1. Bell Work: Simplify (-12) – (-3)

2. Answer: -9

3. Lesson 34: Proportions and Ratio Word Problems

4. Proportion. : a statement that two ratios are equal
Proportion*: a statement that two ratios are equal. The ratios 2/4 and 6/12 are equal and form a proportion.

5. Equal ratios reduce to the same ratio. Both 2/4 and 6/12 reduce to ½
Equal ratios reduce to the same ratio. Both 2/4 and 6/12 reduce to ½. Notice these multiplication relationships between the numbers in the proportion. 2 x 3 = 6 2 x 2 = 4 2 = 6 2 = x 3 = 12 6 x 2 = 12

6. One ratios in a proportion can be expressed as the other ratio by multiplying the terms by a constant factor. 2 x 3 =

7. We can use this method to test whether ratios form a proportion
We can use this method to test whether ratios form a proportion. For example, to park for 2 hours, a lot charges $3. to park for 3 hours, the lot charges $4. Time (hr) 2 3 Charge ($) 3 4 Is the time parked and the fee charged by the lot a proportional relationship?

8. Answer: No, the relationship is not proportional because the ratios are not equal. They do not reduce to the same ratio.

9. Example: Nora is paid $12 an hour
Example: Nora is paid $12 an hour. Is her pay proportional to the number of hours she works?

10. Answer: The ratio of pay to hours is constant. The ratio doesn’t change. The pay is proportional
Nora’s Pay
Hours
Pay 1
$12
12/1 2
$24
24/2 = 12/1 3
$36
36/3 = 12/1 4
$48
48/4 = 12/1

11. Example: Nelson has a paper route
Example: Nelson has a paper route. If he works by himself the job takes 60 minutes. If he splits the route with a friend, it takes 30 minutes. If two friends help, the job takes 20 minutes. Is the amount of time it takes to complete the route proportional to the number of people working?

12. Answer: Relationship is not proportional
Time for Paper Route
Number Working
Time
(min.)
Workers 1 60
60/1 2 30
30/2 = 15/1 3 20
20/3

13. We can use proportions to solve problems where one of the numbers in the proportion is missing. A variable represents the missing number in the proportion. 2 = 6 8 x

14. One way to find the missing number in a proportion is to use the multiple between the terms of the ratios. This method is like finding equivalent fractions. 2 x 3 = 6 2 = 6 8 x 8 x 3 = 24

15. By multiplying 2/8 by 3/3, we find that the missing term is 24
By multiplying 2/8 by 3/3, we find that the missing term is 24. below we show another relationship we can use to find a missing number in a proportion. 2 x 4 = 8 2 = 6 8 x 6 x 4 = 24 Again we find that the missing number is 24

16. Example: Solve 24 = 8 m 5

17. Answer: 24 = 8 m 5 8 x 3 = 24 5 x 3 = 15 m = 15

18. Ratio word problems can include several numbers, so we will practice using a table with two columns to sort the numbers. In one column we write the ratio numbers. In the other column we write the actual counts. We can use a ratio table to help us solve a wide variety of problems.

19. Example: The ratio of boys to girls in the class is 3 to 4
Example: The ratio of boys to girls in the class is 3 to 4. if there are 12 girls, how many boys are there?

20. Answer: 3 = b 4 12 b = 9
Ratio
Actual Count 3 b 4 12

21. Practice:
Which pair of ratios forms a proportion?
3/6, 6/9
3/6, 6/12
3/6, 6/3

22. Answer: B 3/6, 6/12

23. HW: Lesson 34 #1-30 Due Tomorrow