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Properties of Real Numbers

Properties of Real Numbers. TYPES OF NUMBERS. RATIONALS. IRRATIONAL. INTEGERS. WHOLES. NATURALS. NATURAL  5, 3, 1, 700, 26 … positives, no fractions WHOLE  0, 1, 1052, 711, … naturals and 0 INTEGERS  -4, -20, 0, 2, 78 … number line

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Properties of Real Numbers

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  1. Properties of Real Numbers

  2. TYPES OF NUMBERS RATIONALS IRRATIONAL INTEGERS WHOLES NATURALS NATURAL  5, 3, 1, 700, 26 … positives, no fractions WHOLE  0, 1, 1052, 711, … naturals and 0 INTEGERS  -4, -20, 0, 2, 78 … number line RATIONALS  6.2, 1/2, 0, 3.628, -2/3… integers with fractions IRRATIONALS  √2, -√5, ∏… non-terminating decimals (no repeats)

  3. EX - Types -2  -8/5  ∏  9.4421  √7  • Rationals, integers • Rational • Irrational • Rational • Irrational

  4. Graphing Numbers on a Number line 0

  5. More Vocabulary . . . • Opposite or Additive Inverses • A positive and a negative • Ex: a and –a -10 and 10

  6. More Vocabulary . . . • Reciprocals or Multiplicative Inverses • Flip the number and multiply by a negative • Ex: 2 and – 1/2 • -2/3 and 3/2

  7. PROPERTIES COMMUTATIVE ASSOCIATIVE IDENTITY  INVERSE  DISTRIBUTIVE  a+b=b+a or a∙b=b·a a+(b+c) = (a+b)+c a ∙ (b ∙ c) = (a ∙ b) ∙ c a+0=a a ∙1=a a+-a = 0 a ∙(1/a) = 1 a(b + c) = ab + ac

  8. Absolute Value • Absolute Value is the distance away from zero on a number line 0

  9. Practice finding the absolute value

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