This document outlines ratios, proportions, and how to solve ratio and proportion problems. It discusses: - What a ratio is and how ratios are expressed and simplified by reducing to lowest terms. - Properties of proportions including the cross product property (ad = bc) and reciprocal property. - Examples of setting up and solving proportions for an unknown variable using the cross product property. - An example problem walking through setting up and solving a multi-step ratio and proportion word problem about how many gallons of gas Mr. Yu uses in a week for his commute to school.

1. Section 3.6 Ratios and Proportions

7. More examples… = = = = =

8. Now, on to proportions! What is a proportion? A proportion is an equation that equates two ratios The ratio of dogs and cats was 3/2 The ratio of dogs and cats now is 6/4 =3/2 So we have a proportion :

9. Properties of a proportion? 2x6=12 3x4 = 12 3x4 = 2x6 Cross Product Property

11. Properties of a proportion? Let’s make sense of the Cross Product Property… For any numbers a, b, c, d:

13. How about an example? Solve for x: 7(6) = 2x 42 = 2x 21 = x Cross Product Property

14. How about another example? Solve for x: 7x = 2(12) 7x = 24 x = Cross Product Property Can you solve it using Reciprocal Property? If yes, would it be easier?

15. Can you solve this one? Solve for x: 7x = (x-1)3 7x = 3x – 3 4x = -3 x = Cross Product Property Again, Reciprocal Property?

16. Now you know enough about properties, let’s solve the Mysterious problems! If Mr. Yu’s car gets 30 miles/gallon , how many gallons of gas does Mr. Yu needs to commute to school everyday? 5 miles to school 5 miles to home Let x be the number gallons we need for a day: Can you solve it from here? x = Gal

17. So he uses up 1/3 gallon a day. How many gallons does he uses for a week? 5 miles to school 5 miles to home Let t be the number of gallons we need for a week: Gal What property is this?

18. So Mr. Yu uses up 5/3 gallons a week (which is about 1.67 gallons ). Consider if the price of gas is 3.69 dollars/gal , how much would it cost for a week? Let s be the sum of cost for a week: 5 miles to school 5 miles to home 3.69(1.67) = 1s s = 6.16 dollars

19. So what do you think? 10 miles Mr. Yu pays about 6 bucks a week just to get to school! What about weekends? If he travels twice as much on weekends, say drives 10 miles to the Mall and 10 miles back, how many gallons does he need now? How much would it cost totally? How much would it cost for a month? 5 miles Think proportionally! . . . It’s all about proportions!

20. ON YOUR HOMEWORK! PAGE: 158 # 20 – 44 EVEN