Ratios, Rates, and Unit Rates across the Universe

Ratios, Rates, and Unit Rates across the Universe

What is the difference between a ratio and a rate?

706.2.7 use ratios and proportions to solve problems

Ratios

Definition: A comparison of two numbers:

Parts to whole: Or

Parts to Parts:

Finding Missing Part of Ratio:

See how many times it takes to go from one fraction to the other.

Do the same thing to the top or bottom.

Comparing Ratios You can use fraction rules to compare

Or You can turn the ratios into decimals

Written As:Fraction, with :, and to

Examples:

8/35, 8:35, 8 to 35

Equivalent Ratios = Equivalent FractionsYou can multiply the top and bottom by the same # or reduce to get an

Equivalent ratio

RATIOS

A ratio makes a comparison. There are 3 green aliens and 4 purple aliens. The ratio of green aliens to

purple aliens is

3 to 4.

RATIOS

A ratio makes a comparison. The ratio of green aliens to total aliens is 3 to 7. The ratio of total aliens to purple

aliens is 7 to 4.

RATIOS

A ratio makes a comparison. Ratios

can be written in three different

ways.

3 to 4

3:4

3

4

Ratios

• Ratios can be written as a comparison of parts to parts or a comparison of parts to whole.

• Ex: 3 boys to 5 girls (not a true fraction)

• Ex: 3 boys to 8 students (true fraction)

Ratios

Definition: A comparison of two numbers:

Parts to whole: Or

Parts to Parts:

Written As:

Fraction, with :, and to(Out of : part to whole only)

Examples:

8/35, 8:35, 8 to 35

White Board Practice

Wins to LossesWins=17, Losses=14

Write the ratio three different ways:17:14 17 to 14 17/14

Now write a ratio three different ways for the wins to total games played.

17:31 17 to 31 17/31

Definition: A comparison of two numbers:

Parts to whole: Or

Parts to Parts:

Assessment Prompt

• What is a ratio?

• What are different ways to write a ratio?

Ratios

Definition: A comparison of two numbers:

Parts to whole: Or

Parts to Parts:

Written As:Fraction, with :, and to

Examples:

8/35, 8:35, 8 to 35

Equivalent Ratios = Equivalent FractionsYou can multiply the top and bottom by the same # or reduce to get an

Equivalent ratio

White Board PracticeWrite the ratio in simplest form and in an

equivalent form.For every 6 boys there are 10 girls.

3:5 12 to 20 60 to 100

Why would a fraction not be a good choice for this ratio?

Ratios

Definition: A comparison of two numbers:

Parts to whole: Or

Parts to Parts:

Finding Missing Part of Ratio:

See how many times it takes to go from one common part of a fraction to the other. Do the same thing to the top or bottom.

Comparing Ratios You can use fraction rules to compare

Or You can turn the ratios into decimals

Written As:Fraction, with :, and to

Examples:

8/35, 8:35, 8 to 35

Equivalent Ratios = Equivalent FractionsYou can multiply the top and bottom by the same # or reduce to get an

Equivalent ratio

Assessment Prompt

• How do you find the missing part of a ratio? 3/5 x/20

Real World Uses• Population: Ethnicity, gender, etc.

• Sports statistics: ERA, Batting Avg, Free Throw Percent.

• Probability: Odds of occurrences

• Comparison Shopping: items per package

White Board Practice

Who has the greater ratio of Rock CD’s to total CD’s?

Luis RaeRock = 9 Rock = 14Total = 11 Total = 18

Simply turn your fractions into decimals (divide) to see who has the greater amount.

Luis has the greater amount .81

White Board Practice

Who has the greater ratio of Rock CD’s to total CD’s?

Luis RaeRock = 9 Rock = 14Total = 11 Total = 18

You could also use cross products to see which is larger: 18 * 9 = 162 = Luis

11 * 14 = 154 = Rae, Luis has more.

Assessment Prompt

• Text a friend and tell them what a ratio is and how we compare them?

Rates

Unit Cost:Money goes on top because you are

Trying to find the cost per 1 unityou will turn the denominator into a

1 through division

Comparing Rates Compare rates like you would a fraction

Definition: A ratio that compares two different

Units of measurement30 pages : 20 minutes

Unit Rate:How many per 13 corndogs : $1

62 miles per hour

You can also find unit cost by dividing the cost by the number of items. $5 : 15 mini butterfingers = 5 ÷ 15 = $0.33 per 1 mini butterfinger

RATES

A rate is a ratio that compares quantities that

are measured in different units.

This spaceship travels at a certain speed. Speed is an example of a rate.

Speed can be measured in many different ways. This spaceship can travel

100 miles in 5 seconds. 100 miles in 5 seconds is a rate.

RATES

A rate is a ratio that compares quantities that

are measured in different units.

Rates are often written in fraction form.100 miles in 5 seconds is a rate.It can be written as…..

5

100 Miles

Seconds

RATES

A rate is a ratio that compares quantities that

are measured in different units.

One key word that often identifies a rate is PER.Miles per gallon, Points per free throw,slices per pizza, Sticks of gum per pack

What other examples of rates can your group think of?

Assessment Prompt

• What makes a rate different from a ratio?

• Is a rate a ratio? Is a ratio a rate?

Write two equivalent ratios:

5/3 =

Identify the rate:

3 boys: 12 students

4 pencils per 1 bag

Complete the ratios:

5/7 = x / 21

Write two equivalent ratios:

12/20 =

Identify the rate:

2 purple flowers: 1 white flower

350 miles per 5 hours

Compare the ratios

3/8 __ 4/9

Write two equivalent ratios:

15/35=

Identify the rate:

4 pepperoni slices: 3 cheese slices

5 gals per 1 bucket

Complete the ratios

4/11 = 16/X

111

3

2

3

2

3

2

Tic-Tac-Think: Simplifying Radical Expressions: Choose 3 questions that will total at least 5 points

End of Lesson

Activator

• Review: what are ratios and rates?

• In math, how much is a unit?

Rates

Definition: A ratio that compares two different

Units of measurement30 pages : 20 minutes

Unit Rate:How many per 11 corndog : $0.5062 miles per hour

Rates

Unit Cost:Money goes on top because you are

Trying to find the cost per 1 unityou will turn the denominator into a

1 through division

Comparing Rates Find the unit rate, the larger unit rate is

Bigger.

Definition: A ratio that compares two different

Units of measurement30 pages : 20 minutes

Unit Rate:How many per 13 corndogs : $1

62 miles per hour

You can also find unit cost by dividing the cost by the number of items. $5 : 15 mini butterfingers = 5 ÷ 15 = $0.33 per 1 mini butterfinger

White Board Practice

Convert the ratios to a rate80 miles traveled in 2 hours

40 miles : 1 Hour

24 oranges for $3.00

1 orange for $0.13

Assessment Prompt

• What is the difference between a rate and a unit rate?

Two ways to solve:

1. Making equivalent ratio to 1.

$15 / 3 bags = $? / 1 bag

2. Divide the numerator by the denominator:

$15 / 3 bags = $5

2. Key Points: $ should always be on top unless you are finding how much a $1 will buy.

Find the Unit Rate:

• $350/ 5 nights (solve using equivalent rates)

• $1.88 / 20 oz (solve using division)

• 90 miles / 3 hours (your choice)

Finding a rate from a unit rate

• This is real world: You know that 1 bag of dog food costs $5.68. You want to find the rate of 12 bags.

You start with a unit rate and work backwards:

Finding a rate from a unit rate

• This is real world: You can travel 3.8 km per hour. How far could you travel in 4 hours? How far in 270 minutes?

You start with a unit rate and work backwards:

Using unit rate to find a bargain

• You are buying chips for a party. You want to get the most bang for your buck so you want the best price per unit. You have two choices: $8.96 per 40 oz or $9.84 per 48 oz. Which bag of chips should you buy if you want the cheapest unit price?

What is the denominator of a unit rate?

• Explain the error and correct:

$36 $1 4 apples .11 apples

Worksheet

• Turn the camera on and do the worksheet “Is Bigger Always Better?”

Homework

WORKBOOK: pg. 69-70 all (that is a total of 21 problems if you count # 14 as two separate problems.)