Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

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.

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? 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 __ • 600 = 200 This is the estimate. Helpful Hint Think: “35 out of 100 is how many out of 560?”

Additional Example 1 Continued Now solve: Let s represent the number of students who participate in after- school sports. 35 100 ___ s 560 ___ = 100 • s = 35 • 560 The cross products are equal. 100s = 19,600 s is multiplied by 100. 100s 100 ____ 19,600 100 _____ 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.

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

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. % 100 ___ is of __ = Set up a proportion. The “of” part is what you have been asked to find. 25 100 ___ 20 m __ = 100 • 20 = 25 • m The cross products are equal.

Additional Example 2 Continued m is multiplied by 25. 2,000 25 _____ 25m 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.

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? 35 100 ___ 49 p __ = ; 35p = 4,900; p = 140 pages 140 - 49 = 91 pages

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? 75 100 ___ 6 l __ = ; 75 l = 600; l = 8 loads 8 - 6 = 2 loads

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

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

Check It Out: Example 3A Find the percent of each number. 20% of 140 0.2 • 140 = 28

Check It Out: Example 3B Find the percent of each number. 45% of 900 0.45 • 900 = 405

Check It Out: Example 3C Find the percent of each number. 80% of 30 0.8 • 30 = 24

Check It Out: Example 3D Find the percent of each number. 15% of 150 0.15 • 150 = 22.5

Check It Out: Example 3E Find the percent of each number. 75% of 360 0.75 • 360 = 270

Check It Out: Example 3F Find the percent of each number. 30% of 170 0.3 • 170 = 51

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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

Lesson Quiz for Student Response Systems 1. Identify 35% of 260. A. 35 B. 91 C. 260 D. 295

Lesson Quiz for Student Response Systems 2. Identify 60% of 422. A. 253.2 B. 482 C. 362 D. 25320

Lesson Quiz for Student Response Systems 3. Ella has to draw a flowchart as a part of an assignment. She has drawn 40% of the flowchart in 10 minutes. How much longer will it take her to complete the flowchart? A. 10 min B. 25 min C. 15 min D. 35 min

Lesson Quiz for Student Response Systems 4. Of 80 sheep in a field, 65% are ewes. How many ewes are there in the field? A. 28 ewes B. 52 ewes C. 65 ewes D. 108 ewes