3 Chapter Chapter 2 Fractions and Mixed Numbers

Complex Fractions, Order of Operations, and Mixed Numbers Section 3.6 Complex Fractions, Order of Operations, and Mixed Numbers

Simplify Complex Fractions. Objective A Simplify Complex Fractions.

Complex Fraction A fraction whose numerator or denominator or both numerator and denominator contain fractions is called a complex fraction. Objective B

Example (Method 1) Simplify: This method makes use of the fact that a division bar means division. Simplify: Objective B

Example (Method 2) Simplify: The LCD is 12. The second method is to multiply the numerator and the denominator by the LCD. Simplify: The LCD is 12. Objective B

Review the Order of Operations. Objective B Review the Order of Operations.

Reviewing Operations on Fractions Review of Operations on Fractions Procedure Example Multiply Multiply the numerators and multiply the denominators Divide Multiply the first fraction by the reciprocal of the second fraction Add or Subtract Write each fraction as an equivalent fraction whose denominator is the LCD Add or subtract numerators and write the result over the common denominator. Objective C

Chapter 1 / Whole Numbers and Introduction to Algebra Order of Operations Chapter 1 / Whole Numbers and Introduction to Algebra 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.

Example Simplify:

Example Use the order of operations to simplify Objective D

Example Simplify:

Evaluate Expressions Given Replacement Values. Objective C Evaluate Expressions Given Replacement Values.

Evaluating Fractions Evaluate 2x2 + 3y for x = and y = Replace x with and y with in 2x2 + 3y. Objective B

Write Mixed Numbers as Improper Fractions. Objective D Write Mixed Numbers as Improper Fractions.

Writing a Mixed Number as an Improper Fraction To write a mixed number as an improper fraction: 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.

Example Write each as an improper fraction. a. b.

Write Improper Fractions as Mixed Numbers or Whole Numbers. Objective E Write Improper Fractions as Mixed Numbers or Whole Numbers.

Writing an Improper Fraction as a Mixed Number or a Whole Number To write an improper fraction as a mixed number or a whole number: 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.

Example Write each as a mixed number of whole number. a. b.