1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 4.2 Solving Proportions

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Solve proportions. o Use proportions to solve problems.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Solving Proportions To Solve a Proportion 1.Find the cross products (or cross multiply). 2.Divide both sides of the equation by the coefficient of the variable. 3.Simplify.

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Solving Proportions Solve the proportion Solution Step 1: Step 2: Step 3:

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Solving Proportions Notes As you work through solving a proportion, write each new equation below the previous equation. Keep the “=”signs aligned (as shown in Example 1). This will help you organize the steps and avoid simple errors.

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Solving Proportions Find the value of y if Solution Step 1: Step 2: Step 3:

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Solving Proportions Find A if Solution Step 1:

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Solving Proportions (cont.) Step 2: Step 3:

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Here we first change the mixed number to the improper fraction Solve the proportion Solution Completion Example 4: Solving Proportions

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Completion Example 4: Solving Proportions (cont.) Step 1: 18

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Completion Example 4: Solving Proportions (cont.) Step 2: 18 Step 3:

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Problem Solving with Proportions To Solve a Word Problem by Using a Proportion 1.Identify the unknown quantity and use a variable to represent this quantity. 2.Set up a proportion in which the units are compared in the same order. (Make sure that the units are labeled so they can be seen to be in the right order.) 3.Solve the proportion.

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. A motorcycle will travel 352 miles on 11 gallons of gas. How many miles will this motorcycle travel on 15 gallons of gas? Solution Assign the variable: Let x = unknown number of miles. Example 5: Problems with Proportions The units are in the same order (miles to gallons) in each ratio. Set up the proportion:

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Solve the proportion: The motorcycle will travel 480 miles on 15 gallons of gas. Example 5: Problems with Proportions (cont.)

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. An architect draws the plans for a building by using a scale of inch to represent 10 feet. How many feet does 6 inches represent? Solution Assign the variable: Let y = unknown number of feet. Set up the proportion: Example 6: Problems with Proportions

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Solve the proportion: On these plans, 6 inches represents 120 feet. Example 6: Problems with Proportions (cont.)

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. A recommended mixture of weed killer is 3 capfuls for 2 gallons of water. How many capfuls should be mixed with 5 gallons of water? Solution Assign the variable: Let x = unknown number of capfuls of weed killer. Set up the proportion: Completion Example 7: Problems with Proportions

18. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Solve the proportion: _____ capfuls of weed killer should be mixed with 5 gallons of water. Completion Example 7: Problems with Proportions (cont.)

19. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Solve the following proportions. 1.2. 3.4.

20. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Use proportions to solve the following problems. 5. If 1 inch represents 35 miles on a map, how many miles do 4.4 inches represent? 6. You can buy 3 onions for $2.89 at the grocery store. What would be the cost of 9 onions?

21. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1.R = 60 2.x = 80 3.B = 6.75 4.x = 6 5.154 miles 6.$8.67