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Integers
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Integers
• Consist of positive and negative whole numbers
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The Number Line……
• A number line consists of positive numbers (right of 0) and negative numbers (left of 0).
• A real life example of a number line is a temperature thermometer.
Negative Positive0
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For example…..
• -5 would represent 5 degrees below zero.
• +4 would represent 4 degrees above zero.
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Make the Comparison……
• 7 degrees below 0 is (warmer/colder) than 4 degrees above 0.
• 7 degrees below 0 is a (lower/higher) temperature than 4 degrees above 0.
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Coordinates on a Graph….
• Find the best estimate of the point.
a. -2 b. 2 c. -1.75 d. -1.5
0 1 212
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Sets and Subsets……
• A set is a group of numbers.
Example: Set A = {1,2,3,4,5}
• A subset is a group of numbers in which every member is in another set.
Example: Set B = {1,2,3}
• So, B is a subset of A.
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Which of the following would represent a subset of integers?
• States Sales Tax Rate
• Amount of Gas in a Car
• Number of Students in Class
• A Dinner Receipt
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You Try…Which of the following would represent a subset of integers?
• Costs of a TV
• # of miles on the odometer of a car
• A person’s weight
• Number of residents in South Carolina
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Inequalities…..
• We use inequalities to compare numbers.
• The following are inequalities:
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Examples…….
• “4 is less than 7” -
• “9 is greater than or equal to 5” -
74
59
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You Try……Insert the appropriate inequality sign.
1. -5 -2
2. -7 2
3. 4 -12
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We have the Yellow Team and the Red Team….
Assign the left side of the room to the red team and right side to the yellow team.
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Who is favored & by how much if we have…
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So…how can I represent: -7 + 3
Start with:
Add 3: Which Leaves:
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Use the counters….
86
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Use the counters….
5 2
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Use the counters….
3 4
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Use the counters….
6 2
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Use the counters….
5 8
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No Counters!
100 150
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No Counters
220 170
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So…How do I add signed numbers?
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How close were you?
• Same Signs• Add the numbers• Take their sign
• Different Signs• Subtract the numbers• Take the sign of the number with largest absolute
value
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Opposites:
• The opposite of 5 is -5.
• What is –(-2)?
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Use the counters….
3 2( )
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Use the counters….
12 20( )
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Do the following:
• 9 – 8 =
• -6 – (-9)=
• -14 + 3 =
• 10 – 19 =
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Do the following:
• 29 - 32 =
• -82 – 12 =
• -45 + 78 =
• 16- (-27) =
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What’s 4 x -3?
=
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Let’s Multiply:
52
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Let’s Multiply:
3 2
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So…How do I explain -3 x -4?
• I like to think of this as – (3 x -4) and think of it as the opposite of (3 x -4).
• Can you develop a rule for Multiplication?
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Let’s Multiply:
3 2
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So…what’s the rule for multiplying integers?
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Division: 8 2
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Divide: 6 3
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So..what’s the rule for Dividing integers
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Multiplying & Dividing:
• Like signs – positive
• Unlike signs - Negative
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Homework
• Worksheet