1. 7-6 Percent Problems Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 7-6 Percent Problems Warm Up Write each decimal as a percent and fraction. 1. 0.38 2. 0.06 3. 0.2 38%, 6%, 20%, 19 50 __ 3 50 __ 1 5

3. 7-6 Percent Problems Problem of the Day Lucky Jim won $16,000,000 in a lottery. Every year for 10 years he spent 50% of what was left. How much did Lucky Jim have after 10 years? $15,625

4. 7-6 Percent Problems MA.6.A.5.1 Use equivalent forms of fractions, decimals, and percents to solve problems. Also MA.6.A.5.3 Sunshine State Standards

5. 7-6 Percent Problems To find the percent one number is of another, use this proportion: % 100 = is of Because you are looking for 45% of 420, 45 replaces the percent sign and 420 replaces “of.” The first denominator, 100, always stays the same. The “is” part is what you have been asked to find.

6. 7-6 Percent Problems Additional Example 1: Application First estimate your answer. Think: 35% =, which is close to, and 560 is close to 600. So about of the students participate in after-school sports. 35 100 ___ 1 3 __ 1 3 1 3 This is the estimate. 600 = 200 Think: “35 out of 100 is how many out of 560?” Helpful Hint There are 560 students in Ella’s school. If 35% of the students participate in after-school sports, how many students participate in after- school sports?

7. 7-6 Percent Problems Additional Example 1 Continued Now solve: s 560 ___ 35 100 ___ = 100 s = 35 560 100s = 19,600 100s 100 ____ 19,600 100 _____ = s = 196 Let s represent the number of students who participate in after- school sports. The cross products are equal. s is multiplied by 100. Divide both sides of the equation by 100 to undo multiplication. Since 196 is close to your estimate of 200, 196 is a reasonable answer. 196 students participate in after-school sports.

8. 7-6 Percent Problems Check It Out: Example 1 There are 480 students in Tisha’s school. If 70% of the students participate in the fundraising program, how many students participate is that ? 70 100 ___ x 480 ___ = 100x = 33,600; x = 336 students ;

9. 7-6 Percent Problems Additional Example 2: Application Johan is 25% of the way through his exercises. If he has exercised for 20 minutes so far, how much longer does he have to work out? is of __ % 100 ___ = 100 20 = 25 m 25% of the exercises are completed, so 20 minutes is 25% of the total time needed. The cross products are equal. 20 m __ 25 100 ___ = Set up a proportion. The “of” part is what you have been asked to find.

10. 7-6 Percent Problems Additional Example 2 Continued 2,000 = 25m 2,000 25 _____ 25m 25 ____ = 80 = m m is multiplied by 25. Divide both sides by 25 to undo multiplication. The time needed for the exercises is 80 min. So far, the exercises have taken 20 min. Because 80 – 20 = 60, Johan will be finished in 60 min.

11. 7-6 Percent Problems Check It Out: Example 2A Katie has read 35% of a book. If she has read 49 pages, how many more pages does Katie have left to read? 49 p __ 35 100 ___ = ;35p = 4,900; p = 140 pages 140 - 49 = 91 pages

12. 7-6 Percent Problems Check It Out: Example 2B Justin is 75% through washing and folding his laundry. If he has finished 6 loads, how many loads does he still need to do? 6 l __ 75 100 ___ = ;75 l = 600; l = 8 loads 8 - 6 = 2 loads

13. 7-6 Percent Problems Instead of using proportions, you can also multiply to find a percent of a number.

14. 7-6 Percent Problems Additional Example 3: Multiplying to Find a Percent of a Number 36% = 0.36 0.36 50 Write the percent as a decimal. Multiply using the decimal. 18 So 18 is 36% of 50. Find 36% of 50. 0 5 10 15 20 25 30 35 40 45 50 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Check Use a model to check the answer.

15. 7-6 Percent Problems Check It Out: Example 3A 20% of 140 0.2 140 = 28 Find the percent of each number.

16. 7-6 Percent Problems Check It Out: Example 3B 45% of 900 0.45 900 = 405 Find the percent of each number.

17. 7-6 Percent Problems Check It Out: Example 3C 80% of 30 0.8 30 = 24 Find the percent of each number.

18. 7-6 Percent Problems Check It Out: Example 3D 15% of 150 0.15 150 = 22.5 Find the percent of each number.

19. 7-6 Percent Problems Check It Out: Example 3E 75% of 360 0.75 360 = 270 Find the percent of each number.

20. 7-6 Percent Problems Check It Out: Example 3F 30% of 170 0.3 170 = 51 Find the percent of each number.