Lesson 1-1 Real Numbers and Operations

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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

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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.
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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
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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!
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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