Understanding Properties of Inequalities
Presentation
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Easy
Maggie Land
Used 1+ times
FREE Resource
23 Slides • 20 Questions
1
Properties of Inequalities
2
Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
Whole Greater than Part
3
Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
Whole Greater than Part
4
Take a=5 and b= some other number
What relationships can be true of these numbers?
Three Possibilities Property
5
Fill in the Blanks
Type answer...
6
So a could be greater than b...
What else?
7
Fill in the Blanks
Type answer...
8
Fill in the Blanks
Type answer...
9
Either a > b, a = b, or a < b
Three Possibilities Property
The "Three Possibilities" Property
10
Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
Whole Greater than Part
11
The Burj Khalifa is taller than The Shard. The Shard is bigger than Big Ben. What do you know to be true about the relationships between the Burj Khalifa and Big Ben?
The Transitive Property
12
Dropdown
13
The Transitive Property
The Transitive Property
If a > b, and b > c, then a has to be > c
14
Multiple Choice
Choose the correct transitive property for −2<5<10
−2<10
10>2
−2<5
5<10
15
Multiple Choice
Choose the correct transitive property for −15<−8<0
−15<−8
−15<0
−8<0
0>−15
16
Multiple Choice
If A < B and B < C, then....
C < A
C > A
A > C
B > C
17
Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
Whole Greater than Part
18
Addition Property of Inequality
Rex has more points than Monte. They play a game and both get 10 more points. What do you know about the relationships between their points?
19
Labelling
Rex keeps it cool and wears jeans. Monte has flair and loves colored pants. Put the correct labels on the boys.
More points
Fewer points
Equal points
20
Addition Property of Inequality
If R > M, then R + 10 is still > M + 10
If a > b, then a + c > b + c
21
Multiple Choice
s - 4 ≥ 25
s ≥ 18
s ≥ 34
s ≥ 29
22
Multiple Choice
Which step shows the Addition Property of Inequality?
1
3
4
23
Multiple Choice
Rex has more points than Monte. They fail at the next game and both lose 5 points. What do you know about the relationship between their points?
R < M
R > M
M > R
24
Subtraction Property of Inequality
If R > M, then R -5 is still > M - 5
If a > b, then a - c > b - c
25
Multiple Choice
What property justifies step 2?
Given
Addition Property of Eqaulity
Subtraction Property of Inequality
Addition Property of Inequality
26
Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
Whole Greater than Part
27
Multiple Choice
Rex has more points than Monte. They both hit the jackpot and triple their scores. What do you know about the relationship between their points?
R > M
R = M
M > R
R < M
28
Multiple Choice
Solve
20 ≤ 8 + k
28 ≤ k
12 ≤ k
-28 ≥ k
29
Multiplication Property of Inequality
If R > M, then 3R is still > 3M
If a > b, then ac > bc
30
Multiple Choice
Rex has more points than Monte. They both go get a snack while the game is still going! Their scores each get cut in half. What do you know about the relationship between their points?
R > M
R = M
M > R
R < M
31
Multiple Choice
21x>5
x > 10
x > -10
x > 5
32
Multiple Choice
41x>11
x > 1/11
x > 44
x > 4
33
Division Property of Inequality
34
Multiple Choice
5x>35
x > 30
x > 40
x > 7
35
Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
Whole Greater than Part
36
Rex has more points than Monte. Hal has more points than Dougle. Rex and Hal decide to team up, leaving Monte and Dougle on a team. Which team has more points?
The boys invite
their cousins
to play
37
Labelling
Winners on the left, losers on the right.
Remember,
R > M
H > D
Rex + Hal team up
Monte + Dougle team up
Dougle
Hal
Monte
Rex
38
If a > b and c > d
then a + c > b + d
The Addition Theorem of Inequality
39
Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
Whole Greater
than Part
40
Rex and Monte don't stand a chance against Dad. The boys each have some points on the board, but Dad has scored as much as Rex and Monte combined! What do you know about Dad's score compared with each of the boys' scores?
Now Dad plays
41
Open Ended
How does Dad's score compare with Rex's score and with Monte's score?
42
As long as a > 0 and b > 0 and a + b = c
then c > a AND c > b
The "Whole Greater than Part" Theorem
43
Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
Whole Greater
than Part
Properties of Inequalities
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