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
Example: 1/3 X 1/2 1/3 X 1/2 means 1/3 of 1/2
Example: 1/2 X 2/3 1/2 X 2/3 means 1/2 of 2/3
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 RationalNumber 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