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7-9

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

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7-9

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  1. 7-9 Percent Problems Course 1 Warm Up Problem of the Day Lesson Presentation

  2. 19 3 1 __ __ __ 50 50 5 Warm Up Write each decimal as a percent and fraction. 1.0.38 2. 0.06 3. 0.2 38%, 6%, 20%,

  3. 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. Learn to find the missing value in a percent problem.

  5. % 100 is of = To find the percent one number is of another, use this proportion: 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.

  6. 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 1 1 1 ___ __ __ __ 3 3 3 100 Additional Example 1: Application 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? • 600 = 200 This is the estimate. Helpful Hint Think: “35 out of 100 is how many out of 560?”

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

  8. First estimate your answer. Think: 70% = , which is close to , and 480 is close to 500. So about of the students participate in after school sports. • 500 = 375 70 3 3 3 ___ __ __ __ 100 4 4 4 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 in the fundraising program? This is the estimate.

  9. 100s s 70 33,600 _____ ___ ___ ____ 100 100 480 100 Check It Out: Example 1 Continued Now solve: Let s represent the number of students who participate in the fundraising program. = The cross products are equal. 100 •s = 70 • 480 100s= 33,600 s is multiplied by 100. Divide both sides of the equation by 100 to undo multiplication. = s = 336 Since 336 is close to your estimate of 375, 336 is a reasonable answer. 336 students participate in the fundraising program.

  10. is % 25 20 __ ___ ___ __ m 100 100 of 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? 25% of the exercises are completed, so 20 minutes is 25% of the total time needed. = Set up a proportion. The “of” part is what you have been asked to find. = The cross products are equal. 100 • 20= 25 •m

  11. 2,000 25m _____ ____ 25 25 Additional Example 2 Continued 2,000= 25m m is multiplied by 25. Divide both sides by 25 to undo multiplication. = 80 = m 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.

  12. is % 30 15 __ ___ ___ __ m 100 100 of Check It Out: 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? 30% of the exercises are completed, so 15 minutes is 30% of the total time needed. = Set up a proportion. The “of” part is what you have been asked to find. = The cross products are equal. 100 • 15= 30 •m

  13. 1,500 30m _____ ____ 30 30 Check It Out: Example 2 Continued 1,500= 30m m is multiplied by 30. Divide both sides by 30 to undo multiplication. = 50 = m 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.

  14. Instead of using proportions, you can also multiply to find a percent of a number.

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

  16. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 7 14 21 28 35 42 49 56 63 70 Check It Out: Example 3 Find 20% of 70. Write the percent as a decimal. 20% = 0.20 0.20 • 70 Multiply using the decimal. 14 So 14 is 20% of 70. Check Use a model to check the answer.

  17. 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? 86.8 379.4 30 min 18

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