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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

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

29
Read the ratio ___ as “twenty-nine to
12
twelve.”

Course 1
7-1 Ratios and Rates

Course 1
7-1 Ratios and Rates
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
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
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
=
__ = 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
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
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

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