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## 7-9

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**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**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**% 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.**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?”**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.**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.**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.**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**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.**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**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.**Instead of using proportions, you can also multiply to find**a percent of a number.**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.**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.**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