The Real Number Line

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• The Real Number Line

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A picture is worth 1000 words!

• The real number line is a way of giving us a
  picture of the relationships among the real
  numbers

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The origin

• Right in the middle of the number line, we have
  the origin.

0
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Scale

• We have to choose the distance between numbers.
• 2 should be twice as far from 0 as 1 is!

0 1 2
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Positive numbers

• Positive numbers are to the right of zero.

0 1 2
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Negative numbers

• Negative numbers are to the left of zero.

-2 -1 0
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Smaller numbers

• Smaller numbers are to the left on the number
  line.
• -2 is smaller than 0

-2 -1 0
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Magnitude

• The magnitude of a number is just the number
  part without the sign. It tells us how far the
  number is away from zero but not which
  direction it is.
• The magnitude of -2 is 2 because it is 2 steps
  away from zero.

-2 -1 0
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Magnitude

• As negative numbers get smaller and smaller,
  their magnitude increases!
• -500 is smaller than -1
• Things are backwards in the negatives!

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Inequality symbols

• lt means less than
• it looks like a tilted L (for less)

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Inequality symbols

• gt means greater than
• (it doesnt look like a tilted G )

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Inserting Inequality symbols

• If you have two numbers and you need to insert an
  inequality symbol, pretend its an alligator!
• -2 ? 5
• The alligator always has his mouth open toward
  the larger pile of cookies!
• -2 lt 5

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Comparing 2 negatives

• If the numbers that they give you are not in the
  order that they would be on the number line,
  sometimes its easier to draw the number line to
  figure out the answer.
• -20 ? -45

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-20
-45
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Comparing 2 negatives

• Remember, smaller numbers are always to the left
  on the number line!
• The number farther to the left would be -45, so
  the bigger pile of cookies would be the -20!
• -20 gt -45

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Vocabulary
Number line Origin Scale Magnitude Inequalities