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A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.
1. How many people will 10 cups of rice serve?
2. How many cups of rice are needed to serve 45 people?
cups of rice number of people

2 6

3 9

10

45
A recipe says that 6 spring rolls will serve 3 people. Complete the table.

number of spring rolls number of people

6 3

30

40

28

cups of rice	number of people
2	6
3	9
10
	45

number of spring rolls	number of people
6	3
30
40
	28

2.3

Activity

Coco bread is a popular food in Jamaica. To make coco bread, a bakery uses 200 milliliters of coconut milk for every 360 grams of flour. Some days they bake bigger batches and some days they bake smaller batches, but they always use the same ratio of coconut milk to flour.

Complete the table as you answer the questions. Be prepared to explain your reasoning.

How many grams of flour do they use with 500 milliliters of coconut milk?
How many grams of flour do they use with 235 milliliters of coconut milk?
How many milliliters of coconut milk do they use with 450 grams of flour?
What is the proportional relationship represented by this table?

coconut milk (milliliters)	flour (grams)
200	360
500
375
	450

2.4

Activity

4 quarters are equal in value to 10 dimes.

How many dimes equal the value of 6 quarters?
How many dimes equal the value of 14 quarters?
What value belongs next to the 1 in the table? What does it mean in this context?

number of quarters	number of dimes
1
4	10
6
14

Student Lesson Summary

If the ratios between two corresponding quantities are always equivalent, the relationship between the quantities is called a proportional relationship.

This table shows different amounts of milk and chocolate syrup. The ingredients in each row, when mixed together, would make a different total amount of chocolate milk, but these mixtures would all taste the same.

Notice that each row in the table shows a ratio of tablespoons of chocolate syrup to cups of milk that is equivalent to .

About the relationship between these quantities, we could say:

tablespoons of chocolate syrup	cups of milk
4	1
6
8	2

12	3
1

The relationship between the amount of chocolate syrup and the amount of milk is proportional.
The table represents a proportional relationship between the amount of chocolate syrup and amount of milk.
The amount of milk is proportional to the amount of chocolate syrup.

We could multiply any value in the chocolate syrup column by to get the value in the milk column. We might call a unit rate, because cup of milk is needed for 1 tablespoon of chocolate syrup. We also say that is the constant of proportionality for this relationship. It tells us how many cups of milk we would need to mix with 1 tablespoon of chocolate syrup.

In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity. This number is called the constant of proportionality.

In this example, the constant of proportionality is 3.

In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity.

This table shows a proportional relationship between and . Each value of is 4 times a value of . This relationship can be written as .


2	8
3	12
5	20
10	40

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Introducing Proportional Relationships with Tables

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Introducing Proportional Relationships with Tables

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