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
Use the table to write the ratio.
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
Use the table to write the ratio.
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
Use the table to write the ratio.
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
Use the table to write the ratio.
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
Use the table to write the ratio.
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.
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.
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?
Write the rate.$2.10
3 pack_____
$2.10 ÷ 3
3 pack ÷ 3_________ Divide both
terms by 3.
$0.70
1 box_____ $0.70 for 1 juice
box.
Write the rate.$5.58
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
Lesson Quiz for Student Response Systems
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
Lesson Quiz for Student Response Systems
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
Lesson Quiz for Student Response Systems
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
Lesson Quiz for Student Response Systems