, …) Whole (0, 1, 2, …) Natural (1, 2, …) Irrationals (no fractions) pi, e Rational vs. Irrational Rational numbers CAN be expressed as a fraction. 1 2 9 -2.5 Decimals that end or repeat -9.212121… Irrational numbers CANNOT be expressed as a fraction. 2 -2.569234567… The number line -2.5 -5 -4 -3 -2 1 2 -1 2 0 1 2 3 4 5 Rational or Irrational? 1) 3.12112111211112… Irrational 2) 8.974974974… Rational 3) 4.325 Rational 4) Irrational 17 Rational or Irrational? You Try … 5) 32 Irrational 6) 49 Rational 7) .47646464.. Rational 8) 59 37 Rational 9) 2.573407656631…. Irrational Addition Signs are alike, ADD 10) -5 + (-9) = -14 11) 6 + 20 = 26 Subtraction Signs are different, SUBTRACT 12) 23 + (-11) = 12 13) -12 + 7 = -5 keep the sign of the larger number You Try … 14) 5 – (- 4) =5+4=9 15) 8 – (- 9) = 8 + 9 = 17 16) 23.7 – 5.9 =17.8 17) -12 + (-16) = -28 Adding and Subtracting Fractions 18) 19) 20) 5 1 4 7 3 5 8 6 6 23 5 10 Multiplication If signs are the same, POSITIVE. 1) 5 (10) = 50 2) -6 ( -9) = 54 Multiplication If signs are different, NEGATIVE 3) 6(-7) = -42 4) -4(5) = -20 Multiplying Fractions Multiply across 5) 1 3 2 7 6) 1 2 2 5 7) 6 15 3 24 Commutative Properties •Addition: a + b = b + a •Multiplication: a • b = b • a Associative Properties •Addition: a + (b + c) = (a + b) + c •Multiplication: a • (b • c) = (a • b) • c 5.) Use the commutative property of addition to write an expression equivalent to 3x + 4y 6.) Use the associative property of multiplication. to write an expression equivalent to 3x(7y • 9z) Identity Properties •Addition: a + 0 = a 0 is the additive identity •Multiplication: a • 1 = a 1 is the multiplicative identity The identity property allows us to take an expression and multiply it by 1. x 8 8x = 3 y 8 24 y This is 1. These two expressions are equivalent. 7.) Write an expression equivalent to 6 xy by simplifying. 2x 6 xy 2x 2 3 x y 2 x 2 x 3 y 2 x 1 3y Reciprocal 2 3 3 2 8 1 8 2 3 3 2 =1 8 1 = 1 1 8 Division If signs are alike, POSITIVE. 8) 9) 10 5 = 2 24 4 6 Division If signs are different, NEGATIVE 10) 11) -10 5 = -2 10 1 40 4 Dividing Fractions Multiply by the reciprocal 12) 1 3 4 5 13) 2 4 3 9 14) 12 7 5 15 Zero 7 0 0 7 Homework • Get syllabus signed • Get book covered!!!!! • Get notebook together • Homework: 7-9/ 15-54 mult. of 3, 55-58 all