2. Course 1 8-8 Percents, Decimals, and Fractions 6 th Grade Math HOMEWORK Page 424 #1-26 ANSWERS!

3. Course 1 8-9 Percent Problems 6 th Grade Math HOMEWORK Page 428 #1-14

4. Our Learning Goal for Chapter 8 Students will understand ratios, proportions, and percents by being able to write ratios, find unit rates, solve proportions, identify similar figures, find unknown measures, make scale drawings, understand relationships, and solve problems including those involving discounts, tips, sales tax, and simple interest.

5. Our Learning Goal Assignments Learn to write ratios and rates and to find unit rates (8-1) Learn to write and solve proportions (8-2) Learn to use proportions to make conversions within the customary system (8-3) Learn to use ratios to identify similar figures (8-4) Learn to use proportions and similar figures to find unknown measures (8-5) Learn to read and use map scale and scale drawings (8-6) Learn to write percents as decimals and as fractions (8-7) Learn to write decimals and fractions as percents (8-8) Learn to find the missing value in a percent problem (8-9) Learn to solve percent problems that involve discounts, tips, and sales tax (8-10)

6. 8-9 Percent Problems Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation

7. Warm Up Write each decimal as a percent and fraction. 1. 0.38 2. 0.06 3. 0.2 38%, 6%, 20%, Course 1 8-9 Percent Problems 19 50 __ 3 50 __ 1 5

8. 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 Course 1 8-9 Percent Problems

9. Today’s Learning Goal Assignment Learn to find the missing value in a percent problem. Course 1 8-9 Percent Problems

10. Course 1 8-9 Percent Problems To find the percent of one number is of another, use this proportion: % 100 = is of If 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.

11. Course 1 8-9 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?

12. Course 1 8-9 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.

13. Course 1 8-9 Percent Problems Try This: Example 1 There are 480 students in Tisha’s school. If 70% of the students participated in the fundraising program, how many students participated in the fundraising program? First estimate your answer. Think: 70% =, which is close to, and 480 is close to 500. So about of the students participated in the fundraising program. 70 100 ___ 3 4 __ 3 4 This is the estimate. 3 4 __ 500 = 375

14. Course 1 8-9 Percent Problems Try This: Example 1 Continued Now solve: s 480 ___ 70 100 ___ = 100 s = 70 480 100s = 33,600 100s 100 ____ 33,600 100 _____ = s = 336 Let s represent the number of students who participated in the fundraising program. The cross products are equal. s is multiplied by 100. Divide both sides of the equation by 100 to undo multiplication. Since 336 is close to your estimate of 375, 336 is a reasonable answer. 336 students participated in the fundraising program.

15. Course 1 8-9 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.

16. Course 1 8-9 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.

17. Course 1 8-9 Percent Problems Try This: Example 2 Phil is 30% of the way through his homework. If he has worked for 15 minutes so far, how much longer does he have to work? is of __ % 100 ___ = 100 15 = 30 m 30% of the exercises are completed, so 15 minutes is 30% of the total time needed. The cross products are equal. 15 m __ 30 100 ___ = Set up a proportion. The “of” part is what you have been asked to find.

18. Course 1 8-9 Percent Problems Try This: Example 2 Continued 1,500 = 30m 1,500 30 _____ 30m 30 ____ = 50 = m m is multiplied by 30. Divide both sides by 30 to undo multiplication. The time needed for the homework is 50 min. So far, the homework has taken 15 min. Because 50 – 15 = 35, Phil will be finished in 35 min.

19. Course 1 8-9 Percent Problems Instead of using proportions, you can also multiply to find a percent of a number.

20. Course 1 8-9 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. 17% = 0.17 0.17 95 Write the percent as a decimal. Multiply using the decimal. 16.15 So 16.15 is 17% of 95. A. Find 36% of 50. B. Find 17% of 95.

21. Course 1 8-9 Percent Problems Try This: Example 3 20% = 0.20 0.20 70 Write the percent as a decimal. Multiply using the decimal. 14 So 14 is 20% of 70. 12% = 0.12 0.12 83 Write the percent as a decimal. Multiply using the decimal. 9.96 So 9.96 is 12% of 83. A. Find 20% of 70. B. Find 12% of 83.

22. Lesson Quiz 1. Find 28% of 310. 2. Find 70% of 542. 3. Martha is taking a 100-question test. She has completed 60% of the test in 45 minutes. How much longer will it take her to finish the test? 4. Crystal has a collection of 72 pennies. If 25% of them are Canadian, how many Canadian pennies does she have? 379.4 86.8 Insert Lesson Title Here 30 min 18 Course 1 8-9 Percent Problems