Ratios and Rates€¦ · Ratios and Rates For example, you can use a ratio to compare the number of...

Ratios and Rates

Warm Up

Lesson Presentation

Problem of the Day

Lesson Quizzes

Ratios and Rates

Warm UpWrite each fraction in simplest form.

1. 2.

3. 4.

2

6__ 1

3__ 4

16__ 1

4__

25

70___ 5

14__ 6

52__ 3

26__

Ratios and Rates

Problem of the Day

What three consecutive odd numbers are factors of 105?

3, 5, 7

Ratios and Rates

Learn to write ratios and rates and to find

unit rates.

Ratios and Rates

Vocabulary

ratios

equivalent ratios

rate

unit rate

Ratios and Rates

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

Ratios and Rates

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.

2912___

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.

Ratios and Rates

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

Reading Math29

12___

Ratios and Rates

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 5:25

2__ Part to part

Ratios and Rates

Additional Example 1B: Writing Ratios


dogs to total number of pets

or 7 to 14 or 7:147

14__ Part to whole

2Rabbits

7Dogs

5Cats

Animals at the Vet

Ratios and Rates

Additional Example 1C: Writing Ratios


total number of pets to cats

or 14 to 5 or 14:514

5__ Whole to part

2Rabbits

7Dogs

5Cats

Animals at the Vet

Ratios and Rates

Check It Out: Example 1A


birds to total number of pets

3Snakes

9Hamsters

6Birds

Animals at the Vet

or 6 to 18 or 6:186

18__ Part to whole

Ratios and Rates

Check It Out: Example 1B


snakes to birds

or 3 to 6 or 3:63

6__ Part to part

3Snakes

9Hamsters

6Birds

Animals at the Vet

Ratios and Rates

Check It Out: Example 1C


total number of pets to hamsters

or 18 to 9 or 18:918

9__ Whole to part

3Snakes

9Hamsters

6Birds

Animals at the Vet

Ratios and Rates

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.

Ratios and Rates

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

=3

6__

There is 1 diamond for every 2 spades.

3

6__

=3 ÷ 3

6 ÷ 3____

=1

2__

3

6__

=9

18__

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

So , , and are equivalent ratios. 3

6__ 1

2__ 9

18__

3 • 3

6 • 3

Ratios and Rates

Check It Out: Example 2

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

There are 3 triangles and 9 hearts.

number of trianglesnumber of hearts

=3

9__

There is 1 triangle for every 3 hearts.

3

9__

=3 ÷ 3

9 ÷ 3____

=1

3__

3

9__

=9

27__

=If you triple the pattern, there will be 9 triangles for 27 hearts.

So , , and are equivalent ratios. 3

9__ 1

3__ 9

27__

3 • 39 • 3

Ratios and Rates

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_____

Ratios and Rates

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.


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.

Ratios and Rates

Check It Out: Example 3

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


3 pack_____

$2.10 ÷ 3

3 pack ÷ 3_________ Divide both

terms by 3.

$0.70

1 box_____ $0.70 for 1 juice

box.


9 pack_____

$5.58 ÷ 9

9 pack ÷ 9_________ Divide both

terms by 9.

$0.62

1 box_____ $0.62 for 1 juice

box.

The 9-pack of juice boxes is the better deal.

Ratios and Rates

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Ratios and Rates

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

__

Ratios and Rates

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

Ratios and Rates

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

Ratios and Rates

3. Using 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

Ratios and Rates

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


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