7-1 ratios and rates warm up warm up lesson presentation lesson presentation problem of the day...

7-1 Ratios and Rates

Warm UpWarm Up

Lesson PresentationLesson PresentationProblem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

7-1 Ratios and Rates

Warm UpWrite each fraction in simplest form.1. 2.

3. 4.

26__ 1

3__ 4

16__ 1

4__

25 70___ 5

14__ 6

52__ 3

26__

7-1 Ratios and Rates

Problem of the DayWhat three consecutive odd numbers are factors of 105?3, 5, 7

7-1 Ratios and Rates

MA.6.A.2.2 Interpret and compare ratios and rates.

Sunshine State Standards

7-1 Ratios and Rates

Vocabularyratiosequivalent ratiosrateunit rate

7-1 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.

TrombonesHarpPercussionTrumpetsBassesViolas

36Horns14Clarinets58Double reeds35Flutes910Cellos1229Violins

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.

Notice that the ratio of violins to violas, isdifferent 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.

7-1 Ratios and Rates

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

Reading Math29

12___

7-1 Ratios and RatesAdditional Example 1A: Writing Ratios

Use the table to write the ratio.

cats to rabbits

2Rabbits7Dogs5Cats

Animals at the Vet

or 5 to 2 or 5:252__ Part to part

7-1 Ratios and RatesAdditional Example 1B: Writing Ratios

Use the table to write the ratio.

dogs to total number of petsor 7 to 14 or 7:14 7

14 __ Part to whole

2Rabbits7Dogs5Cats

Animals at the Vet

7-1 Ratios and RatesAdditional Example 1C: Writing Ratios

Use the table to write the ratio.

total number of pets to catsor 14 to 5 or 14:514

5__ Whole to part

2Rabbits7Dogs5Cats

Animals at the Vet

7-1 Ratios and Rates

3Snakes9Hamsters6Birds

Animals at the Vet

or 6 to 18 or 6:18 618

__

Also _31 or 1 to 3 or 1 : 3

Use the table to write each ratio.Check It Out: Example 1A

birds to total number of pets

7-1 Ratios and RatesCheck It Out: Example 1B

Use the table to write the ratio or rates.

snakes to hamstersor 3 to 9 or 3:9 3

9 __

3Snakes9Hamsters6Birds

Animals at the Vet

or 1 to 3 or 1 : 3 Also 13

_

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 RatesAdditional 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.

Possible answer : , and39__ 1

3__ 9

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.

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 = pricenumber 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 _____

7-1 Ratios and RatesAdditional 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.

7-1 Ratios and RatesCheck It Out: Example 3A

A 3-pack of juice boxes costs $2.10. A 9-pack costs $5.58. Which is the better deal?

$2.10 3

_____

The 9-pack is a better deal.

= $0.70 per box; = $0.62 per box $5.58 9

____

7-1 Ratios and RatesCheck It Out: Example 3B

A 24 oz bottle of apple juice costs $5.76. A 12 oz bottle of apple juice costs $3.84. Which is the better deal?

$5.76 24

_____

The 24 ounce bottle is a better deal.

= $0.24 per oz; = $0.32 per oz $3.84 12

____