7-1 Fractions and Percents
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1 Write each percent as a fraction or mixed number in simplest form % % % % esolutions Manual - Powered by Cognero Page 1
2 5. Write each fraction as a percent. Round to the nearest hundredth if necessary So, 94.44%. esolutions Manual - Powered by Cognero Page 2
3 8. So, = 87.5%. 9. VACATIONS Of the students in Ms. Villata s classes, 56 out of 128 are planning to go on a summer vacation. What percent is this? So, 43.75% of the students in Ms. Villata s classes plan to go on a summer vacation. 10. TESTS On a recent social studies test, Miguel earned 80 out of 90 points. Find Miguel s grade as a percent. Round to the nearest hundredth. Miguel earned an 88.89% on his social studies test. Write each percent as a fraction or mixed number in simplest form % esolutions Manual - Powered by Cognero Page 3
4 12. 28% % % % esolutions Manual - Powered by Cognero Page 4
5 % % % % esolutions Manual - Powered by Cognero Page 5
6 % % % 23. GEOGRAPHY The tallest mountain in the world is Mt. Everest. It is about 140% as tall as the tallest mountain in the United States, Mt. McKinley. Write 140% as a mixed number in simplest form. esolutions Manual - Powered by Cognero Page 6
7 24. POPULATION According to the U.S. Census Bureau, 0.4% of the population of South Carolina is Native American. Write 0.4% as a fraction in simplest form. 25. Write each fraction as a percent. Round to the nearest hundredth if necessary. So, = 25% esolutions Manual - Powered by Cognero Page 7
8 So, = 87.5%. 30. So, 1.67%. esolutions Manual - Powered by Cognero Page 8
9 31. So, 71.43%. 32. So, 46.15%. 33. FRIENDS Of Mark s friends, 5 out of 8 are planning to go to the concert on Friday night. What percent of Mark s friend are planning to go to the concert? So, 62.5% of Mark s friends plan to go to the concert. esolutions Manual - Powered by Cognero Page 9
10 34. SPORTS There are 18 members on the varsity baseball team. Of these players, 7 are pitchers. What percent of the team are pitchers? Round to the nearest hundredth. On the varsity baseball team, approximately 38.89% of the team members are pitchers. 35. ANIMALS A cheetah can run about times as fast as a squirrel. What percent is this? esolutions Manual - Powered by Cognero Page 10
11 36. GEOMETRY The Martin s patio is shown below. Part of their patio is covered with a mat. What percent of their patio is covered by the mat? (Hint: Area is equal to length times width.) First, find the total area of the patio and the area of the mat. The total area of the patio is 200 square meters, and the area of the mat is 72 square meters. Write the area of the patio covered by the mat in fraction form, then convert to a percent. The mat covers 36% of the Martin s patio. esolutions Manual - Powered by Cognero Page 11
12 37. GEOMETRY For each model below, write a fraction in simplest form that compares the shaded portion of each figure to its total area. Then write each fraction as a percent. Which figure has the greatest part shaded? Figure Fraction of shaded portion to total area Percent of shaded portion to total area A B C Figure C has the greatest part shaded. Replace each _ with <, >, or = to make a true sentence. 38. _ 45% So, < 45%. esolutions Manual - Powered by Cognero Page 12
13 39. 75% _ So, = 75%. So, 75% = % _ So, 116.7%. So, 120% >. esolutions Manual - Powered by Cognero Page 13
14 41. _ 70 % So, < 70 %. 42. _ 0.002% So, > 0.002%. esolutions Manual - Powered by Cognero Page 14
15 % _ So, 300% >. 44. POPULATION The circle graph shows the percent of the world s population on each continent. a. Write each percent as a fraction. b. What fraction of the population lives in the Americas? c. If the world population is about 6.5 billion people, explain how you might determine the number of people who live in Asia. a. Country Percent Fraction Asia 59.4% esolutions Manual - Powered by Cognero Page 15
16 Africa 14.2% Europe 12.3% North America 7.9% South America 5.7% Australia 0.5% b. To find the fraction of the population that lives in the Americas, add fractions living in North America and South America. The fraction of the world population living in the Americas is. c. To find the number of people who live is Asia, multiply the percent who live in Asia by 6.5 billion. esolutions Manual - Powered by Cognero Page 16
17 45. OPEN ENDED Give an example of a percent that is between and. Explain your reasoning. Sample answer: 76% is between and. = 0.75 or 75% and or 77.8%. So, 76% is between 75% and 77.8%. 46. CHALLENGE What percent of the larger triangle shown is not shaded? Round to the nearest hundredth. First, find the area of both triangles. Write the area of the smaller triangle to the larger triangle in fraction form, and convert to a percent. Approximately 11.11% of the larger triangle is shaded. Find the area not shaded by subtracting the percent shaded from = So, approximately 88.89% of the larger triangle is not shaded. esolutions Manual - Powered by Cognero Page 17
18 47. NUMBER SENSE Model the fraction. Then write the fraction as a percent. 48. ERROR ANALYSIS Emma and Anna are changing 0.5% to a fraction. Is either of them correct? Explain your reasoning. Anna is correct. Emma did not multiply by to eliminate the decimal. esolutions Manual - Powered by Cognero Page 18
19 49. CHALLENGE Find the whole number value of x such that equals 50%. Explain your reasoning. Convert 50% to a fraction. Write an equation using the given fraction and, and solve. Check: 50. WRITING IN MATH Describe two ways to write as a percent. Sample answer: You can find the equivalent fraction with a denominator of 100, = = or 80%. Or you can set up and solve a proportion. esolutions Manual - Powered by Cognero Page 19
20 51. Which of the following represents the shaded portion of the figure below? A 25% B 37.5% C 50% D 62.5% Shaded portion = The shaded portion of the figure is 37.5%. Choice B is correct. 52. During her last basketball game, Carmen made 14 field goals out of 30 attempts. What percent of field goals did she make? F 45% G 47% H 50% J 51% Write the field goals made to the total attempts in fraction form, and convert to a percent. Carmen made approximately 47% of the field goals. Choice G is correct. esolutions Manual - Powered by Cognero Page 20
21 53. If 95% of the seventh grade students are going on the trip to the museum, what fraction of the students are not going on the field trip? A B C D The percent of seventh graders not going on the trip is or 5%. Convert 5% to a fraction. So, of the seventh graders are not going on the trip. Choice A is correct. 54. SHORT RESPONSE Helio is installing some software onto his computer. The screen shows that it is 45% complete. Write 45% as a fraction in simplest form. Show all of your work. 55. RIDES Suppose a roller coaster casts a shadow of 31.5 feet. At the same time, a nearby Ferris wheel casts a 19- foot shadow. If the roller coaster is 126 feet tall, how tall is the Ferris wheel? Let x represent the height of the Ferris wheel. Write a proportion and solve for x. The Ferris wheel is 76 feet tall. esolutions Manual - Powered by Cognero Page 21
22 For Exercises 56 and 57 use the figure below. 56. Find the vertices of ABC after a dilation centered at the origin with a scale factor of 3. Then graph the original image and the dilation. The dilation is. Multiply the coordinates of each vertex by 3. esolutions Manual - Powered by Cognero Page 22
23 57. Find the vertices of ABC after a dilation centered at the origin with a scale factor of. Then graph the original image and the dilation. The dilation is. Multiply the coordinates of each vertex by. Solve each inequality. Check your solution. 58. x + 3 < 8 Check: y 7 Check: esolutions Manual - Powered by Cognero Page 23
24 b Check: 61. a 5 > 6 Check: 62. PAINTING A person-day is a unit of measure that represents one person working for one day. A painting contractor estimates that it will take 24 person-days to paint a house. Write and solve an equation to find how many painters the contractor will need to hire to paint the house in 6 days. Words: Number of painters number of days to paint the house = number of person-days. Variable: Let p = the number of painters. Equation: p 6 = 24 The contractor will need to hire 4 painters. Multiply or divide When multiplying by 100, move the decimal point 2 places to the right = 1820 esolutions Manual - Powered by Cognero Page 24
25 When multiplying by 100, move the decimal point 2 places to the right = When dividing by 100, move the decimal point 2 places to the left = When dividing by 100, move the decimal point 2 places to the left = esolutions Manual - Powered by Cognero Page 25
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