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7-1 Ratios and Rates
7-1 Ratios and Rates
Warm Up
Problem of the Day
Lesson Presentation
Course
Course 1 1
7-1 Ratios and Rates
Warm Up
Write each fraction in simplest form.
2 1 4 1
1. __ __ 2. __ __
6 3 16 4
25
___ 5
__ 6
__ 3
__
3. 4.
70 14 52 26
Course 1
7-1 Ratios and Rates
Learn to write ratios and rates and to find unit
rates.
Course 1
7-1 Ratios and Rates
Vocabulary
ratios
equivalent ratios
rate
unit rate
Course 1
7-1 Ratios and Rates
For a time, the Boston Symphony Orchestra was
made up of 95 musicians.
Violins 29 Violas 12
Cellos 10 Basses 9
Flutes 5 Trumpets 3
Double reeds 8 Percussion 5
Clarinets 4 Harp 1
Horns 6 Trombones 3
You can compare the different groups by using
ratios. A ratio is a comparison of two quantities using
division.
Course 1
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.
29
___
Terms 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, ___ .
The order of the terms is important. 29
Ratios can be written to compare a part to a
part, a part to the whole, or the whole to a part.
Course 1
7-1 Ratios and Rates
Reading Math
29
Read the ratio ___ as “twenty-nine to
12
twelve.”
Course 1
7-1 Ratios and Rates
Course 1
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 Part to part
2
Course 1
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
__
or 7 to 14 or 7:14 Part to whole
14
Course 1
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
__
or 14 to 5 or 14:5 Whole to part
5
Course 1
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
__
or 6 to 18 or 6:18 Part to whole
18
Course 1
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 Part to part
6
Course 1
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
__
or 18 to 9 or 18:9 Whole to part
9
Course 1
7-1 Ratios and Rates
Write each ratio three different ways.
6 apples to 11 bananas
40 boys to 30 girls
Course 1
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.
Course 1
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 3
__ There are 3 diamonds
=
number of spades 6 and 6 spades.
__ = 3 ÷ 3 =
3 ____ 1
__ There is 1 diamond for
6 6÷3 2 every 2 spades.
__ = 3 • 3 =
3 9
__ If you triple the pattern,
6 6•3 18 there will be 9 diamonds
for 18 spades.
3 1 9
So __ , __ , and __ are equivalent ratios.
6 2 18
Course 1
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 3
__ There are 3 triangles
=
number of hearts 9 and 9 hearts.
__ = 3 ÷ 3 =
3 ____ 1
__ There is 1 triangle for
9 9÷3 3 every 3 hearts.
__ = 3 • 3 =
3 9
__ If you triple the pattern,
9 9•3 27 there will be 9 triangles
for 27 hearts.
3 1 9
So __ , __ , and __ are equivalent ratios.
9 3 27
Course 1
7-1 Ratios and Rates
Course 1
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.
price
_____________ $1.98
________
rate = = $1.98 for 2 liters
number of liters 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.
_____ $1.98 ÷ 2
$1.98 ________ $0.99 $0.99 for 1 liter
_____
unit rate = = =
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.
Course 1
7-1 Ratios and Rates
Course 1
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
_____ $5.46
_____
Write the rate. Write the rate.
3 rolls 6 rolls
$2.79 ÷ 3
_________ Divide both $5.46 ÷ 6
_________ Divide both
3 rolls ÷ 3 terms by 3. 6 rolls ÷ 6 terms by 6.
$0.93
_____ $0.91
_____
$0.93 for 1 roll. $0.91 for 1 roll.
1 roll 1 roll
The 6-pack of paper towels is the better deal.
Course 1
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
_____ $5.58
_____
Write the rate. Write the rate.
3 pack 9 pack
$2.10 ÷ 3
_________ Divide both $5.58 ÷ 9
_________ Divide both
3 pack ÷ 3 terms by 3. 9 pack ÷ 9 terms by 9.
$0.70
_____ $0.70 for 1 juice $0.62
_____ $0.62 for 1 juice
1 box box. 1 box box.
The 9-pack of juice boxes is the better deal.
Course 1
7-1 Ratios and Rates
A 6-ounce bag of raisins costs $2.26. An
8-ounce bag of raisins costs $3.20. Which
is the better buy? 8-ounce bag of raisins
Cory earns $36.00 for 6 hours of work.
Drew earns $24.00 for 3 hours of work.
Who has the better hourly rate of pay?
Drew
Course 1
7-1 Ratios and Rates
Lesson Quiz
Use the table to write
each ratio.
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
Course 1
7-1 Ratios and Rates
What is a ratio is.
How to write equivalent ratios.
How to find rates and unit rates.
Course 1
7-1 Ratios and Rates
Are there any questions on the
topics covered in class today?
What is a ratio again?
Course 1
