2.3 Proportional Tables
Common Core Standards
7.RP.2. Recognize and represent proportional relationships between
quantities.
a.  Decide whether two quantities are in a proportional relationship, e.g., by
testing for equivalent ratios in a table or graphing on a coordinate plane
and observing whether the graph is a straight line through the origin.
b. Identify the constant of proportionality (unit rate) in tables, graphs,
equations, diagrams, and verbal descriptions of proportional
relationships.
c. Represent proportional relationships by equations. For example, if total
cost t is proportional to the number n of items purchased at a constant
price p, the relationship between the total cost and the number of items
can be expressed as t = pn.
d. Explain what a point (x, y) on the graph of a proportional relationship
means in terms of the situation, with special attention to the points (0, 0)
and (1, r) where r is the unit rate.
WARM-UP (1)
Are the fractions equivalent? Show your work.
1 2
1)
=
3 6
1 3
=
2)
3 9
2 4
=
6 10
2 3
3)
=
6 9
4)
1 2 3
= =
5)
3 6 9
1 2 3 4
= = =
6)
3 6 9 10
Proportional Tables
Can there be more than two ratios or rates in a
proportional relationship?
3 6 9 12
= =
=
4 8 12 16
4
9
6
3
8
12
12
16
NOTES (2)
Two or more proportional relationships can be written
as a series of fractions or displayed in a table.
Examples
Are the ratios of the sides of the triangles a
proportional relationship? Explain your reasoning.
4
9
6
3
8
12
12
16
EXAMPLES (3)
Is the ratio of cost ($) to
apples (lbs) in the table a
proportional relationship?
Apples
(lbs)
Cost
($)
2
8
3
12
4
16
5
20
Is the ratio of oranges to
trees in the table a
proportional relationship?
Trees
Oranges
2
20
3
50
4
80
5
110
EXAMPLES (4)
Fill the table to complete
the proportional
relationship between
dollars earned and hours
worked.
Hours
2
Dollars
Earned
Fill the table to complete
the proportional
relationship between
cashews and peanuts.
Peanuts
2
24
20
36
30
4
Cashews
6
8
60
EXAMPLES (5)
Fill the table to complete the proportional relationship
between words read per minute.
Minutes
Words
3
600
7
1,000
9
NOTES (6)
To find the constant of proportionality from a table we
need to pay attention to the units or the answer can
be upside down.
Examples
Is the ratio of cashews to peanuts as shown in the
table a proportional relationship? If so, what is the
constant of proportionality?
Peanuts Cashews
12
4
15
5
18
6
21
7
EXAMPLES (7)
Is the ratio of miles traveled to gallons of gas
purchased as shown in the table a proportional
relationship? If so, what is the constant of
proportionality?
Gallons
Miles
2
50
4
100
6
150
NOTES (8)
Unfortunately, horizontal tables usually represent the
constant of proportionality upside down.
Examples
Is the ratio of miles to gallons a proportional relationship?
If so, what is the constant of proportionality?
Gallons
Miles
3 4 5
120 160 200
Is the ratio of length to width a proportional relationship?
If so, what is the constant of proportionality?
Width
Length
8
4
10 12 14
5 6 7
PRACTICE (9)
Is the ratio of green chocolate-coated candies to bags of
candy shown in the table a proportional relationship? If
so, what is the constant of proportionality?
Bags
Green
Candies
2
40
4
80
6
120
Is the ratio of cashews to peanuts a proportional
relationship? If so, what is the constant of
proportionality?
Peanuts
6
9
12
Cashews
2
3
4
PRACTICE (10)
Fill in the table to complete the proportional relationship.
Peanuts
Cashews
3
2
6
6
12
Trees
Apples
5
7
100 120
8
FINAL QUESTION (11)
Are the ratio of the sides of the rectangles in a
proportional relationship? Explain your reasoning.
Width
Length
4
6
5
7
7
10
9
5
4
6
9 10
12 20
12
20