Rational Numbers

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Rational Numbers

• Lesson 6.6

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Rational Number

• A rational number is a number that can be written
  as a where a and b are integers.
• b
• b CANNOT be 0!!!!!

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Venn Diagram

• The Venn diagram on the next page shows the
  relationship among rational numbers, integers,
  and whole numbers. Notice that integers include
  whole numbers and rational numbers include
  integers.

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Identifying Rational Numbers

• Example 1

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Identifying Rational Numbers

• You can identify as a rational number by writing
  it as a fraction. Or in a form.
• b
• Example 6 6, so it is rational.
• 1

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Identifying Rational Numbers

• The negative sign in a fraction can be placed in
  front of the fraction bar, in the numerator, of
  in the denominator.
• Example -5, and 5 are the same number.
• 6 -6

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Identifying Rational Numbers

• Examples
• -3 3 C. -2 1 -7
• 5 -5 3 3
• 0.75 3
• 4

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Identifying Rational Numbers

• Copy and solve these problems in your notes.
  Show that they are rational by writing them in
  fraction form.
• 1.) 0.4 3.) -7
• 9
• 2.) -3 5 4.) -12
• 8

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Ordering Rational Numbers

• Order -1, -1.6, 2, -1 1, and -3 from least to
• 5 4 8
• greatest.
• Place the numbers on a number line to order.

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Ordering Rational Numbers

• From least to greatest, the numbers are
• -1.6, -1 1, -1, -3 , 2
• 4 8 5

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Ordering Rational Numbers

• Copy and solve these problems in your notes.
  Order the numbers from least to greatest.
• Hint Change each number to a fraction. It will
  be much easier to order these numbers if they are
  in the same form.

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Ordering Rational Numbers

• 1.) 2.5, -1, -5, -0.8
• 8
• 2.) 4 1, -3.6, 0, -3 8
• 5 9

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Commutative and Associative Properties

• The commutative and associative properties can
  help you add or multiply rational numbers.

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Commutative Properties

• Commutative Property of Addition in a sum, you
  can add terms in any order.
• Example 5 (-6) (-6) 5
• Commutative Property of Multiplication in a
  product, you can multiply factors in any order.
• Example 4(-7) -7(4)

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Associative Properties

• Associative Property of Addition Changing the
  grouping of terms will not change the sum.
• Example (9 8) 6 9 (8 6)

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Associative Properties

• Associative Property of Multiplication Changing
  the grouping of factors will not change the
  product.
• Example (2 3) 4 2 (3 4)

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Inverse and Identity Properties

• The inverse and identity properties help you use
  mental math to evaluate expressions.

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Inverse Properties

• Inverse Property of Addition The sum of a
  number and its additive inverse, or opposite, is
  0.
• Example 5 (-5) 0

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Inverse Properties

• Inverse Property of Multiplication The product
  of a nonzero number and its multiplicative
  inverse, or reciprocal, is 1.
• Example 3 4 1
• 4 3

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Identity Properties

• Identity Property of Addition The sum of a
  number and the additive identity, 0, is the
  number.
• Example -7 0 -7

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Identity Properties

• Identity Property of Multiplication The product
  of a number and the multiplicative identity, 1,
  is the number.
• Example 9 1 9