2. CHAPTER 9 Introduction to Real Numbers and Algebraic Expressions Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 9.1Introduction to Algebra 9.2The Real Numbers 9.3Addition of Real Numbers 9.4Subtraction of Real Numbers 9.5Multiplication of Real Numbers 9.6Division of Real Numbers 9.7Properties of Real Numbers 9.8Simplifying Expressions; Order of Operations

3. OBJECTIVES 9.4 Subtraction of Real Numbers Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aSubtract real numbers and simplify combinations of additions and subtractions. bSolve applied problems involving subtraction of real numbers.

4. 9.4 Subtraction of Real Numbers SUBTRACTION Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The difference a – b is the number c for which a = b + c.

5. EXAMPLE 9.4 Subtraction of Real Numbers a Subtract real numbers and simplify combinations of additions and subtractions. 1 Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Think: What number can we add to 7 to get 3? The number must be negative. Since 7 + (–4) = 3, we know the number is –4: 3 – 7 = –4. That is, 3 – 7 = –4 because 7 + (–4) = 3.

6. 9.4 Subtraction of Real Numbers SUBTRACTING BY ADDING THE OPPOSITE Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. For any real numbers a and b, (To subtract, add the opposite, or additive inverse, of the number being subtracted.)

7. EXAMPLE 9.4 Subtraction of Real Numbers a Subtract real numbers and simplify combinations of additions and subtractions. 2 Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

8. EXAMPLE 9.4 Subtraction of Real Numbers a Subtract real numbers and simplify combinations of additions and subtractions. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

9. EXAMPLE 9.4 Subtraction of Real Numbers a Subtract real numbers and simplify combinations of additions and subtractions. 10 Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

10. EXAMPLE 9.4 Subtraction of Real Numbers b Solve applied problems involving subtraction of real numbers. 13Surface Temperatures on Mars Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Surface temperatures on Mars vary from during polar night to at the equator during midday at the closest point in orbit to the sun. Find the difference between the highest value and the lowest value in this temperature range. Source: Mars Institute

11. EXAMPLE 9.4 Subtraction of Real Numbers b Solve applied problems involving subtraction of real numbers. 13Surface Temperatures on Mars Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We let D = the difference in the temperatures. Then the problem translates to the following subtraction: