1. SOLVING PROPORTIONS
Unit 6
CCMATH 7

2. Warm-Up
1. At Cocoa Bean Chocolate Factory, 2 pounds of their world-famous chocolate fudge sells for $ Use the ratio table to find the costs of different amounts of fudge.
Fudge (pounds) 1 2 3 4 11
Cost (dollars)
1.00
3.00
5.00 6 10
0.50
1.50
2.00
5.50
Adapted from MathScape: Blue “Buyer Beware” R12

3. 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 ?
÷ 2 ?
Fudge (pounds) 2
Cost (dollars)
1.00
5.00
Fudge (pounds) 1 2
Cost (dollars)
1.00
5.00 10 10
0.50
÷ 2 ?
X 10 ?
X 5 ?
1. Multiplication
2. Unit Rate
Adapted from MathScape: Blue “Buyer Beware” R12

4. Any others? How about double number line diagrams? Pounds of fudge 2 42 4 6 8 10
Cost (dollars)
1.00
2.00
3.00
4.00
5.00
Adapted from MathScape: Blue “Buyer Beware” R12

5. Let’s consider something new…
What are the three ways to write 2 pounds for $1.00 as a ratio? Could we use the idea of equivalent ratios to solve our problem?
2 pounds to $1.00 ,
, pounds : $1.00
Adapted from MathScape: Blue “Buyer Beware” R12

6. Equivalent Ratios How many pounds of fudge can we buy for $5.00? X 5 ?
Adapted from MathScape: Blue “Buyer Beware” R12

7. Equivalent Ratios
Let’s take a closer look at these ratios… When two ratios are equivalent, their cross products should be equivalent. Are they? When this is true, the two equivalent ratios are called a proportion.
Adapted from MathScape: Blue “Buyer Beware” R12

8. 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)

9. Take a look at
Mathscape, RATES, RATIOS, PERCENTS, and PROPORTIONS, Blue, “Buyer Beware”, Lesson 7, pages 20-21