Proportions
Unit 5 – Math 7
Warm-Up
At Cocoa Bean Chocolate Factory, 2 pounds of
their world-famous chocolate fudge sells for
$1.00. Use the ratio table to find the costs of
different amounts of fudge.
Fudge
(pounds)
1
2
3
4
6
10
11
Cost
(dollars)
0.50
1.00
1.50
2.00
3.00
5.00
5.50
Adapted from MathScape: Blue “Buyer Beware” R12
What if…
…We add a little more to this problem. If we
had said we wanted to know how much fudge
we could buy with $5.00, how many ways do we
know how to solve the problem?
X?10
X?5
Fudge
(pounds)
2
Cost
(dollars)
1.00
÷?2
10
Fudge
(pounds)
1
2
5.00
Cost
(dollars)
0.50
1.00
10
5.00
÷?2
X?10
X?5
1. Multiplication
2. Unit Rate
Adapted from MathScape: Blue “Buyer Beware” R12
Any others?
How about double number line diagrams?
Pounds of
fudge
0
2
4
6
8
10
Cost
(dollars)
0
1.00
2.00
3.00
4.00
5.00
Adapted from MathScape: Blue “Buyer Beware” R12
Let’s consider something new…
What are the three ways to write 2 pounds for
$1.00 as a ratio?
2 pounds to $1.00
2 pounds : $1.00
2 pounds
$ 1 . 00
Could we use the idea of equivalent ratios to
solve our problem?
Adapted from MathScape: Blue “Buyer Beware” R12
Equivalent Ratios
How many pounds of fudge can we buy for
$5.00?
X?5
2 pounds

10
? pounds
pounds
$ 1 . 00
$$55..00
00
X?5
Adapted from MathScape: Blue “Buyer Beware” R12
Equivalent Ratios
Let’s take a closer look at these ratios…
When two ratios are equivalent, their cross
products should be equivalent. Are they?
2 pounds
$ 1 . 00

10 pounds
$ 5 . 00
2  5  1  10
10  10
When this is true, the two equivalent ratios are
called a proportion.
Adapted from MathScape: Blue “Buyer Beware” R12
To solve proportions…
We can use –
- Cross products
- Double number lines
- Ratio tables
- Scale factors
- Unit rates
- Tape diagrams (when units of measurement
are equivalent)