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Multiplying and Dividing Fractions

6.3 Multiplying and Dividing Fractions
  6.3.1. Modeling multiplication of fractions
    6.3.1.1. Repeated addition can be used when we have a whole number times a rational
number:
    6.3.1.2. Joining of equal-sized groups can be used when we have a mixed number times
a rational number :see figure 6.12, p. 326
    6.3.1.3. Area model can also be used for multiplying a mixed number times a rational
number:see figure 6.13, p. 326
    6.3.1.4. Additionally the area model can be used to show multiplication of a rational
number times a rational number.
    6.3.1.5. Your turn p. 327: Do the practice and reflect
  6.3.2. Multiplying fractions
    6.3.2.1. Fraction with a numerator of one is called a unit fraction
    6.3.2.2. Generalization about multiplying rational numbers represented by unit
fractions: For rational numbers
    6.3.2.3. Procedure for multiplying rational numbers in fraction form: For rational
numbers
    6.3.2.4. Your turn p. 329: Do the practice and reflect
    6.3.2.5. Class demonstration using paper folding to show multiplication of rational
numbers:
      6.3.2.5.1.half OF a third
      6.3.2.5.2.two-thirds OF three-fourths
      6.3.2.5.3.half OF two-thirds
      6.3.2.5.4.three-fourths OF four-fifths
    6.3.2.6. Integer rod steps (always use least number of rods possible)
    6.3.2.7. Class demonstration using integer rods to show multiplication of rational
numbers:
      6.3.2.7.1.
      6.3.2.7.2.
      6.3.2.7.3.
      6.3.2.7.4.
  6.3.3. Properties of rational number multiplication
    6.3.3.1. Basic properties of rational numbers
      6.3.3.1.1. Multiplicative inverse ( reciprocal ) analogous to additive inverse property
    6.3.3.2. Your turn p. 330: Do the practice and reflect
    6.3.3.3. Basic properties for multiplication of rational numbers
      • Closure property: For rational numbers is a unique rational
number
      • Identity property: A unique rational number, 1, exists such that
; 1 is the multiplicative identity element
      Zero property : For each rational number
      • Commutative property: For rational numbers
      • Associative property: For rational numbers
      Distributive property : For rational numbers
      • Multiplicative inverse: For every nonzero rational number b/a , a unique
rational number, a/b , exists such that
    6.3.3.4. Property for multiplying an integer by a unit fraction: For any integer a and
any unit fraction
    6.3.3.5. Using the properties to verify (prove) the procedure for multiplication of rational
numbers: see p. 331
  6.3.4. Modeling Division of fractions
    6.3.4.1. used to separate a quantity into groups of the same size
    6.3.4.2. no remainders in division of rational numbers
    6.3.4.3. Partition model – fig. 6.16 p. 332
    6.3.4.4. Measurement model – fig.6.17 p. 332
    6.3.4.5. Integer rod steps (always use least number of rods possible)
    6.3.4.6. Class demonstration using integer rods to show division of rational numbers:
      6.3.4.6.1.
      6.3.4.6.2.
      6.3.4.6.3.
      6.3.4.6.4. 3/2
      6.3.4.6.5.
      6.3.4.6.6.
      6.3.4.6.7. 3/10
  6.3.5. Definition and properties of rational number division
    6.3.5.1. Definition of rational number division in terms of multiplication : for rational
numbersif and only if e/f is a unique rational number such
that
    6.3.5.2. Closure property of division for nonzero rational numbers: For nonzero
rational numbers is a unique nonzero rational number
  6.3.6. Dividing fractions
    6.3.6.1. Procedure for dividing fractions – multiplying by the reciprocal method : for
rational numbers a/b and c/d , where c, b, and d ≠ 0,
    6.3.6.2. Procedure for dividing fractions – common denominator method: for rational
numbers a/b and c/d , where c ≠ 0,
    6.3.6.3. Procedure for dividing fractions – complex fraction method: for rational
numbers a/b and c/d , where c ≠ 0,
    6.3.6.4. Procedure for dividing fractions – missing factor method: for rational
numbers a/b and c/d , where c, b, and d ≠ 0,, where To find f,

  6.3.7. Estimation strategies
    6.3.7.1. rounding
    6.3.7.2. front-end estimation
    6.3.7.3. substituting compatible numbers
    6.3.7.4. Where does the decimal point go?
      6.3.7.4.1. 6.25 x 0.89 = 55625
      6.3.7.4.2. 4.3 x 0.49 = 2107
      6.3.7.4.3. 5.75 x 1.39 = 79925
  6.3.8. Problems and Exercises p. 340
    6.3.8.1. Home work: 1, 6, 7, 8, 9ac, 10, 14, 15, 16, 17, 18
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