7-1 ratios and rates learn to write ratios and rates and to find unit rates

7-1 Ratios and Rates

Learn to write ratios and rates and to find unit rates.


Vocabulary

ratiosequivalent ratiosrateunit rate


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


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.

29 12___

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.


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

Reading Math29

12___


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 5:252__ Part to part


Additional Example 1B: Writing Ratios


dogs to total number of pets

or 7 to 14 or 7:14 714

__ Part to whole

2Rabbits

7Dogs

5Cats

Animals at the Vet


Additional Example 1C: Writing Ratios


total number of pets to cats

or 14 to 5 or 14:5145

__ Whole to part

2Rabbits

7Dogs

5Cats

Animals at the Vet


Check It Out: Example 1A


birds to total number of pets

3Snakes

9Hamsters

6Birds

Animals at the Vet

or 6 to 18 or 6:18 618

__ Part to whole


Check It Out: Example 1B


snakes to birds

or 3 to 6 or 3:6 3 6

__ Part to part

3Snakes

9Hamsters

6Birds

Animals at the Vet


Check It Out: Example 1C


total number of pets to hamsters

or 18 to 9 or 18:9189

__ Whole to part

3Snakes

9Hamsters

6Birds

Animals at the Vet


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.


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 =

36__

There is 1 diamond for every 2 spades.

36__ =

3 ÷ 36 ÷ 3____

=12__

36__ =

918

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

So , , and are equivalent ratios. 36__ 1

2__ 9

18 __

3 • 36 • 3

7-1 Ratios and RatesCheck 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 =

39__

There is 1 triangle for every 3 hearts.

39__ =

3 ÷ 39 ÷ 3____

=13__

39__ =

927

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

So , , and are equivalent ratios. 39__ 1

3__ 9

27 __

3 • 39 • 3


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 _____


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.


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.

7-1 ratios and rates learn to write ratios and rates and to find unit rates

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