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Lesson 1-1 Real Numbers and Operations

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Lesson 1-1 Real Numbers and Operations Objectives: 8N2, 7N6, 9N2 (Do not write) Show that a number is rational and distinguish between rational and irrational numbers – PowerPoint PPT presentation

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Title: Lesson 1-1 Real Numbers and Operations


1
Lesson 1-1Real Numbers and Operations
  • Objectives 8N2, 7N6, 9N2
  • (Do not write)
  • Show that a number is rational and distinguish
    between
  • rational and irrational numbers
  • Add positive and negative numbers
  • Subtractive positive and negative numbers

2
Real Numbers The set of numbers consisting of
all points on the number line.
  • Subset of the Real Numbers
  • Natural Numbers ? 1, 2, 3, 4,
  • Whole Numbers ? 0, 1, 2, 3, 4,
  • Integers ? ,-3, -2, -1, 0, 1, 2, 3,
  • Rational Numbers
  • A ratio of integers ? , b 0

Set up 3 ratios of integers. Show their decimal
equivalents.
Rational decimals make sense they end
or repeat.
3
Irrational Numbers a subset of real numbers
that are not rational
Examples
Caution! Not all square roots are irrational.
Irrational decimals do not make sense! Never
end or repeat
Real Numbers Fill in 3 examples for each area
4
Operations with Real Numbers
Absolute Value the distance a number is from 0
Absolute value is never negative (just like
distance!)
Additive Inverse For every real number, a,
there is a number, b such that a b 0 ( b
-a additive inverse means opposite!)
Subtraction Theorem For all real numbers, a
b a (-b)
This is important in realizing that in the
expressions a b the b number is actually a
negative!
5
Examples
Evaluate.
Rational or Irrational?
4) -11 7
1)
5) -14 23
2) 0.315215
Show common denominators
6)
3)
7) -18.73 4.11
Solutions
  1. Irrational
  2. Rational
  3. Rational
  1. -4
  2. -37
  3. 13/10 or 1.3
  4. -14.62
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