6.3 Multiplying and Dividing Fractions Remember to Silence Your Cell Phone and Put It In Your Bag!

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Presentation transcript:

6.3 Multiplying and Dividing Fractions Remember to Silence Your Cell Phone and Put It In Your Bag!

Multiplication Models Remember - Multiplication is the joining together of equal-sized sets (equivalent sets) or equal-sized lengths. Repeated Addition Rectangular array model Area model Cartesian Product

Procedure for Multiplying Rational Numbers in Fraction Form

Properties of Multiplication of Rational Numbers Closure Identity Zero Commutative Associative Distributive  Inverse

Inverse Property of Multiplication of Rational Numbers For every nonzero rational number, there exists a unique rational number,, such that and Multiplicative Inverse or Reciprocal

Definition of Rational Number Division,  Q, c  0, iff is a unique rational number such that

12 pages of space in the school newspaper are to be shared evenly by 5 student organizations. How many pages does each organization get? (Top of p. 332) Sharing or Partitioning Model of Division

Suppose that space in the school newspaper is being allotted for sale in sets of 5 pages each. How many allotments can we get from the 12 pages? (Bottom of p. 332) Repeated Subtraction or Measurement Model of Division

Closure Property of Division for Nonzero Rational Numbers is a unique nonzero rational number.

Procedure for Dividing Fractions—Multiply by the Reciprocal Method where c, b, and d  0,

Optional Division Methods Common Denominator – p. 337 Complex Fractions – p. 338 Missing Factor Method – p. 338