1.3 Tables of Ratios

​Tables of Ratios
Tutorial

​Objective
In this lesson, you will make tables of equivalent ratios and use them to compare ratios.

​Introduction

Roger's father visits an electronics superstore to check out cell phone plans from different telephone companies. Out of curiosity, Roger tags along with his father. Roger's father narrows his choice down to two companies, Dial It Up and Ring Ring. Dial It Up sells data plans at $16 for 2 gigabytes, and Ring Ring sells data plans at $9 for 1 gigabyte. Roger's father finally decides that Dial It Up is the better option and buys a smart phone with the Dial It Up plan for 4 gigabytes. Roger wants to understand how his father decided which plan was better. In this lesson, you will see how Roger's father compared the two plans and made his decision.

Multiple Choice

The table shows the number of miles Ken's car travels and the number of gallons of gas that it uses to travel that distance. What is the equivalent ratio in the table?

• 30:1

• 15:1

• 10:2

• 15:2

​Let's look at how to complete a table of ratios if one column is already filled in.

Matt's roommate Zac owns a car that gets 10 miles per gallon. In the table's empty cells, we need to fill in the number of miles for each number of gallons.

 

​Now let's see how to complete a table of ratios using any number. Say that Laurie wants to buy 9 cartons of fruit juice concentrate. The store offers a discount of $2 on every 3 cartons of concentrate. Laurie wants to know how much her discount will be. You can create a table of ratios as shown to find the discount on 9 cartons. But you don't need to fill in all the values for the number of cartons from 3 to 9 to get the answer. The simplest form of the ratio of the number of cartons to the discount in dollars is 3 : 2. Look at the table that you need to create to compare the number of cartons and the discount. The values that go into the first row of the table are the numbers in the simplest form of the ratio.

​Let's fill in the rest of the table.

Activity

​Question 1

Comparing Data Plans

In this part of the activity, you will use tables of ratios to learn how Roger’s father compared the data plans that Dial It Up and Ring Ring offer.

Dropdown

Part A: Roger’s father knows that Dial It Up sells data plans at $16 for 2 gigabytes and Ring Ring sells data plans at $9 for 1 gigabyte. The ratio of gigabytes to price is ​

Select answer

for Dial It Up and ​

Select answer

for Ring Ring.

Labelling

Part B: Assuming that the ratio of gigabytes to price for each company is fixed, fill in the table below.

Drag labels to their correct position on the image

32

54

20

8

24

50

26

48

40

45

Labelling

Part B: Assuming that the ratio of gigabytes to price for each company is fixed, fill in the table below.

Drag labels to their correct position on the image

54

45

50

52

36

28

27

29

18

20

Dropdown

Part C: Roger’s father wants to get a 4-gigabyte plan.

Dial it Up charges ​

Select answer

for 4 gigabytes, and Ring Ring charges ​

Select answer

for the same amount of data. The difference of the plan prices is ​

Select answer

Open Ended

Part D: Which company offers a better data plan? Explain your answer

Activity

​Question 2

Comparing Text Message Plans

Roger’s father also compares the text plans from the two companies. He knows that Dial It Up charges $5 for 100 text messages and Ring Ring charges $8 for 200 text messages.

Dropdown

Part A: What is the ratio of the number of text messages to the price in dollars offered by each company?

Roger’s father also compares the text plans from the two companies. He knows that Dial It Up charges $5 for 100 text messages and Ring Ring charges $8 for 200 text messages. The ratio of the number of text messages to the cost in dollars is ​

Select answer

: ​

Select answer

for Dial It Up and ​

Select answer

: ​

Select answer

for Ring Ring.

Labelling

Part B: Assuming that the ratio of the number of text messages to price is the same for both companies, fill in the table below.

Drag labels to their correct position on the image

20

55

50

40

25

45

35

10

15

30

Labelling

Part B: Assuming that the ratio of the number of text messages to price is the same for both companies, fill in the table below.

Drag labels to their correct position on the image

20

50

24

16

12

35

4

40

45

Multiple Choice

Part C: Compare the rates for different numbers of texts. If Roger’s father wants to get a 600-text message plan, what is the difference in price for the Dial It Up and Ring Ring plans?

• $6

• $4

• $5

• $10

• $8

Open Ended

Part D: Which company offers a better text plan? Explain your answer.

Activity

​Question 3

Comparing Call Plans

While they are at the electronics store, Roger’s father compares the calling plans that Dial It Up and Ring Ring offer. He found out that Dial It Up charges $20 for 100 minutes and Ring Ring charges $50 for 200 minutes.

Drag and Drop

Comparing Call Plans

While they are at the electronics store, Roger’s father compares the calling plans that Dial It Up and Ring Ring offer. He found out that Dial It Up charges $20 for 100 minutes and Ring Ring charges $50 for 200 minutes.

Part A: Assuming that the ratio of the number of minutes of talk time to price offered by both companies is fixed, fill in the table below.

Drag these tiles and drop them in the correct blank above

Labelling

Comparing Call Plans

While they are at the electronics store, Roger’s father compares the calling plans that Dial It Up and Ring Ring offer. He found out that Dial It Up charges $20 for 100 minutes and Ring Ring charges $50 for 200 minutes.

Part A: Assuming that the ratio of the number of minutes of talk time to price offered by both companies is fixed, fill in the table below.

Drag labels to their correct position on the image

70

30

40

50

120

90

60

110

80

100

Labelling

Comparing Call Plans

While they are at the electronics store, Roger’s father compares the calling plans that Dial It Up and Ring Ring offer. He found out that Dial It Up charges $20 for 100 minutes and Ring Ring charges $50 for 200 minutes.

Part A: Assuming that the ratio of the number of minutes of talk time to price offered by both companies is fixed, fill in the table below.

Drag labels to their correct position on the image

75

125

90

30

150

50

110

70

100

25

Open Ended

Part B: Based on your comparison of the unit costs of data, text messages, and calls from Dial It Up and Ring Ring, which company offers a better choice if Roger’s father considers a plan for data and calls, but not text messages?

Open Ended

Self-Evaluation

How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

​In the Lesson Activity, you calculated ratios from tables of values and used equivalent ratios to complete tables. You also compared two tables of ratios to figure out the better cell plan option using information about plan costs and amounts of usage. Now you know how Roger's father compared the plans from the two companies and decided that Dial It Up was better suited to his needs than Ring Ring.

​Now that you know how to complete and use tables to compare ratios, let's look at another example. The two tables list the gas mileage of Matt's and Zac's cars. Matt and Zac are planning to drive 120 miles to the beach for the weekend but haven't decided whose car to take. They want to use the car that gets the best gas mileage. They can make their decision by comparing the mileage of Matt's car with the mileage of Zac's car in the given tables of ratios.
Because a table of ratios contains equivalent ratios, we'll find a number to multiply each of the first rows by to get to 120 miles. We'll use this method to find the number of gallons of gas each car requires for the 120-mile trip. The car that needs fewer gallons of gas is the one that Matt and Zac will use.

​To compare the gas mileage of Matt's and Zac's cars, we start by adding a new row in each table and filling in the value of 120 in the column for miles.
Matt's car runs 40 miles on 2 gallons of gas. The number of gallons of gas it needs to run 120 miles is the unknown quantity in the equal ratios 40 : 2 = 120 : __.
We find the number that is multiplied by 40 to get 120:
40 × __ = 120
40 × 3 = 120.
Now we multiply the number of gallons of gas needed to drive 40 miles, 2, by 3 to find the number of gallons of gas needed to drive 120 miles: 2 × 3 = 6. Matt's car would use 6 gallons of gas for the 120-mile trip.
Zac's car travels 30 miles on 3 gallons of gas. Again, we can write the number of gallons of gas that Zac's car needs as an unknown quantity in the equal ratios 30 : 3 = 120 : __.
Then we find the number that is multiplied by 30 to get 120:
30 × __ = 120
30 × 4 = 120.
Now we multiply the number of gallons of gas needed to drive 30 miles, 3, by 4 to find the number of gallons of gas needed to drive 120 miles: 3 × 4 = 12. Zac's car would need 12 gallons of gas for the 120-mile trip.
Matt's car needs much less gas for the trip than Zac's car, so it's a better choice for the trip to the beach.

Open Ended

Giselle is baking cookies. The recipe calls for 2 eggs for every 3 cups of flour. What are the amounts needed for larger batches of cookies? Drag the items on the left to the correct location on the right.

Multiple Choice

Compare the price per dozen eggs at the local grocery store and at the supermarket. Edward bought 8 dozen eggs at the supermarket. How much did he save buying eggs at the supermarket instead of the local store?

• 6

• 8

• 10

• 12

​Summary

In this lesson, you learned how to create and fill tables of ratios and compare them to find the best option possible. Knowing how to use and compare ratios is useful in situations such as measuring ingredients in recipes, comparing prices and discounts when shopping, and determining unit rates.

Comparing ratios can help us make good decisions when we have to choose between different options. For example, before buying groceries that are on sale, it's a good idea to check the unit price on different brands to see if the sale item really offers the best price. And when choosing a car, you can use ratios to compare the gas mileage of different cars to select the best option.
 

​Congratulations!
You have completed the tutorial
Tables of Ratios.