Understanding Properties of Inequalities

Presentation

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Easy

Maggie Land

Used 1+ times

FREE Resource

23 Slides • 20 Questions

Properties of Inequalities

Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
Whole Greater than Part

Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
Whole Greater than Part

Take a=5 and b= some other number

What relationships can be true of these numbers?

Three Possibilities Property

Fill in the Blanks

If b = 3, then a _ b (use a symbol)

Type answer...

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

Fill in the Blanks

What if b also equals 5? Then a _ b (use a symbol)

Type answer...

Fill in the Blanks

What if b = 8? Then a _ b (use a symbol)

Type answer...

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

Three Possibilities Property

The "Three Possibilities" Property

Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
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

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

Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
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?

Labeling

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

Fewer points

Equal points

More 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?

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

Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
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

Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
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

Labeling

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

Dougle

Monte

Hal

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

The Addition Theorem of Inequality

Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
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?

Type response here

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

The "Whole Greater than Part" Theorem

Three Possibilities
Transitive
Addition/Subtraction
Multiplication/Division
Addition Theorem
Whole Greater
than Part

Properties of Inequalities

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