1. Ratios, Proportions

2. A ratio can be written in a variety of ways. You can use ratios to compare quantities or describe rates. Proportions are used in many fields, including construction, photography, and medicine. a:ba/ba to b

3. ProportionsProportions Two ratios that are equal

4. A proportion is an equation that states that two ratios are equal, such as:

5. In simple proportions, you can use this same approach when solving for a missing part of a proportion. Remember that both fractions must reduce to the same value. To determine the unknown value you must cross multiply. (3)(x) = (2)(9) 3x = 18 x = 6 Check your proportion (3)(x) = (2)(9) (3)(6) = (2)(9) 18 = 18 True!

6. So, ratios that are equivalent are said to be proportional. Cross Multiply makes solving or proving proportions much easier. In this example 3x = 18, x = 6. If you remember, this is like finding equivalent fractions when you are adding or subtracting fractions.

7. 2) Solve for x: 4 x 6 42 =

8. 3) Solve for x: 25 5 x 2 =

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

10. 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?

11. Solve the following problems. 4) If 4 tickets to a show cost $9.00, find the cost of 14 tickets. 5) A house which is appraised for $10,000 pays $300 in taxes. What should the tax be on a house appraised at $15,000.

12. Try one on your own… Jasmine bought 32 kiwi fruit for $16. How many kiwi can Jasmine buy if she only had $4? –First set up a proportion then solve for your variable. –Remember proportions are two equivalent ratios set equal to each other.

13. And another… Jenny was planning a trip to the United Arab Emirates. Before going, she did some research and learned that the exchange rate is 4 Dirhams for every $1. How many Dirhams would she get if she exchanged $5?

14. And one more… Shawna reduced the size of a rectangle to a height of 2 in. What is the new width if it was originally 24 in wide and 12 in tall?