Lesson 1: Ratios, rates, and proportions

Pepper has 3 hats and 2 scarves. What are two ways you can write this ratio?

2 : 3 or 2/3

A recipe calls for 3 cups of flour for every 1 cup of water, but we want to use 6 cups of flour. Write a proportion to see how much water we’d use for 6 cups of flour

3 cups flour/1 cup water = 6 cups flour/x cups water

A bird flies 45 meters in 3 seconds. Write a proportion to find the rate of the bird flying

45/3

A ratio is comparing the amount of two things. What kind of ratio is this?

Part to part ratio

A ratio is comparing the amount of one thing to the sum of all things. What kind of ratio is this?

Part to whole ratio

A high school randomly selected 50 students to take a survey about extending their lunch period. Of students selected for the survey, 14 were freshmen and 13 were sophomores

13:14 is what kind of ratio?

Part to part ratio

A high school randomly selected 50 students to take a survey about extending their lunch period. Of students selected for the survey, 14 were freshmen and 13 were sophomores.

13:50 is what kind of ratio?

Part to whole ratio

A high school randomly selected 50 students to take a survey about extending their lunch period. Of students selected for the survey, 14 were freshmen and 13 were sophomores.

14:50 is what kind of ratio, and what is its simplified form?

Part to whole, 7:25

A bag is filled with red marbles and blue marbles. There are 54 total marbles in the bag, and 1/3 of the marbles are blue.

What is the ratio of red marbles to the total marbles?

2/3

A bag is filled with red marbles and blue marbles. There are 54 total marbles in the bag, and 1/3 of the marbles are blue.

What is the ratio of red marbles to blue marbles?

2 : 1

A bag is filled with red marbles and blue marbles. There are 54 total marbles in the bag, and 1/3 of the marbles are blue.

How many red marbles are in the bag?

36

9 markers cost $11.50. How much would 7 markers cost? Write a proportion

Ether one of these answers are good

We're making cookies, and the recipe calls for 1 cup of sugar for every 3 cups of flour. What if we want to use 9 cups of flour: how much sugar do we need? Make a proportion

1/3 = x/9

We're making cookies, and the recipe calls for 1 cup of sugar for every 3 cups of flour. What if we want to use 9 cups of flour: how much sugar do we need? Make a proportion and solve

3 cups of sugar

For a proportion to work, it must keep the same units either on the ___ side of the equation or on the ____ side of the divisor line

Same, same

There are 340 students at Du Bois Academy. If the student-to-teacher ratio is 17: 2, how many teachers are there? Write the proportion

340/x = 17/2

There are 340 students at Du Bois Academy. If the student-to-teacher ratio is 17: 2, how many teachers are there? Write a proportion and solve

40 teachers

Jayda takes 3 hours to deliver 189 newspapers on her paper route. How many newspapers does she deliver per hour?

63

Building A is 140 feet tall, and Building B is 85 feet tall. The ratio of the heights of Building A to Building B is equal to the ratio of the heights of Building C to Building D. If Building C is 90 feet tall, what is the height of Building D to the nearest foot?

Write a proportion

140/85 = 90/x

Building A is 140 feet tall, and Building B is 85 feet tall. The ratio of the heights of Building A to Building B is equal to the ratio of the heights of Building C to Building D. If Building C is 90 feet tall, what is the height of Building D to the nearest foot?

Write a proportion and solve (round answer)

55 feet

The 36-inch tires on a pickup truck have a circumference of 9.42 feet. To the nearest whole rotation, how many rotations must the tires make for the truck to travel 2 miles in straight line? (1 mile = 5,280 feet)

1,121 miles