Understanding Properties of Inequalities

Properties of Inequalities

1. Three Possibilities

2. Transitive

3. Addition/Subtraction

4. Multiplication/Division

5. Addition Theorem

6. Whole Greater than Part

1. Three Possibilities

2. Transitive

3. Addition/Subtraction

4. Multiplication/Division

5. Addition Theorem

6. Whole Greater than Part

Take a=5 and b= some other number

What relationships can be true of these numbers?

Three Possibilities Property

So a could be greater than b...
What else?

Either a > b, a = b, or a < b

Three Possibilities Property

​The "Three Possibilities" Property

1. Three Possibilities

2. Transitive

3. Addition/Subtraction

4. Multiplication/Division

5. Addition Theorem

6. Whole Greater than Part

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

Dropdown

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is ​ ​

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​

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The Transitive Property

​The Transitive Property

​If a > b, and b > c, then a has to be > c

Multiple Choice

Choose the correct transitive property for $$-2<5<10$$  

• $$-2<10$$  

• $$10>2$$  

• $$-2<5$$  

• $$5<10$$  

Multiple Choice

Choose the correct transitive property for $$-15<-8<0$$  

• $$-15<-8$$  

• $$-15<0$$  

• $$-8<0$$  

• $$0>-15$$  

Multiple Choice

If A < B and B < C, then....

• C < A

• C > A

• A > C

• B > C

1. Three Possibilities

2. Transitive

3. Addition/Subtraction

4. Multiplication/Division

5. Addition Theorem

6. Whole Greater than Part

^{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?

Labelling

Rex keeps it cool and wears jeans. Monte has flair and loves colored pants. Put the correct labels on the boys.

Drag labels to their correct position on the image

More points

Fewer points

Equal points

^{Addition Property of Inequality}

​If R > M, then R + 10 is still > M + 10

If a > b, then a + c > b + c

Multiple Choice

s - 4 ≥ 25

• s ≥ 18

• s ≥ 34

• s ≤ 18
• s ≥ 29

Multiple Choice

Which step shows the Addition Property of Inequality?

• 1

• 3

• 4

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

^{Subtraction Property of Inequality}

​If R > M, then R -5 is still > M - 5

If a > b, then a - c > b - c

Multiple Choice

What property justifies step 2?

• Given

• Addition Property of Eqaulity

• Subtraction Property of Inequality

• Addition Property of Inequality

1. Three Possibilities

2. Transitive

3. Addition/Subtraction

4. Multiplication/Division

5. Addition Theorem

6. Whole Greater than Part

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

Multiple Choice

Solve
20 ≤ 8 + k

• 28 ≤ k

• 12 ≤ k

• -28 ≥ k

^{Multiplication Property of Inequality}

​If R > M, then 3R is still > 3M

If a > b, then ac > bc

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

Multiple Choice

$$\frac{1}{2}x>5$$  

• x > 10

• x > -10

• x > 5

Multiple Choice

$$\frac{1}{4}x>11$$  

• x > 1/11

• x > 44

• x > 4

^{Division Property of Inequality}

Multiple Choice

$$5x>35$$  

• x > 30

• x > 40

• x > 7

1. Three Possibilities

2. Transitive

3. Addition/Subtraction

4. Multiplication/Division

5. Addition Theorem

6. Whole Greater than Part

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

Labelling

Winners on the left, losers on the right.

Remember,

R > M

H > D

Rex + Hal team up

Monte + Dougle team up

Drag labels to their correct position on the image

Rex

Monte

Hal

Dougle

If a > b and c > d
then a + c > b + d

The Addition Theorem of Inequality

1. Three Possibilities

2. Transitive

3. Addition/Subtraction

4. Multiplication/Division

5. Addition Theorem

6. Whole Greater
   than Part

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

Open Ended

How does Dad's score compare with Rex's score and with Monte's score?

As long as a > 0 and b > 0 and a + b = c
then c > a AND c > b

The "Whole Greater than Part" Theorem

1. Three Possibilities

2. Transitive

3. Addition/Subtraction

4. Multiplication/Division

5. Addition Theorem

6. Whole Greater
   than Part