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8-1: Ratios and Equivalent Ratios

IWBAT read and write ratios and equivalent ratios

Ratio

Ratio – A comparison of two quantities

9 girls and 7 boys

Three ways to write ratios:

1. 9:72. 9 to 7

Equivalent Ratios

Two ratios that are equal to each other

97=9 ∙57 ∙5

=4535

97=4535

Are the ratios equivalent?

5:8 _____ 15:24

1) Rewrite as in fraction form and make equal to each other

58=1524

2) Cross-multiply (multiply diagonally)

120 = 120

3) If cross-products are equal, the ratios are equivalent (=). If cross-products are not equal ()

Examples

1)

108 = 108

2)

8096

3) 9 to 8 ____ 45 to 4098¿

40

360 = 360

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8-2 and 8-3: Proportions

IWBAT solve proportions using equivalent ratios using Cross-Products (Cross-Multiplication)

Do these ratios make a proportion?

45,1215

Use the cross-multi plying method

45,1215

60 = 60

Yes

Examples

1)

63 72

No

2)

54 = 54Yes

3)

320 = 320Yes

Find the missing number

23=𝑛21

1) Simplify vertically and/or horizontally, if possible

21=𝑛7

2) Cross-multiply 𝑛=14

3) Solve for , if needed

Examples

1) 2) 3) 4)

5) Three boxes of cereal cost $10.50. What does one box cost?

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8-4: Too Much or Too Little Information

IWBAT determine which information is missing and identify extraneous information in problems.

{8-5: Rates

IWBAT use rates to solve problems.

Rate – A ratio that compares two quantities that have different units of measure

Unit Rate – A rate where the second quantity is a unit of one (denominator)

Vocabulary

Find the Unit Rate

You travel 99 miles in 90 minutes. What is your average rate of speed in miles per hour?

1) Write as a rate in fraction form

99𝑚𝑖𝑙𝑒𝑠90𝑚𝑖𝑛𝑢𝑡𝑒𝑠

2) Divide 9.5

3) Rewrite as a phrase or as a fraction with labels

9.5 miles per minute

9.5𝑚𝑖𝑙𝑒𝑠𝑚𝑖𝑛𝑢𝑡𝑒

Examples

1) 90 miles in 75 minutes

2) 252 miles every 9 gallons

3) 48 chairs for 6 tables 4) 96 students in 3 classrooms

5) Respiration rate is the number of breaths you take per minute. You count 48 breaths in 3 minutes and your friend counted 34 breaths in 2 minutes. Who had the higher respiration rate?

{8-6: Unit Price

IWBAT find unit prices to determine the better buy.

Unit Price – The cost per item Similar to unit rate but money amount

always is the numerator Round to the nearest cent (hundredth), if

necessary

Vocabulary

Unit Price

Find the unit price. Round to the nearest cent.

$60.00 for 12 books

1) Write as a rate in fraction form with the price in the numerator

$ 6012𝑏𝑜𝑜𝑘𝑠

2) Divide $5

3) Rewrite as a phrase or as a fraction with labels

$5 per book

$ 5𝑏𝑜𝑜𝑘

Examples

1) $46.20 for 6 shirts 2) $14.28 for 12 lb of turkey

3) $1.47 for 1.5 lb broccoli 4) $0.60 for 12 oz of rolls

Which is the better buy?

12 bananas for $1.80 or 15 bananas for $2

1) Find the unit price for each item.

$1.8012𝑏𝑎𝑛𝑎𝑛𝑎𝑠

$215𝑏𝑎𝑛𝑎𝑛𝑎𝑠

2) Compare. The better buy is the cheaper (lesser) amount.

$ 0.15𝑏𝑎𝑛𝑎𝑛𝑎

$ 0.13𝑏𝑎𝑛𝑎𝑛𝑎

15 bananas for $2 is the better buy.

Examples

1) 3 tacos for $3.50 or 4 tacos for $5.00

2) 12 books for $119.40 or 6 books for $53.34

{8-7: Make a List

IWBAT solve problems by making an organized list

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8-8: Similar Figures

IWBAT use proportions to solve problems involving similar figures

Similar Figures – Figures that have the same shape but not necessarily the same size.

Vocabulary

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8-9: Scale Drawings

IWBAT interpret scale drawings.

Scale Drawing – a reduction or enlargement of an actual object.

Scale – a ratio that compares a measure on a drawing with the actual measure.

Vocabulary

{8-10: Using Maps

IWBAT use map scales and proportions to find actual distances