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 4.3 Subtraction, Equations, and Applications Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aSubtract using fraction notation. bSolve equations of the type x + a = b and a + x = b, where a and b may be fractions. cSolve applied problems involving subtraction with fraction notation.

4.3 Subtraction, Equations, and Applications a Subtract using fraction notation. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Title 4.3 Subtraction, Equations, and Applications Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.3 Subtraction, Equations, and Applications a Subtract using fraction notation. Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Subtract and, if possible, simplify.

Title 4.3 Subtraction, Equations, and Applications Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To subtract when denominators are different: a) Find the least common multiple of the denominators. That number is the least common denominator, LCD. b) Multiply by 1, using an appropriate notation, n/n, to express each fraction in an equivalent form that contains the LCD. c) Subtract the numerators, keeping the same denominator. d) Simplify, if possible.

EXAMPLE 4.3 Subtraction, Equations, and Applications b Solve equations of the type x + a = b and a + x = b, where a and b may be fractions. 5 Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.3 Subtraction, Equations, and Applications b Solve equations of the type x + a = b and a + x = b, where a and b may be fractions. 5 Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.3 Subtraction, Equations, and Applications b Solve equations of the type x + a = b and a + x = b, where a and b may be fractions. 7 Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.3 Subtraction, Equations, and Applications b Solve equations of the type x + a = b and a + x = b, where a and b may be fractions. 7 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.3 Subtraction, Equations, and Applications b Solve equations of the type x + a = b and a + x = b, where a and b may be fractions. 8 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

4.3 Subtraction, Equations, and Applications c Solve applied problems involving subtraction with fraction notation. Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The addition principle is one way to form equivalent equations. We can use that principle to solve equations containing fractions.

EXAMPLE 4.3 Subtraction, Equations, and Applications c Solve applied problems involving subtraction with fraction notation. 9 Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.3 Subtraction, Equations, and Applications c Solve applied problems involving subtraction with fraction notation. 9 Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.3 Subtraction, Equations, and Applications c Solve applied problems involving subtraction with fraction notation. 9 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.3 Subtraction, Equations, and Applications c Solve applied problems involving subtraction with fraction notation. 9 Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

4.3 Subtraction, Equations, and Applications b Solve equations of the type x + a = b and a + x = b, where a and b may be fractions. Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Recall that we can also create equivalent equations if we subtract the same number on both sides of an equation.

EXAMPLE 4.3 Subtraction, Equations, and Applications b Solve equations of the type x + a = b and a + x = b, where a and b may be fractions. 10 Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 4.3 Subtraction, Equations, and Applications c Solve applied problems involving subtraction with fraction notation. 13Fraction of the Moon Illuminated. Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. From anywhere on earth, the moon appears to be a circular disk. At midnight on October 15, 2010 (Eastern Daylight Time), of the moon appeared illuminated. By October 18, 2010, the illuminated portion had increased to How much more of the moon appeared illuminated on October 18 than on October 15? Source: Astronomical Applications Department, U.S. Naval Observatory, Washington DC 20392

EXAMPLE 4.3 Subtraction, Equations, and Applications c Solve applied problems involving subtraction with fraction notation. 13Fraction of the Moon Illuminated. Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We let m = the additional part of the moon that appeared illuminated. 2. Translate.

EXAMPLE 4.3 Subtraction, Equations, and Applications c Solve applied problems involving subtraction with fraction notation. 13Fraction of the Moon Illuminated. Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Solve.

EXAMPLE 4.3 Subtraction, Equations, and Applications c Solve applied problems involving subtraction with fraction notation. 13Fraction of the Moon Illuminated. Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check. To check, we add: 5. State. On October 18, more of the moon was illuminated than on October 15.