6-3 Percents Greater Than 100% or Less Than 1% 6-3 1. Plan What You’ll Learn Check Skills You’ll Need For help, go to Lesson 6-1. Lesson Preview OBJECTIVE To use percents PowerPoint 1 Model each percent. 1–3. See below left. greater than 100% or less than 1% 1. 40% 2. 1% 3. 100% Check Skills You’ll Need Writing and Modeling Percents ...And Why Write each ratio as a percent. Lesson 6-1: Examples 2, 4. Extra To find a percent in the Practice p. 689. 1 1% 49 98% 19 2 8% U.S. House, as in Example 4 4.100 5.50 6.20 95% 7. 25 Lesson Resources OBJECTIVE Interactive lesson includes instant self-check, tutorials, and activities. 1 Using Percents Greater Than 100% or Less Than 1% Teaching Resources Practice, Reteaching, Enrichment 1. A percent is a ratio that compares a number to 100. If the number Reaching All Students compared to 100 is greater than 100, the percent is greater than 100%. If Practice Workbook 6-3 the number compared to 100 is less than 1, the percent is less than 1%. Spanish Practice Workbook 6-3 Guided Problem Solving 6-3 Real Technology Activities 25 1 EXAMPLE Rewriting Percents Greater Than 100 World Nutrition You get 110% of the Recommended Daily Allowance of vitamin Presentation Assistant Plus! 2. C from one half of a grapefruit. Write 110% as a decimal and as a fraction. Transparencies • Check Skills You’ll Need 6-3 110% = 1.10 d To write as a decimal, move the decimal point two places to the left. • Problem of the Day 6-3 110 • Additional Examples 6-3 110% = d To write as a fraction, use the definition of percent. 100 • Student Edition Answers 6-3 11 1 = d • Lesson Quiz 6-3 10,or110 Simplify the fraction. 1 • Classroom Aid 9–11 110% equals 1.10 in decimal form and1 10 in fraction form. PH Presentation Pro CD-ROM 6-3 5 1 Check Understanding 1 Write 125% as a decimal and as a fraction in simplest form. 1.25; 4 or 14 Computer Test Generator CD 2 EXAMPLE Rewriting Percents Less Than 1 Technology 3. Write 0.7% as a decimal and a fraction. Resource Pro® CD-ROM 0.7% = 0.007 d To write as a decimal, move the decimal point two places to the left. Computer Test Generator CD = 0.7 d PH Presentation Pro CD-ROM 0.7% 100 To write as a fraction, use the definition of percent. = 0.7 ? 10 d www.PHSchool.com ? Multiply numerator and denominator by 10. 100 10 Student Site = 7 d • Teacher Web Code: abk-5500 1,000 Simplify as a fraction with a whole number numerator. • Self-grading Lesson Quiz 7 0.7% equals 0.007 in decimal form and1,000 in fraction form. PH SuccessNet Teacher Center • Lesson Planner Check Understanding 2 Write 0.35% as a decimal and as a fraction in simplest form. 0.0035; 7 2,000 • Resources 6-3 Percents Greater Than 100% or Less Than 1% 301 Plus ANT ST C H N I E C K M S E Y T S Ongoing Assessment and Intervention Before the Lesson During the Lesson After the Lesson Diagnose prerequisite skills using: Monitor progress using: Assess knowledge using: • Check Skills You’ll Need • Check Understanding • Lesson Quiz • Additional Examples • Computer Test Generator CD • Test Prep 301 2. Teach A mixed number represents a percent greater than 100%. Real 3 EXAMPLE Writing Mixed Numbers as Percents World Math Background Entertainment You want to see a movie. The cost of admission to a movie is A percent can be greater than 7 1 8 times the cost of renting a video. Write this mixed number as a percent. 100% or less than 1%. Percents greater than 100% convert to 7 = 1.875 d 1 8 178 Use a calculator. mixed numbers. Percents less 1% 1 ==1.87.5 187.5% d Move the decimal point two places to the right. convert to fractions less than 100. u 150 u 1 The cost of admission to a movie is 187.5% of the cost of renting a video. 150% 100 12 0.15% u 15 u 3 10,000 2,000 Check Understanding 3 Write each mixed number or decimal as a percent. When necessary, round To convert a mixed number to a to the nearest hundredth of a percent. percent, first write it as a decimal. 5 4 341.67% 280% 171% 400.5% a.312 b.25 c. 1.71 d. 4.005 Teaching Notes A proper fraction represents a percent less than 100%. 1 EXAMPLE Visual Learners Provide students with two 10 x 10 4 EXAMPLE Real-World Problem Solving grids to model percents greater than 100. One grid will become Government West Virginia has 3 members in the U.S. House of completely shaded and the part Representatives. There are a total of 435 representatives. What percent greater than 100 will be shaded in of the representatives are from West Virginia? Round to the nearest the second grid. hundredth of a percent. 2 EXAMPLE Teaching Tip West Virginia representatives = 3 d total number of representatives 435 Write the fraction. Remind students that they can = 0.0068965517 d Use a calculator. write zeros to the right of decimals without changing the < 0.69% d Write as a percent, and round. value of the decimals. Encourage About 0.69% of the representatives are from West Virginia. students to insert these zeros before moving the decimal point. Check Understanding 4 Idaho has two members in the U.S. House of Representatives. Find the PowerPoint percent of the representatives that are from Idaho. Round to the nearest Additional Examples hundredth of a percent. 0.46% Write each percent as a decimal and a fraction in simplest form. 2 1 140% 1.40; 15 For more practice, see Extra Practice. 3 EXERCISES 2 0.75% 0.0075; 400 Write each fraction or decimal as a Write each percent as a decimal and as a fraction in simplest form. percent. When necessary, round to A Practice by Example the nearest hundredth of a 4 1.3; 1 3 3 Example 1 1. 180% 1.8; 15 2. 130% 10 3. 175% 1.75; 14 percent. (page 301) 9 2.4; 22 4.52; 413 2 4. 345% 3.45; 320 5. 240% 5 6. 452% 25 3 a. 43 466.67%b. 2.557 255.7% 1 3 9 1 6 Example 2 7. 0.1% 0.001; , 8. 0.75% 0.0075; 9. 0.09% 0.0009; 4 a. 325 0.31% b. 875 0.69% 1 000 400 10,000 (page 301) 1 1 1 10. 0.16% 0.0016; 625 11. 0.5% 0.005; 200 12. 0.05% 0.0005; 2,000 Closure • How do you write a percent greater than 100 as a mixed 302 Chapter 6 Percents number? Sample: Rewrite the percent as a fraction with denominator of 100, simplify, Reaching All Students and write the improper fraction as a mixed number. Below Level To change percents less Advanced Learners Change each to Visual Learners • How do you write a percent than 1 into fractions, review place a decimal. Place in order from least See note on page 302. greater than 100 or less than 1 values with students. “Count off” the to greatest. If necessary, round to Error Prevention 7 as a decimal? Move the decimal decimal places (tenths, hundredths, the nearest hundredth. 400 0.0175 See note on page 303. 3 point two places to the left. thousands) and write the correct 0.08% 0.000825 2.60 6.2% 0.062 302 number as the denominator. 0.0008, 0.0175, 0.062, 2.60 Write each number as a percent. When necessary, round to the nearest hundredth of a percent. 3. Practice 3 3 1 475% 160% 101% Example 3 13.44 14.15 15. 1100 (page 302) Assignment Guide 29 7 3 16.2 258% 17.3 335% 18. 2 237.5% 50 20 8 1 Objective 1 19. 1.034 103.4% 20. 2.65 265% 21. 4.81 481% A B Core 1–31, 32–37 7 1 3 C Extension 38 –52 Example 4 22.1,000 0.7% 23.400 0.25% 24. 500 0.6% (page 302) Test Prep 53–56 25.7 0.70% 26.5 0.73% 27. 2 0.61% 998 684 329 Mixed Review 57–68 28. 0.00675 0.68% 29. 0.0028 0.28% 30. 0.0001 0.01% Error Prevention! 31. Reading A library finds that borrowing reference books between 9 libraries is1 10 of what it was 15 years ago. Write this fraction as a Exercises 13–18 Watch for percent. 190% students who add the whole number part and the numerator B Write each percent as a decimal and a fraction. before dividing. 33 32. Sales Jewelry sales in December were 166% of sales in November. 32. 1.66; 150 33. Weather On March 1, the snowpack in the Northern Great Basin of 13 GPS 1.26; 1 Nevada was 126% of the average snowpack. 50 Practice 6-3 Percents Greater Than 100 or Less Than 1 Classify each of the following as: (A) less than 1%, (B) greater than 34. Environment Some studies indicate that the desert shrublands could 100%, or (C) between 1% and 100%. 1 (C)4 (B)2 (A)3 (C) 1.2 2.3 3.300 4.