CHAPTER 2 Introduction to Integers and Algebraic Expressions Slide 2Copyright 2012, 2008, 2004, 2000...
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Transcript of CHAPTER 2 Introduction to Integers and Algebraic Expressions Slide 2Copyright 2012, 2008, 2004, 2000...
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
2.2 Addition of Integers
Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
a Add integers without using the number line.
2.2 Addition of Integers
a Add integers without using the number line.
Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
EXAMPLE
2.2 Addition of Integers
a Add integers without using the number line.
1
Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
EXAMPLE
2.2 Addition of Integers
a Add integers without using the number line.
2
Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2 Addition of Integers
ADDING NEGATIVE INTEGERS
Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
To add two negative integers, add their absolute values and change the sign (making the answer negative).
EXAMPLE
2.2 Addition of Integers
a Add integers without using the number line.
Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Add.
2.2 Addition of Integers
a Add integers without using the number line.
Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
When the number 0 is added to any number, that number remains unchanged. For this reason, the number 0 is referred to as the additive identity.
EXAMPLE
2.2 Addition of Integers
a Add integers without using the number line.
6
Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Add.
2.2 Addition of Integers
ADDING POSITIVE AND NEGATIVE INTEGERS
Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
To add a positive integer and a negative integer, find the difference of their absolute values.a) If the negative integer has the greater absolute value, the answer is negative.b) If the positive integer has the greater absolute value, the answer is positive.
EXAMPLE
2.2 Addition of Integers
a Add integers without using the number line.
Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Add.
For any integer a,
(The sum of any number and its additive inverse, or opposite, is 0.)
2.2 Addition of Integers
ADDING OPPOSITES
Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
EXAMPLE
2.2 Addition of Integers
a Add integers without using the number line.
13
Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Add.
2.2 Addition of Integers
RULES FOR ADDITION OF INTEGERS
Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
1. Positive numbers: Add the same way as arithmetic numbers. The answer is positive.2. Negative numbers: Add absolute values. The answer is negative.
2.2 Addition of Integers
RULES FOR ADDITION OF INTEGERS
Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
3. A positive and a negative number: Subtract absolute values.a) If the positive number has the greater absolute value, the answer is positive.b) If the negative number has the greater absolute value, the answer is negative.c) If the numbers have the same absolute value, they are additive inverses and the answer is 0.4. One number is zero: The sum is the other number.
EXAMPLE
2.2 Addition of Integers
a Add integers without using the number line.
Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Add.
2.2 Addition of Integers
a Add integers without using the number line.
Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Suppose we wish to add several numbers, positive and negative. Because of the commutative and associative laws for addition, we can group the positive numbers together and the negative numbers together and addthem separately. Then we add the two results.
EXAMPLE
2.2 Addition of Integers
a Add integers without using the number line.
17
Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
EXAMPLE
2.2 Addition of Integers
a Add integers without using the number line.
17
Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
