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Do Now: 1) Given triangle UAF with coordinates

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EQ: How do I use ratios to

compare numbers

Do Now:

1) Given triangle UAF with coordinates

U(O, 4), A(8, -9), and F(-IO, -12), find the image of point A after a reflection in the y-axis.

2) After a reflection in the y-axis, (-1,-1) is the image of point B. What is the original location of point B?

HWK: WB p 42, even, p43, odd:

5-1

Ratios, Rates and Unit Rates

Course 2

Learn to identify, write, and compare ratios and find units and compare unit rates, such as average speed and unit price..

M7P1.b Solve problems that arise in mathematics and in other contexts;

M7P1.d Monitor and reflect on the process

of mathematical problem solving

5-1

Ratios

Course 2

Insert Lesson Title Here

Vocabulary

A ratio is a comparison of two quantities by division.

A rate is a ratio that compares two quantities measured in different units.

A unit rate is a rate whose denominator is 1. To change a rate to a unit rate, divide both the numerator and denominator by the denominator.

5-1

Ratios

Course 2

Sometimes a ratio can be simplified. To simplify a ratio, first write it in fraction form and then simplify the fraction.

5-1

Ratios

Course 2

To compare ratios, write them as fractions with common denominators. Then compare the numerators.

5-2

Rates

Course 2

An average rate of speed is the ratio of distance traveled to time. The ratio is a rate because the units in the numerator and denominator are different.

5-1

Ratios

Course 2

In basketball practice. Kathlene made 17 baskets in 25 attempts. She compared the number of baskets she made to the total number of attempts she made by using the

ratio . A ratio is a comparison of two

quantities by division.

17

25

Kathlene can write her ratio of baskets made

to attempts in three different ways.

17

25

17 to 25

17:25

5-1

Ratios

Course 2

Twenty students are asked to choose their favorite music category. Eight chose pop, seven chose hip hop, and five chose rock. Write each ratio in all three forms.

A. rock to hip hop

The ratio of rock to hip hop is 5 to 7, which can be written as follows:

5

7

, 5 to 7, 5:7

B. hip hop to pop

The ratio of hip hop to pop is 7 to 8, which can be written as follows:

7

8

, 7 to 8, 7:8

5-1

Ratios

Course 2

Twenty students are asked to choose their favorite music category. Eight chose pop, seven chose hip hop, and five chose rock. Write each ratio in all three forms.

C. rock to pop and hip hop

The ratio of rock to pop is 5 to 8 and rock to hip hop is 5 to 7, which can be written as follows:

5

15

, 5 to 15, 5:15

5-1

Ratios

Course 2

Nineteen students are asked to choose their favorite sport. Nine chose rock climbing, four chose kite surfing, and six chose snow boarding. Write each ratio in all three forms.

A. snow boarding to rock climbing

The ratio of snow boarding to rock climbing is 6 to 9, which can be written as follows:

6

9

, 6 to 9, 6:9

B. kite surfing to snow boarding

The ratio of kite surfing to snow boarding is 4 to 6, which can be written as follows:

4

6

, 4 to 6, 4:6

5-1

Ratios

Course 2

Nineteen students are asked to choose their favorite sport. Nine chose rock climbing, four chose kite surfing, and six chose snow boarding. Write each ratio in all three forms.

C. rock climbing to kite surfing and snowboarding

The ratio of rock climbing to kite surfing is 9 to 4 and rock climbing to snow boarding is 9 to 6, which can be written as follows:

9

10

, 9 to 10, 9:10

5-1

Ratios

Course 2

On average, most people can read about 600 words in 3 minutes. Write the ratio of words to minutes in all three forms. Write your answer in simplest form.

words

minute

600

3

Write the ratio as a fraction.

=

words

minute

600 ÷ 3

3 ÷ 3

=

Simplify.

words

minute

200

1

For every minute, there are 200 words read.

=

The ratio of words to minutes is 200 to 1.

5-1

Ratios

Course 2

At Casitas Middle School there are 456 microscopes for 152 students. Write the ratio of microscopes to students in all three forms. Write your answer in simplest form.

microscopes

students

Write the ratio as a fraction.

456

152

=

microscope

students

456 ÷ 152

152 ÷ 152

=

Simplify.

microscope

students

3

1

For every microscope, there are 3 children.

=

The ratio of microscopes to students is 3 to 1.

5-1

Ratios

Course 2

Honey-lemon cough drops come in packages of 30 drops per 10-ounce bag. Cherry cough drops come in packages of 24 drops per 6-ounce bag. Compare the ratio of drops per ounces for each bag of cough drops.

3

1

drops

ounces

30

10

Write the ratios as fractions with common denominators.

=

=

Honey-lemon:

drops

ounces

24

6

4

1

=

Cherry:

=

Because 4 > 3 and the denominators are the same, the drops to ounces is greater in the bag of cherry cough drops.

5-1

Ratios

Course 2

Jelly beans come in small packages of 25 per 5 ounce package and large packages of 56 per 8 ounce package. Compare the ratio of jelly beans per ounce for each of the packages.

7

1

jelly beans

ounces

56

8

Write the ratios as fractions with common denominators.

=

=

Large:

jelly beans

ounces

25

5

5

1

=

Small:

=

Because 7 > 5 and the denominators are the same, jelly beans to ounces is greater in the small package.

5-2

Rates

Course 2

Find the rate.

A Ferris wheel revolves 35 times in 105 minutes. How many minutes does 1 revolution take?

Write a rate that compares minutes and revolutions.

105 minutes

35 revolutions

Divide the numerator and denominator by 35.

105 minutes ÷ 35

35 revolutions ÷ 35

3 minutes

1 revolution

Simplify.

The Ferris wheel revolves 1 time in 3 minutes.

5-2

Rates

Course 2

Find the rate.

Sue walks 6 yards and passes 24 security lights set along the sidewalk. How many security lights does she pass in 1 yard?

Write a rate that compares security lights and yards.

24 lights

6 yards

Divide the numerator and denominator by 6.

24 lights ÷ 6

6 yards ÷ 6

4 lights

1 yard

Simplify.

Sue passes 4 security lights in 1 yard.

5-2

Rates

Course 2

Find the rate.

A dog walks 696 steps in 12 minutes. How many steps does the dog take in 1 minute?

Write a rate that compares steps and minutes.

696 steps

12 minutes

Divide the numerator and denominator by 12.

696 steps ÷ 12

12 minutes ÷ 12

58 steps

1 minute

Simplify.

The dog walks 58 steps per minute.

5-2

Rates

Course 2

Find the rate.

To make 12 smoothies, Henry needs 30 cups of ice. How many cups of ice does he need for one smoothie?

Write a rate that compares cups of ice and smoothies.

30 cups of ice

12 smoothies

Divide the numerator and denominator by 12.

30 cups of ice ÷ 12

12 smoothies ÷ 12

2.5 cups of ice

1 smoothie

Simplify.

Henry needs 2.5 cups of ice per smoothie.

5-2

Rates

Course 2

Danielle is cycling 68 miles as a fundraising commitment. She wants to complete her ride in 4 hours. What should be her average speed in miles per hour?

68 miles

4 hours

Write the rate as a fraction.

68 miles ÷ 4

4 hours ÷ 4

Divide the numerator and denominator by the denominator

17 miles

1 hour

=

Danielle’s average speed should be 17 miles per hour.

5-2

Rates

Course 2

Rhett is a pilot and needs to fly 1191 miles to the next city. He wants to complete his flight in 3 hours. What should be his average speed in miles per hour?

1191 miles

3 hours

Write the rate as a fraction.

Divide the numerator and denominator by the denominator

1191 miles ÷ 3

3 hours ÷ 3

397 miles

1 hour

=

Rhett’s average speed should be 397 miles per hour.

5-2

Rates

Course 2

A unit price is the price of one unit of an item. The unit used depends on how the item is sold. The table shows some examples.

5-2

Rates

Course 2

Consumer Math Application

A 12-ounce sports drink costs $0.99, and a 16-ounce sports drink costs $1.19. Which size is the best buy?

Divide the price by the number of ounces (oz) to find the unit price of each size.

$0.99

12 oz

$1.19

16 oz

$0.08

oz

$0.07

oz

≈

≈

Since $0.07 < $0.08, the 16 oz sports drink is the best buy.

5-2

Rates

Course 2

A 1.5 gallon container of milk costs $4.02, and a 3.5 gallon container of milk costs $8.75. Which size is the best buy?

Divide the price by the number of gallons (g) to find the unit price of each size.

$4.02

1.5 gal

$8.75

3.5 gal

$2.68

gal

$2.50

gal

=

=

Since $2.50 < $2.68, the 3.5 gallon container is the best buy.

Ratios and Rates

5-1&2

Course 2

Insert Lesson Title Here

TOTD

A coin bank contains 16 quarters, 12 dimes, and 8 nickels.

1. nickels to quarters

2.On a school trip, Bus 1 has 3 teachers and 14 students. Bus 2 has 4 teachers and 28 students. Which bus has the greater ratio of teachers to students?

3. There are 220 calories in 5 crackers. Write the ratio of calories to crackers in all three forms. Write your answers in simplest form.