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Thursday, December 1 stPowerPoint Presentation

Thursday, December 1 st

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Thursday, December 1 st

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Thursday, December 1st

Warm Up

Write a rule for each sequence using “n”

15, 24, 33, 22

-11, -15, -19, -24

Please Complete warm up and take out homework (worksheet)

Did you write down the homework?

For most people, the ratio of the

length of their head to their total

height is 1:7. Use proportions to test

your measurements and see if they

match this ratio.

How did the hammerhead shark do on his quiz?

He Nailed it!

Next Checkpoint is

FRIDAY

Homework

Answers

Equivalent

Ratios

- Equivalent ratios
- are ratios that name the same comparison.
- You can find an equivalent ratio by multiplying or dividing both terms of a ratio by the same number.

1. 4.

2.5. 5 to 9

3. 6 : 12

Rates

RATE: compares two quantities that have different units of measure

For example:

Abbey charges $28 dollars for 3 hours of swimming lessons. David charges $18 dollars for 2 hours of swimming lessons. Which instructor offers a better deal?

Divide!

Set up your Rate

Abbey: charges $28 dollars for 3 hours of swimming lessons.

Rate= == 9.33

Who had a better deal?

Set up your Rate

David: charges _______dollars for _______ hours of swimming lessons.

Rate= ==__________

An 8-ounce bag ____________chips costs $1.68. A 4-ounce bag of __________chips costs $0.88. Which is the better deal?

Example

#2

The new movie “Hunger Games” is expected to draw large crowds. Several cinemas have already started making package deals for movie tickets. In your groups determine which Theater has the best deal!

Mall of Georgia Regal Cinema

5 tickets for $112

Hollywood 24

7 tickets for $135.60

Proportions

- Basketball is to hoop as soccer ball to ____________.
- pumpkin is to Halloween as fireworks are to ________________
- Fish is to water as bird is to _________

These are all

PROPORTIONS!

4

2

2

6

4

2

4

8

__

__

__

__

__

__

__

__

=

=

=

4

1

2

1

1

2

2

3

A proportion is an equation that shows two equivalent ratios.

Reading Math

Read the proportion = as “two is to

one as four is to two.”

=

3

9

9

2

4

3

14

2

__

__

__

__

__

__

__

___

=

=

=

15

6

5

1

2

7

4

8

6 •3 =

9 • 2

7 •2 =

14 • 1

8 • 2 =

4 • 4

5 • 9 =

3 • 15

16= 16

18 = 18

14 = 14

45= 45

This is how

you prove proportions!

How would you find the missing value to complete proportion

Method #1

Criss Cross and algebra

Cross Multiply and Divide

- Cross multiply
- Set up equation
- Use inverse operations to solve for missing variable

5

6n

90

n

__

__

___

___

=

6

18

6

6

Criss-Cross and Solve!

Find the missing value in the proportion.

Find the cross products.

6 •n=

The cross products are equal.

5 • 18

6n= 90

n is multiplied by 6.

Divide both sides by 6 to undo the multiplication.

=

n = 15

Cross

Multiply

And

Divide!!!!

Method #2

Use guess and check

Caution: doesn’t work if the answer is a fraction!

Soooooooooooo

easyyyyyyyyyyy

Real World Application

f

f

1 tbsp

1 tbsp

____

_____

_____

____

4 gal

6 gal

6 gal

4 gal

According to the label, 1 tablespoon of plant fertilizer should be used per 6 gallons of water. How many tablespoons of fertilizer would you use for 4 gallons of water?

Let f be the amount of fertilizer for 4 gallons of water.

=

=

Write a proportion.

6 •f= 1 • 4

The cross products are equal.

2

2

6f

4

__

__

__

___

3

6

6

3

Continued

f is multiplied by 6.

6f= 4

Divide both sides by 6 to undo the multiplication.

=

Write your answer in simplest form.

f = tbsp

You would use tbsp of fertilizer for 4 gallons of water.

tbsp

tbsp

gal

gal

___

___

___

___

tbsp

tbsp

gal

gal

Caution!

In a proportion, the units must be in the same order in both ratios.

=

or

=

Fives pounds of sugar cookies cost $20 dollars, but he only needs 3 pounds