Unit Rates and Constants

Rates and Unit Rates

Multiple Choice

What is Constant of Proportionality?

• Rate

• Unit Rate

• Whole Numbers

• I don't Know

Multiple Choice

Which is the better buy?

2 flutes for $311.40

4 flutes for 684.80

• 2 flutes for $311.40

• 4 flutes for $684.80

Multiple Choice

Which is the better buy?

7 tons of soil for $7,089.60

8 tons of soil for $8,110.40

• 7 tons of soil

• 8 tons of soil

Rates and Unit Rates

Standards : 7.RP.1, 7.RP.2d

Rates and Unit Rates

Essential Question - How is finding a unit rate different from simplifying a fraction?

Rates and Unit Rates

Rate is a special Ratio in which the two terms are in different units example 3 pizzas for $19.99

Unit Rate - This is when rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour.

Rates and Unit Rates

Examples

800 words in 10 minutes (Rate)

800/10 = 80 words per minute (Unit Rate)

$37.29 for 2 pairs of jeans

$37.29/2 = $18.65 per jeans

Multiple Choice

Questions

What is the best better buy?

A 12.5 oz bag of Doritos for $3.79 or a 3 oz bag for $1.00

• A 3 oz bag of Doritos for $1.00

• A 12.5 oz bag of Doritos for $3.79

Multiple Choice

351 chairs in 27 rows ________ chairs in each row

• 14

• 15

• 13

Fill in the Blank

351 chairs in 27 rows

How many chairs in each row

351/27 = 13 chairs in each row

Multiple Choice

7 penguins for $188.88 ________ each

• $26.98

• $27.98

• $25.89

Open Ended

7 penguins for $188.88. Find the price of each penguin

$188.88/7 = $26.98

Unit Rate with Fractions

Jacob walks 1⁄2 mile in 1⁄4 hour. How far does he walk in one hour?

1/2 divide by 1/4

Keep, change, flip (kcf)

= 1/2 x 4/1 = 2 miles per hour

Unit rates with fractions cont

Caleb is painting his bedroom. It takes 1/3 gallon to cover 1/6 of a wall. How

much paint is needed to cover the entire wall?

1/3 divided by 1/6

keep, change, flip

1/3 x 6/1 = 2 gallons

Unit rates with fractions contd

A brownie recipe requires 1/3 cup of sugar for 1/4 batch of brownies. How

much sugar is needed for a whole batch of brownies?

keep, change, flip (kcf)

1/3 divided by 1/4

1/3 x 4/1 = 4/3 sugar for a whole batch of brownies

Multiple Choice

Susie ran 2/3 of a mile in 1/20 of an hour. What was Susie's rate of speed?

• 40 miles per hour

• 40/3 miles per hour

• 20/3 miles per hour

• 30 miles per hour

Multiple Choice

Jack made a half of a loaf of bread. He used 5/3

cup of flour. How much

flour will he need for a whole loaf of bread?

• 10/3 cups of flour

• 10 cups of flour

• 5/3 cups of flour

• 5 cups of flour

Multiple Choice

It took Jamie 3/4 of an

hour to complete 1/4

of a puzzle.

How many hours will it

take to complete a puzzle?

• 3 hours

• 3.5 hours

• 2 hours

• 1 hour

Multiple Choice

Angie painted 1/20 of a

fence in 1/2 an hour.

How long will it take

Angie to paint one

fence?

• 5 hours

• 10 hours

• 15 hours

• 20 hours

Multiple Choice

Write the ratio three different ways and simplify! 20 blue jays out of 35 birds

• 4 blue jays to 7 birds, 4/7, 4:7

• 4 blue jays to 7 birds, 7/4, 7:4

• 10 blue jays to 35 birds

• 10 blue jays to 15 birds, 4/7, 4:7

Multiple Choice

Write the ratio three different ways and simplify

12 circles to 8 squares

• 3 to 2, 3/2, 3:2

• 6 to 2, 3/1, 3:1

• 4 to 5, 4/5, 4:5

• 2 to 3, 2/3, 2:3

Multiple Choice

Ratio can be written as

• A fraction only!

• As a fraction and using a colon!

• Can be written using a colon only!

• Can be written using colon, fraction and words!

Multiple Choice

Simplify the ratio 10 apples to 20 oranges

• 1:3

• 1:4

• 1:2

• 1:1

Multiple Choice

The ratio of blue and green marbles is 5:6. If there are 40 blue marbles, how many green marbles are there?

• 40

• 36

• 48

• 52

Multiple Choice

Tell if the the following ratios are proportional

2/3 and 12/18

• No

• Yes

• Not sure

• I don't know

Multiple Choice

Tell if they are proportional

4/9 and 11/6

• Yes

• No

• Don't Know

• Not sure

Multiple Choice

Tell if the ratios are proportional

8/24 and 6/20

• No

• Yes

• I don't know

Multiple Choice

Tell if the ratios are proportional

2/7 and 6/21

• No

• Yes

• Don't know

Multiple Choice

Tell if the ratios are proportional?

4.8/6 = 8/10

• No

• Yes

• Don't Know

Multiple Choice

What is a constant of proportionality?

• A ratio

• The unit rate

• I don't know

• 0

Multiple Choice

What is the constant of proportionality when a car travels 60 miles in 3 hours and when the same car travels 120 miles in 6 hours?

• 10

• 30

• 40

• 20

Multiple Choice

What is the constant of proportionality for the equation y = 15x

• 25

• 10

• 15

• 5

Multiple Choice

What is the constant of proportionality?

• Unit rate

• rate

• Don't know

• 1

Multiple Choice

What is the constant of proportionality of the following ratios?

50/2, 100/4, 150/6, 200/8

• 20

• 30

• 40

• 25

Multiple Choice

From the equation y = kx

k and x stand for

• Constant of proportionality only

• Constant of proportionality and the variable x

• Variable only

• I don't know

Multiple Choice

In order for a set of data to be proportional, it must have a constant of proportionality(constant ratio) must be a straight line and start at the origin.

• No

• Yes

• Does not need to be a straight line

• I don't know

Multiple Choice

If the scale is 1 : 4 miles and measurement on drawing is 15 inches . What is the actual distance on the ground?

• 60 miles

• 40

• 30

• 20

Multiple Choice

If a scale reads 1 in : 10 miles, what is the distance on a drawing where the actual distance on the ground is 200 miles?

• 20 inches

• 20 miles

• 40 inches

• 49 mikes

Multiple Choice

The distance ,measured on the drawing is 5 inches and the actual distance on the ground is 100 feet. What is the scale of the drawing/

• 1in : 10 feet

• 1 in : 20 feet

• 1 in : 30 feet

• 1 in : 15 feet