2. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Introduction to Integers and Algebraic Expressions 2
2.1
Integers and the Number Line
2.2
Addition of Integers
2.3
Subtraction of Integers
2.4
Multiplication of Integers
2.5
Division of Integers and Order of Operations
2.6
Introduction to Algebra and Expressions
2.7
Like Terms and Perimeter
2.8
Solving Equations
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 2

3. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers a
Add integers without using the number line. d
Find the opposite of any integer.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 3

4. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers a
Add integers without using the number line.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 4

5. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers a
Add integers without using the number line. 1
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 5

6. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers a
Add integers without using the number line. 2
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 6

7. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers
ADDING NEGATIVE INTEGERS a
To add two negative integers, add their absolute values and change the sign (making the answer negative).
Add integers without using the number line.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 7

8. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers a
Add integers without using the number line.
Add.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 8

9. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers a
Add integers without using the number line.
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.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 9

10. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers a
Add integers without using the number line. 6
Add.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 10

11. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers
ADDING POSITIVE AND NEGATIVE INTEGERS
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. a
Add integers without using the number line.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 11

12. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers a
Add integers without using the number line.
Add.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 12

13. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers
ADDING OPPOSITES
For any integer a,
(The sum of any number and its additive inverse, or opposite, is 0.) a
Add integers without using the number line.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 13

14. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers a
Add integers without using the number line. 13
Add.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 14

15. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers
RULES FOR ADDITION OF INTEGERS
1. Positive numbers: Add the same way as arithmetic numbers. The answer is positive.
2. Negative numbers: Add absolute values. The answer is negative. a
Add integers without using the number line.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 15

16. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers
RULES FOR ADDITION OF INTEGERS
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. a
Add integers without using the number line.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 16

17. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers a
Add integers without using the number line.
Add.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 17

18. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers a
Add integers without using the number line.
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 add
them separately. Then we add the two results.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 18

19. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers a
Add integers without using the number line. 17
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 19

20. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.2
Addition of Integers a
Add integers without using the number line. 17
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 20