CHAPTER 4 Fraction Notation: Addition, Subtraction, and Mixed Numerals Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.1Least Common Multiples 4.2Addition, Order, and Applications 4.3Subtraction, Equations, and Applications 4.4Solving Equations: Using the Principles Together 4.5Mixed Numerals 4.6Addition and Subtraction of Mixed Numerals; Applications 4.7Multiplication and Division of Mixed Numerals; Applications 4.8Order of Operations and Complex Fractions

OBJECTIVES 4.4 Solving Equations: Using the Principles Together Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aSolve equations that involve fractions and require use of both the addition principle and the multiplication principle. bSolve equations by using the multiplication principle to clear fractions.

4.4 Solving Equations: Using the Principles Together a Solve equations that involve fractions and require use of both the addition principle and the multiplication principle. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Recall that we use the addition and multiplication principles to write equivalent equations.

EXAMPLE 4.4 Solving Equations: Using the Principles Together a Solve equations that involve fractions and require use of both the addition principle and the multiplication principle. 1 Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.4 Solving Equations: Using the Principles Together a Solve equations that involve fractions and require use of both the addition principle and the multiplication principle. 1 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.4 Solving Equations: Using the Principles Together a Solve equations that involve fractions and require use of both the addition principle and the multiplication principle. 1 Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.4 Solving Equations: Using the Principles Together a Solve equations that involve fractions and require use of both the addition principle and the multiplication principle. 1 Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

4.4 Solving Equations: Using the Principles Together a Solve equations that involve fractions and require use of both the addition principle and the multiplication principle. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Sometimes the variable appears on the right side of the equation. The strategy for solving the equation remains the same.

EXAMPLE 4.4 Solving Equations: Using the Principles Together a Solve equations that involve fractions and require use of both the addition principle and the multiplication principle. 3 Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Our plan is to first use the addition principle to isolate and then use the multiplication principle to isolate x.

EXAMPLE 4.4 Solving Equations: Using the Principles Together a Solve equations that involve fractions and require use of both the addition principle and the multiplication principle. 3 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.4 Solving Equations: Using the Principles Together a Solve equations that involve fractions and require use of both the addition principle and the multiplication principle. 3 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.4 Solving Equations: Using the Principles Together a Solve equations that involve fractions and require use of both the addition principle and the multiplication principle. 3 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

4.4 Solving Equations: Using the Principles Together b Solve equations by using the multiplication principle to clear fractions. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We can now use the multiplication principle in the first step to produce an equivalent equation that is “cleared of fractions.” To “clear fractions,” we identify the LCM of the denominators and use the multiplication principle. Because the LCM is a common multiple of the denominators, when both sides of the equation are multiplied by the LCM, the resulting terms can all be simplified. An equivalent equation can then be written without using fractions.

4.4 Solving Equations: Using the Principles Together b Solve equations by using the multiplication principle to clear fractions. Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We can “clear fractions” in equations, not in expressions. Do not multiply to clear fractions when simplifying an expression.

EXAMPLE 4.4 Solving Equations: Using the Principles Together b Solve equations by using the multiplication principle to clear fractions. 4 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Solve Example 1 by clearing fractions:

EXAMPLE 4.4 Solving Equations: Using the Principles Together b Solve equations by using the multiplication principle to clear fractions. 4 Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The LCM of the denominators is 8, so we begin by multiplying both sides of the equation by 8:

EXAMPLE 4.4 Solving Equations: Using the Principles Together b Solve equations by using the multiplication principle to clear fractions. 4 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.4 Solving Equations: Using the Principles Together b Solve equations by using the multiplication principle to clear fractions. 4 Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.