Introduction to Real Numbers and
Algebraic Expressions
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
CHAPTER
9
Introduction to Algebra
The Real Numbers
Addition of Real Numbers
Subtraction of Real Numbers
Multiplication of Real Numbers
Division of Real Numbers
Properties of Real Numbers
Simplifying Expressions; Order of Operations
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 2
9.4
Subtraction of Real Numbers
OBJECTIVES
a Subtract real numbers and simplify combinations of
additions and subtractions.
b Solve applied problems involving subtraction of
real numbers.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 3
9.4
Subtraction of Real Numbers
SUBTRACTION
The difference a – b is the number c for which a = b + c.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 4
9.4
Subtraction of Real Numbers
Subtract real numbers and simplify combinations of
a
additions and subtractions.
EXAMPLE 1
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.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 5
9.4
Subtraction of Real Numbers
SUBTRACTING BY ADDING THE OPPOSITE
For any real numbers a and b,
(To subtract, add the opposite, or additive inverse, of
the number being subtracted.)
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 6
9.4
Subtraction of Real Numbers
Subtract real numbers and simplify combinations of
a
additions and subtractions.
EXAMPLE 2
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 7
9.4
Subtraction of Real Numbers
Subtract real numbers and simplify combinations of
a
additions and subtractions.
EXAMPLE
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 8
9.4
Subtraction of Real Numbers
Subtract real numbers and simplify combinations of
a
additions and subtractions.
EXAMPLE 10
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 9
9.4
Subtraction of Real Numbers
Solve applied problems involving subtraction of
b
real numbers.
EXAMPLE 13 Surface Temperatures on Mars
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
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 10
9.4
Subtraction of Real Numbers
Solve applied problems involving subtraction of
b
real numbers.
EXAMPLE 13 Surface Temperatures on Mars
We let D = the difference in the temperatures. Then the
problem translates to the following subtraction:
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 11