Properties of Real Numbers Math 0099

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Properties of Real NumbersMath 0099

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Opposites

• Two real numbers that are the same distance from
  the origin of the real number line are opposites
  of each other.
• Examples of opposites
• 2 and -2 -100 and 100 and

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Reciprocals

• Two numbers whose product is 1 are reciprocals
  of each other.
• Examples of Reciprocals
• and 5 -3 and

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Absolute Value

• The absolute value of a number is its distance
  from 0 on the number line. The absolute value of
  x is written .
• Examples of absolute value

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Commutative Property of Addition

• a b b a
• When adding two numbers, the order of the
  numbers does not matter.
• Examples of the Commutative Property of Addition
• 2 3 3 2 (-5) 4 4 (-5)

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Commutative Property of Multiplication

• a ? b b ? a
• When multiplying two numbers, the order of the
  numbers does not matter.
• Examples of the Commutative Property of
  Multiplication
• 2 ? 3 3 ? 2 (-3) ? 24 24 ? (-3)

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Associative Property of Addition

• a (b c) (a b) c
• When three numbers are added, it makes no
  difference which two numbers are added first.
• Examples of the Associative Property of Addition
• 2 (3 5) (2 3) 5
• (4 2) 6 4 (2 6)

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Associative Property of Multiplication

• a(bc) (ab)c
• When three numbers are multiplied, it makes no
  difference which two numbers are multiplied
  first.
• Examples of the Associative Property of
  Multiplication
• 2 ? (3 ? 5) (2 ? 3) ? 5
• (4 ? 2) ? 6 4 ? (2 ? 6)

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Distributive Property

• a(b c) ab ac
• Multiplication distributes over addition.
• Examples of the Distributive Property
• 2 (3 5) (2 ? 3) (2 ? 5)
• (4 2) ? 6 (4 ? 6) (2 ? 6)

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Additive Identity Property

• The additive identity property states that if 0
  is added to a number, the result is that number.
• Example 3 0 0 3 3

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Multiplicative Identity Property

• The multiplicative identity property states that
  if a number is multiplied by 1, the result is
  that number.
• Example 5 ? 1 1 ? 5 5

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Additive Inverse Property

• The additive inverse property states that
  opposites add to zero.
• 7 (-7) 0 and -4 4 0

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Multiplicative Inverse Property

• The multiplicative inverse property states that
  reciprocals multiply to 1.

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Identify which property that justifies each of
the following.

• 4 ? (8 ? 2) (4 ? 8) ? 2

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Identify which property that justifies each of
the following.

• 4 ? (8 ? 2) (4 ? 8) ? 2
• Associative Property of Multiplication

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Identify which property that justifies each of
the following.

• 6 8 8 6

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Identify which property that justifies each of
the following.

• 6 8 8 6
• Commutative Property of Addition

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Identify which property that justifies each of
the following.

• 12 0 12

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Identify which property that justifies each of
the following.

• 12 0 12
• Additive Identity Property

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Identify which property that justifies each of
the following.

• 5(2 9) (5 ? 2) (5 ? 9)

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Identify which property that justifies each of
the following.

• 5(2 9) (5 ? 2) (5 ? 9)
• Distributive Property

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Identify which property that justifies each of
the following.

• 5 (2 8) (5 2) 8

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Identify which property that justifies each of
the following.

• 5 (2 8) (5 2) 8
• Associative Property of Addition

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Identify which property that justifies each of
the following.

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Identify which property that justifies each of
the following.

• Multiplicative Inverse Property

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Identify which property that justifies each of
the following.

• 5 ? 24 24 ? 5

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Identify which property that justifies each of
the following.

• 5 ? 24 24 ? 5
• Commutative Property of Multiplication

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Identify which property that justifies each of
the following.

• 18 -18 0

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Identify which property that justifies each of
the following.

• 18 -18 0
• Additive Inverse Property

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Identify which property that justifies each of
the following.

• -34 ??1 -34

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Identify which property that justifies each of
the following.

• -34 ??1 -34
• Multiplicative Identity Property

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Least Common Denominator

• The least common denominator (LCD) is the
  smallest number divisible by all the
  denominators.
• Example The LCD of is 12 because
  12 is the smallest number into which 3 and 4 will
  both divide.

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Adding Two Fractions

• To add two fractions you must first find the
  LCD. In the problem below the LCD is 12. Then
  rewrite the two addends as equivalent expressions
  with the LCD. Then add the numerators and keep
  the denominator.