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Objective

Objective. SWBAT review Chapter 2 concepts for Mid-Term. “Real Numbers”. Real Numbers. Rational Numbers. Rational Numbers numbers that can represented as a ratio or fraction. Integers. Integers -3,-2,-1, 0,1,2,3…. Whole Numbers. Whole Numbers 0,1,2,3,4,5…. Key Vocabulary.

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Objective

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  1. Objective • SWBAT review Chapter 2 concepts for Mid-Term

  2. “Real Numbers” Real Numbers Rational Numbers Rational Numbers numbers that can represented as a ratio or fraction Integers Integers -3,-2,-1, 0,1,2,3… Whole Numbers Whole Numbers 0,1,2,3,4,5…

  3. Key Vocabulary • OPPOSITES • Two numbers that are the same distance from ZERO. -5 -4 -3 -2 -1 0 1 2 3 4 5 negative zero positive Opposite of -3 = 3 What is the opposite of -3? What is the opposite of x - 3? Opposite of x-3 = -x + 3

  4. Key Vocabulary • ABSOLUTE VALUE • The distance a number is away from ZERO. Distance is always positive. -5 -4 -3 -2 -1 0 1 2 3 4 5 negative zero positive What is the absolute value of -4? or |-4| |-4| = 4 What is -|-4| -|-4| = -4

  5. Properties of Real Numbers 1). Commutative Property 2). Associative Property 3). Identity Property 4). Inverse Property 5). Property of Zero 6). Property of -1

  6. Commutative Property The order of numbers when you add or multiply numbers does not change the solution. (-2) + 3 = 3 + (-2) (a) + (b) = (b) + (a) (-2) ·3=3· (-2) (a) ·(b)=(b) · (a) Think of it as COMMUTING to work!

  7. Associative Property REGROUPING of numbers when adding or multiplying does not change the solution (-2 + 3) + 4 = -2+ (3 +4) (ab)c= a(bc) Think of it as changing your GROUP of friends!

  8. Identity Property “No change” property 5 + 0 = 5 3 x 1 = 3 Think of it as "I" LOOK IN THE MIRROR and see myself! For addition, the sum of any number plus 0 is that number. a + 0 = 0 + a = a For multiplication, the product of any number times 1 is that number. b · 1 = 1b = b

  9. Inverse Property The sum of a number and its opposite is ZERO. 5 + (-5) = 0 (-a) + a = 0 Property of Zero The product of a number and ZERO is ZERO. 5 · 0 = 0 (-a) · 0 = 0

  10. Property of -1 The product of a number and -1 is its opposite. a · (-1) = -a (-1)· 3 = -3 (-x)(-1) = x -(-4) = 4

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