Post on 15-Dec-2015
CHAPTER
2Introduction to Integers and Algebraic Expressions
Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.1 Integers and the Number Line2.2 Addition of Integers2.3 Subtraction of Integers2.4 Multiplication of Integers2.5 Division of Integers and Order of Operations2.6 Introduction to Algebra and Expressions2.7 Like Terms and Perimeter2.8 Solving Equations
OBJECTIVES
2.3 Subtraction of Integers
Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
a Subtract integers and simplify combinations ofadditions and subtractions.
b Solve applied problems involving addition andsubtraction of integers.
2.3 Subtraction of Integers
THE DIFFERENCE
Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
The difference a – b is the number that when added to b gives a.
EXAMPLE
2.3 Subtraction of Integers
a Subtract integers and simplify combinations ofadditions and subtractions.
1
Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Think: 5 – 8 is the number that when added to 8 gives 5. What number can we add to 8 to get 5? The number must be negative. The number is –3: 5 – 8 = –3.That is, 5 – 8 = –3 because 8 + (–3) = 5.
Subtract: 5 – 8.
2.3 Subtraction of Integers
a Subtract integers and simplify combinations ofadditions and subtractions.
Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
The definition of a – b does not always provide the most efficient way to subtract.
2.3 Subtraction of Integers
SUBTRACTING BY ADDING THE OPPOSITE
Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
To subtract, add the opposite, or additive inverse, of the number being subtracted:
EXAMPLE
2.3 Subtraction of Integers
a Subtract integers and simplify combinations ofadditions and subtractions.
Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Equate each subtraction with a corresponding addition. Then write the equation in words.
Negative twelve minus thirty is negative twelve plus negative thirty.
EXAMPLE
2.3 Subtraction of Integers
a Subtract integers and simplify combinations ofadditions and subtractions.
Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Negative twenty minus negative seventeen is negative twenty plus seventeen.
EXAMPLE
2.3 Subtraction of Integers
a Subtract integers and simplify combinations ofadditions and subtractions.
Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Subtract.
EXAMPLE
2.3 Subtraction of Integers
a Subtract integers and simplify combinations ofadditions and subtractions.
Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.3 Subtraction of Integers
a Subtract integers and simplify combinations ofadditions and subtractions.
Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
When several additions and subtractions occur together, we can make them all additions. The commutative law for addition can then be used.
EXAMPLE
2.3 Subtraction of Integers
a Subtract integers and simplify combinations ofadditions and subtractions.
10
Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
EXAMPLE
2.3 Subtraction of Integers
b Solve applied problems involving addition andsubtraction of integers.
11 Temperature Changes.
Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Denver, Colorado, experienced its greatest temperature change in one day on January 25, 1872. From the lowof –20 F(degrees Fahrenheit), the temperature increased 66 . If it later decreased 10 , what was the final temperature?Source: Based on information from www.examiner.com
EXAMPLE
2.3 Subtraction of Integers
b Solve applied problems involving addition andsubtraction of integers.
11 Temperature Changes.
Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
We let T represent the final temperature.