Complex Fractions Method 1 Method 2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

7.5 Complex Fractions Simplify a complex fraction by writing it as a division problem (Method 1). Simplify a complex fraction by multiplying the least common denominator (Method 2). 1 2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Complex Fractions. The quotient of two mixed numbers in arithmetic, such as can be written as a fraction. The last expression is the quotient of expressions that involve fractions. In algebra, some rational expressions also have fractions in the numerator, or denominator, or both. A rational expression with one or more fractions in the numerator, or denominator, or both is called a complex fraction. The parts of a complex fraction are named as follows. Numerator of complex fraction Main fraction bar Denominator of complex fraction Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.5 - 3

Objective 1 Simplify a complex fraction by writing it as a division problem (Method 1). Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.5 - 4

Simplify a complex fraction by writing it as a division problem (Method 1). Since the main fraction bar represents division in a complex fraction, one method of simplifying a complex fraction involves division. Step 1: Write both the numerator and denominator as single fractions. Step 2: Change the complex fraction to a division problem. Step 3: Perform the indicated division. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.5 - 5

EXAMPLE 1 Simplify each complex fraction. Solution: Simplifying Complex Fractions (Method 1) Simplify each complex fraction. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.5 - 6

EXAMPLE 2 Simplify the complex fraction. Solution: Simplifying a Complex Fraction (Method 1) Simplify the complex fraction. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.5 - 7

EXAMPLE 3 Simplify the complex fraction. Solution: Simplifying a Complex Fraction (Method 1) Simplify the complex fraction. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.5 - 8

Objective 2 Simplify a complex fraction by multiplying by the least common denominator (Method 2). Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.5 - 9

Simplify a complex fraction by multiplying the least common denominator (Method 2). Since any expression can be multiplied by a form of 1 to get an equivalent expression, we can multiply both the numerator and denominator of a complex fraction by the same nonzero expression to get an equivalent rational expression. If we choose the expression to be the LCD of all the fractions within the complex fraction, the complex fraction will be simplified. Step 1: Find the LCD of all fractions within the complex fraction. Step 2: Multiply both the numerator and denominator of the complex fraction by this LCD using the distributive property as necessary. Write in lowest terms. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.5 - 10

EXAMPLE 4 Simplify each complex fraction. Solution: Simplifying Complex Fractions (Method 2) Simplify each complex fraction. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.5 - 11

EXAMPLE 5 Simplify the complex fraction. Solution: Simplifying a Complex Fraction (Method 2) Simplify the complex fraction. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.5 - 12

EXAMPLE 6 Simplify each complex fraction. Deciding on a Method and Simplifying Complex Fractions Simplify each complex fraction. Remember the same answer is obtained regardless of whether Method 1 or Method 2 is used. Some students prefer one method over the other. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.5 - 13