7-1 Ratios and Rates
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
7-1 Ratios and Rates
Warm Up
Write each fraction in simplest form.
2
1. __
6
25
___
3.
70
1
__
3
5
__
14
4
2. __
16
1
__
4
6
__
4.
52
3
__
26
7-1 Ratios and Rates
Problem of the Day
What three consecutive odd numbers
are factors of 105?
3, 5, 7
7-1 Ratios and Rates
Learn to write ratios and rates and to find
unit rates.
7-1 Ratios and Rates
Vocabulary
ratios
equivalent ratios
rate
unit rate
7-1 Ratios and Rates
For a time, a local symphony orchestra was made
up of 95 musicians.
Violins
Cellos
Flutes
Double reeds
Clarinets
Horns
29
10
5
8
4
6
Violas
Basses
Trumpets
Percussion
Harp
Trombones
12
9
3
5
1
3
You can compare the different groups by using
ratios. A ratio is a comparison of two quantities
using division.
7-1 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.
Terms
29
___
12
29 to 12
29:12
29
Notice that the ratio of violins to violas, ___ is
12
12 .
different from the ratio of violas to violins, ___
29
The order of the terms is important.
Ratios can be written to compare a part to a part,
a part to the whole, or the whole to a part.
7-1 Ratios and Rates
Reading Math
29 as “twenty-nine to
Read the ratio ___
12
twelve.”
7-1 Ratios and Rates
Additional Example 1A: Writing Ratios
Use the table to write the ratio.
Animals at the Vet
Cats
5
Dogs
7
Rabbits
2
cats to rabbits
5 or 5 to 2 or 5:2
__
2
Part to part
7-1 Ratios and Rates
Additional Example 1B: Writing Ratios
Use the table to write the ratio.
Animals at the Vet
Cats
5
Dogs
7
Rabbits
2
dogs to total number of pets
7
__
Part to whole
or 7 to 14 or 7:14
14
7-1 Ratios and Rates
Additional Example 1C: Writing Ratios
Use the table to write the ratio.
Animals at the Vet
Cats
5
Dogs
7
Rabbits
2
total number of pets to cats
14
__
Whole to part
or 14 to 5 or 14:5
5
7-1 Ratios and Rates
Check It Out: Example 1A
Use the table to write the ratio.
Animals at the Vet
Birds
6
Hamsters
9
Snakes
3
birds to total number of pets
6
__
Part to whole
or 6 to 18 or 6:18
18
7-1 Ratios and Rates
Check It Out: Example 1B
Use the table to write the ratio.
Animals at the Vet
Birds
6
Hamsters
9
Snakes
3
snakes to birds
3
__
or 3 to 6 or 3:6
6
Part to part
7-1 Ratios and Rates
Check It Out: Example 1C
Use the table to write the ratio.
Animals at the Vet
Birds
6
Hamsters
9
Snakes
3
total number of pets to hamsters
18
__
Whole to part
or 18 to 9 or 18:9
9
7-1 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.
7-1 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.
number of diamonds
number of spades
3
__
6
There are 3 diamonds
and 6 spades.
3 = 3
÷ 3 __
1
__
____
There is 1 diamond for
=
6
6÷3 2
every 2 spades.
If you triple the pattern,
3 = 3 • 3 = __
9
__
6
6•3
18 there will be 9 diamonds
for 18 spades.
3 , __
1 , and __
9 are equivalent ratios.
So __
6
2
18
=
7-1 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.
number of triangles
number of hearts
3
__
9
There are 3 triangles
and 9 hearts.
3 = 3
÷ 3 __
1
__
____
There is 1 triangle for
=
9
9÷3 3
every 3 hearts.
If you triple the pattern,
3 = 3 • 3 = __
9
__
9 • 3 27 there will be 9 triangles
9
for 27 hearts.
3 , __
1 , and __
9 are equivalent ratios.
So __
9
3
27
=
7-1 Ratios and Rates
A rate compares two quantities that have
different units of measure. Suppose a 2-liter bottle
of soda costs $1.98.
rate =
price
$1.98
_____________
________
=
number of liters
2 liters
$1.98 for 2 liters
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.
unit rate =
$1.98
÷2
$0.99
_____ $1.98
________
_____ $0.99 for 1 liter
=
=
2
2÷2
1
When the prices of two or more items are
compared, the item with the lowest unit rate is the
best deal.
7-1 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?
$2.79
_____
3 rolls
Write the rate.
$5.46
_____
6 rolls
Write the rate.
$2.79
÷3
Divide both
_________
3 rolls ÷ 3 terms by 3.
$5.46
÷6
Divide both
_________
6 rolls ÷ 6 terms by 6.
$0.93
_____
1 roll
$0.91
_____
1 roll
$0.93 for 1 roll.
$0.91 for 1 roll.
The 6-pack of paper towels is the better deal.
7-1 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?
$2.10
_____
3 pack
Write the rate.
$5.58
_____
9 pack
Write the rate.
$2.10
÷3
Divide both
_________
3 pack ÷ 3 terms by 3.
$5.58
÷9
Divide both
_________
9 pack ÷ 9 terms by 9.
$0.70
_____
1 box
$0.62
_____
1 box
$0.70 for 1 juice
box.
$0.62 for 1 juice
box.
The 9-pack of juice boxes is the better deal.
7-1 Ratios and Rates
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
7-1 Ratios and Rates
Lesson Quiz
Use the table to write
ratio.
each
1. tulips to daffodils 9:17
2. crocuses to total number of bulbs 20:51
3. total bulbs to lilies 51:5
4. A dozen eggs cost $1.25 at one market. At a
1
__
competing market, 1 dozen eggs cost $2.00.
2
Which is the better buy? eggs from the first market
7-1 Ratios and Rates
Lesson Quiz for Student Response Systems
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
7-1 Ratios and Rates
Lesson Quiz for Student Response Systems
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
7-1 Ratios and Rates
Lesson Quiz for Student Response Systems
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
7-1 Ratios and Rates
Lesson Quiz for Student Response Systems
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