MSCC3 Green PE 05CO

5.5PercentsWhat is the connection between ratios,fractions, and percents?1ACTIVITY: Writing RatiosWork with a partner. Write the fraction of the squares that are shaded. Write the ratio of the number of shaded squares to the total numberof squares. How are the ratios and the fractions related? When can you write ratios as fractions?a.b.c.PercentA century is 100 years.A cent is one hundredthof a dollar.In Mexico, a centavo isone hundredth of a peso.COMMONCOREPercentsIn this lesson, you will write percents asfractions withdenominatorsof 100. write fractionsas percents.Learning Standard6.RP.3c218Cent means one hundred, so percent means per one hundred. The symbolfor percent is %.Chapter 5MSCC3 Green PE 0505.indd 218Ratios and Rates11/15/12 12:22:30 PM

2ACTIVITY: Writing Percents as FractionsWork with a partner. What percent of each diagram in Activity 1 is shaded? What percent of each diagram below is shaded? Write each percent asa fraction in simplest form.b.a.3c.ACTIVITY: Writing Fractions as PercentsWork with a partner. Draw a model to represent the fraction. How can youwrite the fraction as a percent?25—a. —100 %MathPracticeConsider SimilarProblemsHow is this problemsimilar to ones youhave seen before?How does thishelp you findthe solution?710c. —34e. —b. —d. —353254. IN YOUR OWN WORDS What is the connection between ratios, fractions,and percents? Give an example with your answer.5. REASONING Your score on a test is 110%. What does this mean?Use what you learned about percents to complete Exercises 5–7on page 222.Section 5.5MSCC3 Green PE 0505.indd 219Percents21911/15/12 12:22:40 PM

5.5LessonLesson TutorialsKey Vocabularypercent, p. 220Writing Percents as FractionsWordsA percent is a part-to-whole ratio where the whole is 100. So,you can write a percent as a fraction with a denominator of 100.partNumbers6010060% 60 out of 100 —perone hundred (whole)nAlgebra n% —100EXAMPLE1Writing Percents as Fractionsa. Write 35% as a fraction in simplest form.Study Tip35100Write as a fraction witha denominator of 100.720Simplify.35% —Equivalent fractionsand percents representthe same number usingdifferent notations. —720So, 35% —.b. Write 100% as a fraction in simplest form.Write as a fraction witha denominator of 100.100100100% — 1Simplify.So, 100% 1.c. Write 174% as a mixed number in simplest form.Write as a fraction witha denominator of 100.174100174% —87503750 —, or 1 —Simplify.3750So, 174% 1 —.Write the percent as a fraction or mixed number in simplest form.Exercises 8–19220Chapter 5MSCC3 Green PE 0505.indd 2201. 5%2. 168%3. 36%4. 83%Ratios and Rates11/15/12 12:22:47 PM

Writing Fractions as PercentsWrite an equivalent fraction with a denominator of 100.Then write the numerator with the percent symbol.Words 2514 —Numbers25100— 25% 25EXAMPLE2Writing a Fraction as a Percent350Write — as a percent. 2350— Because 50 2 100, multiply the numeratorand denominator by 2. Write the numeratorwith a percent symbol.6100— 6% 2EXAMPLEMidwestern United States3Real-Life ApplicationA drought affects 9 out of 12 midwestern states. What percent of themidwestern states are affected by the drought?91234— —75100 — 75%Simplify.3 254 2575100— —Write the numerator with a percent symbol.So, 75% of the midwestern states are affected by the drought.Write the fraction or mixed number as a percent.Exercises 21–2831505. —7256. —19207. —128. 1—9. WHAT IF? In Example 3, it rains in all the midwestern states.In what percent of the states affected by drought does it rain?Section 5.5MSCC3 Green PE 0505.indd 221Percents22111/15/12 12:22:52 PM

Exercises5.5Help with Homework1. WRITING Explain how you can use a 10-by-10 grid to model 42%.2. WHICH ONE DOESN’T BELONG? Which one does not have the same value asthe other three? Explain your reasoning.1010010%—1100.01—3. OPEN-ENDED Write three different fractions that are less than 40%.144. NUMBER SENSE Can 1 — be written as a percent? Explain.6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Use a 10-by-10 grid to model the percent.5. 10%6. 55%7. 35%Write the percent as a fraction or mixed number in simplest form.18. 45%9. 90%10. 15%11. 7%12. 34%13. 79%14. 77.5%15. 188%16. 8%17. 224%18. 0.25%19. 0.4%20. ERROR ANALYSIS Describe and correct theerror in writing 225% as a fraction. 2251000940225% — —Write the fraction or mixed number as a percent.11022. —275026. —2 21. —25. —1523. —1120182527. 1—29. ERROR ANALYSIS Describe and correct the1425error in writing — as a percent.22524. —1720 415028. 2 —142514 425 456100— — — 0.56%30. LEFT-HANDED Of the students in your class, 12% are left-handed. Whatfraction of the students are left-handed? Are there more right-handed orleft-handed students? Explain.31. ARCADE You have 125% of the tickets required for a souvenir. What fraction of therequired tickets do you have? Do you need more tickets for the souvenir? Explain.222Chapter 5MSCC3 Green PE 0505.indd 222Ratios and Rates11/15/12 12:22:54 PM

Find the percent.32. 3 is what percent of 8?33. 13 is what percent of 16?34. 9 is what percent of 16?35. 33 is what percent of 40?36. SOCIAL NETWORKING A survey asked students tochoose their favorite social networking website.The results are shown in the table.Social NetworkingWebsiteNumber ofStudentsWebsite A35a. What fraction of the students chose Website A?Website B13b. What percent of the students chose Website C?Website C22Website D1037. GEOGRAPHY The percent of the total area of the United States that is in eachof four states is 8%a. Write the percents as fractions in simplest form.b. How many times larger is Illinois than Hawaii?c. Compared to the map of Florida, is the map of Alaska the correct size?Explain your reasoning.d. RESEARCH Which of the 50 states are larger than Illinois?38. CRITICAL THINKING A school fundraiser raised 120% of its goal last year and125% of its goal this year. Did the fundraiser raise more money this year?Explain your reasoning.1239. CRITICAL THINKING How can you use a 10-by-10 grid to model — %?112Write — as a percent. Explain how you found your answer.40.Divide. Write the answer in simplest form.16133441. — —(Section 2.2)165842. 9 —43. 10 —44. — 245. MULTIPLE CHOICE Which of the following is not equal to 15? (Section 2.1)A 34— 20B 59— 27C 35 —37D 28 Section 5.5MSCC3 Green PE 0505.indd 223 —57Percents22311/15/12 12:22:56 PM

b. Write 100% as a fraction in simplest form. 100% 100 — 100 Write as a fraction with a denominator of 100. 1 Simplify. So, 100% 1. c. Write 174% as a mixed number in simplest form. 174% 174 — 100 Write as a fraction with a denominator of 100. 87 — 50, or 1 37 — 50 S