Download Section 8.1 – Addition and Subtraction of Integers

Chapter 8. Section 1
Page 1
Section 8.1 – Addition and Subtraction of Integers
Homework (page 328) problems 1-6, 7 (models only), 9, 12-17
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The set of integers is given by I = { . . . , –3, –2, –1, 0, 1, 2, 3, . . . }
The set of integers contain negative values, positive values and 0
Zero is classified as neither positive or negative
What is the relationship between the set of integers, and the set of whole numbers?
We can still use base 10 blocks for integers, like we did for whole numbers, but we need to use two
different colors (one for positive and one for negative)
Properties of Addition of Integers:
• The Closure property says that when you add any two integers, you get another integer
• Commutative : a + b = b + a
• Associative: (a + b) + c = a + (b + c)
• Identity: a + 0 = 0 + a = a
• Additive Inverse: For every a, there is an additive inverse (–a) such that a + –a = 0
Approaches to Subtraction:
• Subtraction of two integers (a – b) can be thought of as adding the opposite, or a + (–b)
• Subtraction can also be thought of as the missing-addend approach, where a – b = c if and only if
a=b+c
Exercises:
• Example, page 330 number 1. Which are integers, and identify 3/4, 556, –252/5
3/4 is not an integer
556 is a positive integer
–252/5 is not an integer
• Example, page 330 number 2. (see book)
a. BBBRR is 3 black chips plus 2 red chips. Since red are negative, this would represent 1
b. BRRRRBRR is 2 black and 6 red. This would represent –4
c. 5
d. –3
• Example, page 330 number 4. What is the additive inverse of –b?
–(–b) = b
• Example, page 330 number 6a. Write an addition statement for the given sentence (see book)
7 + (–4) + (–2) + 8 = 9
• Example, page 330 number 7. Show how you could find 4 + (–7) with chips and number line
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Example, page 330 number 9. Identify the property in 3 + [(–3) + 6] = [3 + (–3)] + 6
Associative
Chapter 8. Section 1
Page 2
Absolute Value
• The absolute value of a number is often mis-represented when taught. It is NOT about throwing out
the minus sign, but multiplying by a negative if your input is negative
• In other words,
|–5| = –(–5) = 5
• What is |x|?
 x x ≥ 0
x =
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− x x < 0
• So it is entirely reasonable that |a| = –a ! This would be confusing for anyone who thought of 'taking
away' the minus sign