Proper fractions

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Proper fractions

• The value of the numerator is less than the value
  of the denominator.
• Proper in this case does not mean correct or best.

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Improper fractions

• The value of the numerator is greater than or
  equal to the value of the denominator.

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Exploration 5.12

• Drawn to scale
• Part 1 Use reasoning not algorithms to answer 1
• Part 2 Use reasoning to answer 1 and 2

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Mixed numbers

• Meaning of

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Writing mixed numbers as improper fractions

• The algorithm that is taught in schools obscures
  the meaning. This is true for many algorithms,
  which are efficient ways of carrying out
  operations.

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Write mixed number as improper fraction and vice
versa
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Adding and subtracting fractions
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1/2 1/3
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Multiplying fractions

• Repeated addition model
• Area model

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Multiplication of fractions

• Fraction as operator
• The multiplication algorithm is best explained by
  the area model.

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2/3 of 2 1/2
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Mixed number times mixed number
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Dividing fractions

• Division of fractions is most easily understood
  as repeated subtraction.

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11 divided by 1 1/2
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Multiplicative inverses

• The multiplicative inverse of a is 1/a

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Dividing fractions

• Because division is the inverse operation of
  multiplication, dividing a number by a fraction
  is equivalent to multiplying the number by the
  multiplicative inverse, called the reciprocal, of
  the fraction.

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Explorations 5.13 and 5.14

• 5.13 In Class Part 1, 2, 3
• For HW 4-7 and Part 2, 1
• 5.14 1-5