Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 3 Fractions

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 3.6 Complex Fractions, Order of Operations, and Mixed Numbers

33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Complex Fraction A fraction whose numerator or denominator or both numerator and denominator contain fractions is called a complex fraction.

44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplifying Complex Fractions (Method 1) EXAMPLE This method makes use of the fact that a division bar means division. Simplify:

55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Simplifying Complex Fractions (Method 2) EXAMPLESimplify: The second method is to multiply the numerator and the denominator by the LCD. The LCD is 12.

66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Reviewing Operations on Fractions Review of Operations on Fractions OperationProcedureExample MultiplyMultiply the numerators and multiply the denominators DivideMultiply the first fraction by the reciprocal of the second fraction Add or Subtract 1. Write each fraction as an equivalent fraction whose denominator is the LCD 2. Add or subtract numerators and write the result over the common denominator.

77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Order of Operations 1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as fraction bars, starting with the innermost set. 2.Evaluate any expressions with exponents. 3.Multiply or divide in order from left to right. 4.Add or subtract in order from left to right.

88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Using Order of Operations EXAMPLE Use the order of operations to simplify

99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluating Fractions EXAMPLE Evaluate 2x 2 + 3y for x = and y = Replace x with and y with in 2x 2 + 3y.

10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Writing Mixed Numbers as Improper Fractions Step 1: Multiply the denominator of the fraction by the whole number. Step 2: Add the numerator of the fraction to the product from Step 1. Step 3: Write the sum from Step 2 as the numerator of the improper fraction over the original denominator. Step 1 Step 2 Step 3

11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Write each as an improper fraction. a.b.

12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Writing Improper Fractions as Mixed Numbers Step 1: Divide the denominator into the numerator. Step 2: The whole number part of the mixed number is the quotient. The fraction part of the mixed number is the remainder over the original denominator. Step 1 Step 2

13 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Write each as a mixed number of a whole number. a.b.