7-1 ratios and rates warm up warm up lesson presentation lesson presentation problem of the day...

7-1 Ratios and Rates

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpWrite each fraction in simplest form.

1. 2.

3. 4.

26__ 1

3__ 4

16__ 1

4__

25 70___ 5

14__ 6

52__ 3

26__


Problem of the Day

What three consecutive odd numbers are factors of 105?

3, 5, 7


MAFS.6.NS.2.4 Interpret and compare ratios and rates.

FLorida State Standards


Vocabulary

ratiosequivalent ratiosrateunit rate


You can compare the different groups by using ratios. A ratio is a comparison of two quantities using division.

For a time, a local symphony orchestra was made up of 95 musicians.

Trombones

Harp

Percussion

Trumpets

Basses

Violas

36Horns

14Clarinets

58Double reeds

35Flutes

910Cellos

1229Violins


For example, you can use a ratio to compare the number of violins (29) with the number of violas (12). This ratio can be written in three ways.

Notice that the ratio of violins to violas, is

different from the ratio of violas to violins, . The order of the terms is important.

29 12___

29 12___

12 29___

29 to 12 29:12Terms

Ratios can be written to compare a part to a part, a part to the whole, or the whole to a part.


Read the ratio as “twenty-nine to twelve.”

Reading Math29

12___


Additional Example 1A: Writing Ratios

Use the table to write the ratio.

cats to rabbits

2Rabbits

7Dogs

5Cats

Animals at the Vet

or 5 to 2 or 5:252__ Part to part


Additional Example 1B: Writing Ratios


dogs to total number of pets

or 7 to 14 or 7:14 714

__ Part to whole

2Rabbits

7Dogs

5Cats

Animals at the Vet


Additional Example 1C: Writing Ratios


total number of pets to cats

or 14 to 5 or 14:5145

__ Whole to part

2Rabbits

7Dogs

5Cats

Animals at the Vet


3Snakes

9Hamsters

6Birds

Animals at the Vet

or 6 to 18 or 6:18 618

__

Also _3

1or 1 to 3 or 1 : 3

Use the table to write each ratio.

Check It Out: Example 1A

birds to total number of pets


Check It Out: Example 1B

Use the table to write the ratio or rates.

snakes to hamsters

or 3 to 9 or 3:9 3 9

__

3Snakes

9Hamsters

6Birds

Animals at the Vet

or 1 to 3 or 1 : 3 Also1

3 _


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.


Additional Example 2: Writing Equivalent Ratios

Write three equivalent ratios to compare the number of diamonds to the number of spades in the pattern.

There are 3 diamonds and 6 spades.

number of diamondsnumber of spades =

36__

There is 1 diamond for every 2 spades.

36__ =

3 ÷ 36 ÷ 3____

=12__

36__ =

918

__=If you triple the pattern, there will be 9 diamonds for 18 spades.

So , , and are equivalent ratios. 36__ 1

2__ 9

18 __

3 • 36 • 3

7-1 Ratios and RatesCheck It Out: Example 2

Write three equivalent ratios to compare the number of triangles to the number of hearts in the pattern.

Possible answer : , and3

9__ 1

3__ 9

27 __


A rate compares two quantities that have different units of measure. Suppose a 2-liter bottle of soda costs $1.98.

When the comparison is to one unit, the rate is called a unit rate. Divide both terms by the second term to find the unit rate.

When the prices of two or more items are compared, the item with the lowest unit rate is the best deal.

rate =price

number of liters_____________ $1.98

2 liters ________= $1.98 for 2 liters

unit rate =$1.98

2 _____ $1.98 ÷ 2

2 ÷ 2 ________= $0.99 for 1 liter=

$0.99 1 _____


Additional Example 3: Consumer Application

A 3-pack of paper towels costs $2.79. A 6-pack of the same paper towels costs $5.46. Which is the better deal?

Write the rate. $2.79 3 rolls _____

$2.79 ÷ 3 3 rolls ÷ 3 _________ Divide both

terms by 3.

$0.93 1 roll _____ $0.93 for 1 roll.

Write the rate. $5.46 6 rolls _____

$5.46 ÷ 6 6 rolls ÷ 6 _________ Divide both

terms by 6.

$0.91 1 roll _____ $0.91 for 1 roll.

The 6-pack of paper towels is the better deal.

7-1 Ratios and RatesCheck It Out: Example 3A

A 3-pack of juice boxes costs $2.10. A 9-pack costs $5.58. Which is the better deal?

$2.10

3 _____

The 9-pack is a better deal.

= $0.70 per box; = $0.62 per box $5.58

9 ____


Check It Out: Example 3B

A 24 oz bottle of apple juice costs $5.76. A 12 oz bottle of apple juice costs $3.84. Which is the better deal?

$5.76

24 _____

The 24 ounce bottle is a better deal.

= $0.24 per oz; = $0.32 per oz $3.84

12 ____


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz

Use the table to write each ratio.

1. tulips to daffodils

2. crocuses to total number of bulbs

3. total bulbs to lilies

4. A dozen eggs cost $1.25 at one market. At a

competing market, 1 dozen eggs cost $2.00.

Which is the better buy?

20:51

9:17

51:5

eggs from the first market

1

2__


1. Use the table to identify the ratio of lions to elephants.

A. 8:7

B. 8:12

C. 7:8

D. 7:12


Animals in a Zoo

Lions 8

Tigers 12

Elephants 7

Others 15


2. Use the table to identify the ratio of game CDs to total number of CDs.

A. 25:8

B. 17:8

C. 8:17

D. 8:25


Gina’s CD Collection

Music 5

Games 8

Cartoons 12


3. Use the table to identify the ratio of total number of grades to number of students with a C.

A. 9:30

B. 9:21

C. 21:9

D. 30:9


Grades on Final Exam

A 8

B 13

C 9


4. Jeff sells a pack of 36 pencils for $3.25. Betsy sells a pack of 12 pencils for $1.50. Which is the better buy?

A. a pack of 12 pencils from Betsy

B. a pack of 36 pencils from Jeff

C. Both

D. None


7-1 ratios and rates warm up warm up lesson presentation lesson presentation problem of the day...

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