1. Drill #32 Solve the following equations: Check your solutions!
– 0.97x = 0.6 – x 2.
3. x + (3 – x) = 2 – (x + 1)

2. Drill #33 Solve the following equations: Check your solutions!
x = x – 0.4 2.
3. x + 4 – x = 3(x + 1) – 2x

3. 2-6 Ratios and Proportions
Objective: to solve proportions by applying Means-Extremes Property of Proportions
You can use proportions to draw things to scale
Open Books to page 105

4. (1.) Ratios **
A ratio is a comparison of two numbers by division.
The ratio of x to y can be written
x to y x:y

5. (2.) Proportion ** An equation stating that two ratios are equal.
Examples:

6. Determine whether ratios form a proportion*
Ex1: 4/5 and 24/30
Ex1A: 6/10 and 2/5
Ex1B: 1/6 and 5/30

7. Means-Extremes Property of Proportions*
In a proportion, the product of the extremes is equal to the product of the means.
If = then ad = bc
Extremes Means
Comparing rational numbers

8. Use Cross Products*
Use cross products to determine whether each pair of ratios forms a proportion:
Ex2
Ex2A, Ex2B.

9. Solve Proportions*
To solve proportions that involve a variable use cross products to rewrite the proportion.
Ex3:
3A, 3B

10. Solving Complex Proportions*
When solving proportions that involve a sum or difference of a variable, you need to use the distributive property.
Ex:
Ex A, B: 2-6 Study Guide #4, 7

11. (3.) Rate **
The ratio of two measurements having different units of measure.
30 miles per gallon
50 miles per hour
10 meters per second
60 words per minute

12. Setting up Rate Proportions*
Example 4: Bicycle
Ex 4A: Exercise

13. (4.) Scale**
Ratio that is used when making a model to represent something that is too large or too small to be conveniently drawn at actual size.
The scale compares the size of the model to the actual size of the object being modeled.

14. Setting up Scale Proportions
Example 5: Crater Lake
Ex 5A: Airplanes

15. Making Oatmeal
Cooking instructions for Giant Old Fashioned Oatmeal calls for water, oats, and salt to be mixed in the proportions according to the chart below. If the proportions remain the same, how many cups of oats would be required to make:
a. 1 serving of oatmeal?
b. 5 servings of oatmeal?
Servings 2
Oats
1 Cup
Water
2 Cups
Salt
½ tsp