1. Ratios and Proportions
Lesson 3-6
Ratios and Proportions

4. Objectives Determine whether two ratios form a proportion
Solve proportions

5. Vocabulary Ratio – a comparison of two numbers by division
Proportion – an equation stating that two ratios are equal
Extremes – the large and small numbers in a proportion
Means – the middle numbers in a proportion
Rate – ration of two measurements with different units of measure
Scale – ratio or rate using in modeling

6. Four Step Problem Solving Plan
Step 1: Explore the Problem
Identify what information is given (the facts)
Identify what you are asked to find (the question)
Step 2: Plan the Solution
Find an equation the represents the problem
Let a variable represent what you are looking for
Step 3: Solve the Problem
Plug into your equation and solve for the variable
Step 4: Examine the Solution
Does your answer make sense?
Does it fit the facts in the problem?

7. Example 1 Determine whether the ratios and form a proportion.
Answer: The ratios are equal. Therefore, they form a proportion.

8. Example 2
Use cross products to determine whether the pair of ratios below forms a proportion.
Write the equation.
Find the cross products.
Simplify.
Answer: The cross products are not equal, so the ratios do not form a proportion.

9. Example 3 Answer: Solve the proportion . Original equation
Find the cross products.
Simplify.
Divide each side by 8.
Answer:
Simplify.

10. Example 4
Bicycling The gear on a bicycle is 8:5. This means that for every eight turns of the pedals, the wheel turns five times. Suppose the bicycle wheel turns about times during a trip. How many times would you have to turn the pedals during the trip?
Explore Let p represent the number of times needed to crank the pedals.
Plan Write a proportion for the problem.
turns of the pedals
wheel turns

11. Example 4 cont Solve Original proportion Find the cross products.
Simplify.
Divide each side by 5.
Answer: 3896 = p
Simplify.

12. Example 5
The scale on a map of the United States is 1 and 3/8 inches = 750 miles. The distance, on the map, between Los Angeles and Washington, D.C., is about 3 and 7/8 inches. What is the distance in miles between the two locations?
changing fractions
1 3/8 in /8 in =
750 miles d miles
11/8 in /8 in =
750 miles d miles
map scale
cross multiplication
multiply by inverse
11/8 d = 31/8 (750)
d = (8/11) (31/8) (750)
cancel 8’s out
d = (31/11) (750) = 2, miles
Answer: The distance in miles between Los Angeles and Washington, D.C., is about 2,114 miles.

13. Summary & Homework Summary: Homework:
A ratio is a comparison of two numbers by division
A proportion is an equation stating that two ratios are equal
A proportion can be solved by finding the cross products
Remember the distributive property!
Homework:
pg 158: even