Big Ideas Math Book 7th Grade Answer Key Chapter 6 Percents<\/h2>\n
Big ideas Math Book 7th Grade Answer Key Chapter 6 percents pdf is given here. It gives the most accurate answers to all the problems which are related to the given chapter. This chapter of percents contains various topics like Fractions, Decimals and Percents, The Percent Proportion, The Percent Equation, Percents of Increase and Decrease, Discounts and Markups, Simple Interest, and so on.<\/p>\n
With the help of Big Ideas Math Book 7th Grade Solution Key Chapter 6 Percents,<\/b> you can prepare the timetable. With the help of the timetable prepared, you can easily manage your syllabus and include all the topics into it as per the time remaining. In the further sections, you will know all the concepts that are present in Grade 7 Chapter 6 Percents. Check out all the information and kickstart your preparation.<\/p>\n
STEAM Video\/Performance Task<\/strong><\/p>\n Getting Ready for Chapter 6<\/strong><\/p>\n Lesson 1 : Fractions, Decimals, and Percents<\/strong><\/p>\n Lesson 2 : The Percent Proportion<\/strong><\/p>\n Lesson 3 : The Percent Equation<\/strong><\/p>\n Lesson 4 : Percents of Increase and Decrease<\/strong><\/p>\n Lesson 5 : Discounts and Markups<\/strong><\/p>\n Lesson 6 : Simple Interest<\/strong><\/p>\n Percents Connecting Concepts<\/strong><\/p>\n STEAM Video<\/strong><\/p>\n Tornado! Performance Task<\/strong><\/p>\n Tornado Alley Chapter Exploration<\/strong> Answer : The Percent and decimal for the given models are Explanation: 2. 3. 4. 5. 6. 7. 8. WRITE A PROCEDURE Work with a partner. Write a procedure for rewriting a percent as a decimal. Use examples to justify your procedure.<\/p>\n Answer: Vocabulary<\/strong> Answer: percent of decrease: discount: A reduction of price\u00a0 is known as discount .Sometimes discounts are in percent, such as a 10% discount, and then you need to do a calculation to find the price reduction.<\/p>\n percent of increase : percent error : markup: EXPLORATION 1<\/strong><\/p>\n Comparing Numbers in Different Forms Explanation: b. 0.37 cup of flour or \\(\\frac{1}{3}\\) cup for flour c. \\(\\frac{5}{8}\\) inch wrench or 0.375 inch wrench d. \\(12\\) \\({\\Large\\frac{3}{5}}\\) dollars or 12.56 dollars e.\u00a0 \\(5\\) \\({\\Large\\frac{5}{6}}\\) fluid ounces or 5.6 fluid ounces <\/p>\n EXPLORATION 2<\/strong><\/p>\n Work with a partner and follow the steps below. Answer: 78%, 0.95, \\(\\frac{83}{45}\\), 6, 21<\/p>\n Explanation: Try It<\/strong><\/p>\n Write the percent as a decimal or the decimal as a percent. Use a model to represent the number.<\/strong> Explanation: Question 2. Explanation: Question 3. Explanation: Question 4. Explanation: Write the fraction as a decimal and a percent.<\/strong> Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanation: Self-Assessment for Concepts & Skills<\/strong> CONVERTING BETWEEN PERCENTS AND DECIMALS<\/strong> Write the percent as a decimal or the decimal as a percent. Use a model to represent the number. Explanation: Question 10. Explanation: Question 11. Explanation: Question 12. Explanation: WRITING FRACTIONS AS DECIMALS AND PERCENTS<\/strong> Write the fraction as a decimal and a percent. Explanation: Question 14. Explanation: Question 15. Explanation: Question 16. Explanation: Self-Assessment for Problem Solving<\/strong> Question 17. Explanation: Question 18. Explanation:<\/p>\n Review & Refresh<\/strong><\/p>\n Find the missing dimension. Use the scale 1 : 15.<\/strong> Explanation: Let the Actual length is y Simplify the expression.<\/strong> Explanation: Question 4. Explanation: Question 5. Explanation: Concepts, Skills, & Problem Solving<\/strong> Explanation: Question 7. Explanation: CONVERTING BETWEEN PERCENTS AND DECIMALS<\/strong> Write the percent as a decimal or the decimal as a percent. Use a model to represent the number. Explanation: Question 9. Explanation: Question 10. Explanation: Question 11. Explanation: Question 12. Explanation: Question 13. Explanation: Question 14. Explanation: Question 15. Explanation: Question 16. Explanation: Question 17. Explanation: Question 18. Explanation: Question 19. Explanation: Question 20. Explanation: WRITING FRACTIONS AS DECIMALS AND PERCENTS<\/strong> Write the fraction as a decimal and a percent. Explanation: Question 22. Explanation: Question 23. Explanation: Question 24. Explanation: Question 25. Explanation: Question 26. Explanation: Question 27. Explanation: Question 28. Explanation: Question 29. Explanation: Question 30. Explanation: Question 31. Explanation: Question 32. Explanation: PRECISION<\/strong> Order the numbers from least to greatest. Explanation: Question 34. Explanation: MATCHING<\/strong> Tell which letter shows the graph of the number. Explanation: Question 36. Question 37. Explanation: Question 38. Explanation: Question 39. Explanation: Question 40. Explanation: Question 41. Explanation: Question 42. Explanation: Question 43. Explanation: Question 44. Explanation: EXPLORATION 1<\/strong><\/p>\n Using Percent Models c. How can you use ratio tables to check your answers in part(b)? How can you use proportions? Provide examples to support your reasoning. Explanation: b. As shown in the models in part (a) 15 is the number which is 50% of 30, c. The models provided in the part (a) are representing the each of the number individually which are divided in to equal number of parts in respective of their numbers , Also the divided parts can be represented as percent and number form In the picture shown The number 30 is divided into 1:1 ratio equally which is exactly the half of the number and percent that is 15 is 50% of 30.<\/p>\n d. From the figure 2 of part (a), we can assume the question as Answer: 60 is the number which is 80% of 75 , as shown in the model above.<\/p>\n Try It<\/strong><\/p>\n Write and solve a proportion to answer the question.<\/strong> Explanation: Question 2. Explanation: Write and solve a proportion to answer the question.<\/strong> Explanation: Question 4. Explanation: Write and solve a proportion to answer the question.<\/strong> Explanation: Question 6. Explanation: Self-Assessment for Concepts & Skills<\/strong> Question 7. Explanation: Question 8. Explanation: Question 9. Explanation: Self-Assessment for Problem Solving<\/strong> Question 10. Explanation: Question 11. Explanation: Review & Refresh<\/strong><\/p>\n Write the fraction as a decimal and a percent.<\/strong> Explanation: Question 2. Explanation: Question 3. Explanation: Question 4. Explanation: Evaluate the expression when a = – 15 and b = – 5.<\/strong> Explanation: Question 6. Explanation: Question 7. Explanation: What is the solution of 9x = 1.8? Explanation: Concepts, Skills, &Problem Solving<\/strong><\/p>\n CHOOSE TOOLS<\/strong> Use a model to answer the question. Use a proportion to check your answer. (See Exploration 1, p. 241.) Explanation: Question 10. Explanation: Question 11. Explanation: Question 12. Explanation: Question 13. Explanation: Question 14. Explanation: USING THE PERCENT PROPORTION<\/strong> Write and solve a proportion to answer the question. Explanation: Question 16. Explanation: Question 17. Explanation: Question 18. Explanation: Question 19. Explanation: Question 20. Explanation: Question 21. Explanation: Question 22. Explanation: Question 23. Explanation: Question 24. Explanation: Question 25. Explanation: USING THE PERCENT PROPORTION<\/strong> Write and solve a proportion to answer the question. Explanation: Question 27. Explanation: Question 28. Explanation: Question 29. Explanation: Question 30. Explanation: Question 31. Explanation: Question 32. Explanation: Saturday reservations are 30, so Totally, The percent of reservations For Friday is 74.2% and for Saturday is\u00a0 85%.<\/p>\n Question 33. b. In order to calculate the percent of the votes does the least popular mascot received will be halted due to lack of clear mentioning of of the proportion of the votes or the ratio of the votes.<\/p>\n c. The votes acquired by the tiger are cannot be determined because of figure which does not contain proper information.<\/p>\n Question 34. Explanation: Hence, Quarterback thrown 20.6 passes in the fourth quarter<\/p>\n Question 35. Explanation: Question 36. Explanation: b. By using percent proportion , we have EXPLORATION 1<\/strong><\/p>\n Using Percent Equations b. The equation is a = \\(\\frac{w \u00d7 p}{100}\\)<\/p>\n c. The number of students who voted for each candidate are d. ratio proportion is used as another method.<\/p>\n Explanation: For person B , w = 60 , a = 15 , p = ? For person C , w = 60 , a = 9 , p = ? For person D , w = 60 , a = 24 , p = ? b. we know that percent proportion is \\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\) c. The figure showing the percent of all the candidates individually are after the final results , For person B , w\u00a0 = 120 , p = 20 , a = ? For person C , w\u00a0 = 120 , p = 20 , a = ? For person D , w\u00a0 = 120 , p = 35 , a = ? d. We are using ratio proportion method , To check the answers of\u00a0 part (c), For person B , 20 % \u00d7 120 = For person C , 20% \u00d7 120 is same as person B For person D , 35 % \u00d7 120 = Try It<\/strong><\/p>\n Write and solve an equation to answer the question.<\/strong> Explanation: Question 2. Explanation: Write and solve an equation to answer the question.<\/strong> Explanation: Question 4. By using proportion , we have Write and solve an equation to answer the question.<\/strong> Explanation: Question 6. Explanation: Self-Assessment for Concepts & Skills<\/strong> Question 7. USING THE PERCENT EQUATION<\/strong> Write and solve an equation to answer the question. Explanation: Question 9. Explanation: Question 10. Explanation: Question 11. Explanation: Question 12. Explanation: But this 55 is 20% of what number ? is different\u00a0 from other three, because here we have to find out the whole number Self-Assessment for Problem Solving<\/strong> Question 13. Explanation: For Band , w = 1200 , p = 28 , a = ? The total number of students enrolled for both classes\u00a0 are 408 + 336 = 744.<\/p>\n Question 14. b. The percent of the total volume of both tanks is filled with water is 58.5%.<\/p>\n Explanation: Given, Water Tank B is 53% full. b. To know the percent of the total volume of both tanks is filled with water, we have Review & Refresh<\/strong><\/p>\n Write and solve a proportion to answer the question.<\/strong> Explanation: Question 2. Explanation: Question 3. Explanation: Question 4. Explanation: Find the distance between the two numbers on a number line.<\/strong> Explanation:\u00a0 Question 6. Explanation: Question 7. Explanation: Question 8. Explanation: Question 9. Explanation: Concepts, Skills, & Problem Solving<\/strong><\/p>\n USING PERCENT EQUATIONS<\/strong> The circle graph shows the number of votes received by each candidate during a school election. Find the percent of students who voted for the indicated candidate. Each Candidate(See Exploration 1, p. 247.) Explanation: Question 11. Explanation: Question 12. Explanation: USING THE PERCENT EQUATION<\/strong> Write and solve an equation to answer the question. Explanation: Question 14. Explanation: Question 15. Explanation: Question 16. Explanation: Question 17. Explanation: Question 18. Explanation: Question 19. Explanation: Question 20. Explanation: YOU BE THE TEACHER<\/strong> Your friend uses the percent equation to answer the question. Is your friend correct? Explain your reasoning. Explanation: Question 22. Explanation: Question 23. Explanation: Question 24. Explanation: Question 25. Explanation: PUZZLE<\/strong> There were n signers of the Declaration of Independence. The youngest was Edward Rutledge, who was x years old. The oldest was Benjamin Franklin, who was y years old. Explanation: Question 27. Explanation: Question 28. Explanation: Question 29. Explanation: If the percent of a number is 100% , Then the percent of the number will be equal the number. If the percent of a number is greater than 100% , Then the percent of the number will be greater than the number. Question 30. Explanation: b. 80 students are participated , so w = 80 Question 31. Explanation: Question 32. Explanation: Question 33\n
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<\/a>STEAM Video\/Performance Task<\/h3>\n
\nMore tornadoes occur each year in the United States than in any other country. How can you use a percent to describe the portion of tornadoes in the United States that occur in your state?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-1.png\")
\nWatch the STEAM Video \u201cTornado!\u201d Then answer the following questions.
\n1. The map below shows the average annual number of tornadoes in each state. Which regions have the most tornadoes? the fewest tornadoes?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-2.png\")
\n2. Robert says that only Alaska, Hawaii, and Rhode Island average less than 1 tornado per year. What percent of states average more than 1 tornado per year?<\/p>\n
\nAfter completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given information about the average annual numbers of tornadoes in several states over a 25-year period. For example:
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-3.png\")
\nYou will be asked to solve various percent problems about tornadoes. Why is it helpful to know the percent of tornadoes that occur in each state?<\/p>\n<\/a>Getting Ready for Chapter 6<\/h3>\n
\nWork with a partner. Write the percent of the model that is shaded. Then write the percent as a decimal.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-4.png\")
<\/p>\n
\n1. percent = 30%, decimal = 0.3
\n2. percent = 100%, decimal = 1
\n3. percent = 33%, decimal = 0.33
\n4. percent = 50%, decimal = 0.5
\n5. percent = 40%, decimal = 0.4
\n6. percent = 64%, decimal = 0.64
\n7. percent = 60%, decimal = 0.6<\/p>\n
\nAll the models given here are 10 by 10 grid forming a Square of 100 equal sections.
\nThis entire square represents a whole and the shaded part is fraction.
\nEach of these shaded squares represents 1\/100. So by using this data we have ,
\n1.\u00a0 ![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.1.png\")
\u00a0 = ![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.8.png\")
\nFrom the shaded part and the whole, we have the fraction of \\(\\frac{30}{100}\\),
\nThen the percent will be \\(\\frac{30}{100}\\) = 30%,
\nBy rewriting it in decimal form we have 0.3<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.2.png\")
\u00a0 = ![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.9.png\")
\nFrom the shaded part and the whole, we have the fraction of \\(\\frac{100}{100}\\),
\nThen the percent will be \\(\\frac{100}{100}\\) = 100%,
\nBy rewriting it in decimal form we have 1<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.3.png\")
\u00a0 = ![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.10.png\")
\nFrom the shaded part and the whole, we have the fraction of \\(\\frac{33}{100}\\),
\nThen the percent will be\u00a0\\(\\frac{33}{100}\\) = 33%,
\nBy rewriting it in decimal form we have 0.33<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.4.png\")
\u00a0 = ![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.11.png\")
\nFrom the shaded part and the whole, we have the fraction of \\(\\frac{50}{100}\\),
\nThen the percent will be \\(\\frac{50}{100}\\) = 50%,
\nBy rewriting it in decimal form we have 0.5<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.5.png\")
\u00a0 = ![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.12.png\")
\nFrom the shaded part and the whole, we have the fraction of \\(\\frac{40}{100}\\),
\nThen the percent will be \\(\\frac{40}{100}\\) = 40%,
\nBy rewriting it in decimal form we have 0.4<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.6.png\")
\u00a0 = ![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.13.png\")
\nFrom the shaded part and the whole, we have the fraction of \\(\\frac{64}{100}\\),
\nThen the percent will be \\(\\frac{64}{100}\\) = 64%,
\nBy rewriting it in decimal form we have 0.64<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.7.png\")
\u00a0 = ![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.14.png\")
\nFrom the shaded part and the whole, we have the fraction of \\(\\frac{60}{100}\\),
\nThen the percent will be \\(\\frac{60}{100}\\) = 60%,
\nBy rewriting it in decimal form we have 0.6<\/p>\n
\nLet us say that the fraction be \\(\\frac{44}{100}\\),
\nThen its percentage will be 44%,
\nTo rewrite it as decimal, we divide 44 by 100 we get 0.44 (a decimal number). So, to convert from percent to decimal divide by 100 and remove the “%” sign.
\nWe get 0.44 as decimal of 44%.<\/p>\n
\nThe following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.
\npercent of change
\npercent of decrease
\ndiscount
\npercent of increase
\npercent error
\nmarkup<\/p>\n
\npercent of change:
\nPercentage Change is all about comparing old values to new values.<\/p>\n
\npercent of decrease is a measure of percent change, which is the extent to which something loses value. or
\nA negative\u00a0percent of change\u00a0indicates a decrease from the original value to the second value.<\/p>\n
\nPercent increase\u00a0is a measure of\u00a0percent change, which is the extent to which something gains value. or
\nA positive\u00a0percent of change\u00a0indicates an\u00a0increase\u00a0from the original value to the second value.<\/p>\n
\nPercent error\u00a0is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a\u00a0percentage.<\/p>\n
\nMarkup is all about how much a retailer increases the price over what they paid for it to buy the product or item in order to which is how they make money to pay for all their costs and hopefully make a profit.<\/p>\n<\/a>Lesson 6.1 Fractions, Decimals, and Percents<\/h3>\n
\nWork with a partner. Determine which number is greater. Explain your method.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-6.1-1.png\")
\nAnswer:
\na. 7% sales tax is greater than 5% sales tax
\nb. 0.37 cup of flour is greater than 0.33 cup of flour
\nc. 0.625 inch wrench is greater than 0.375 inch wrench
\nd. 12.6 dollars are greater than 12.56 dollars
\ne. 5.83 fluid ounces is greater than 5.6 fluid ounces<\/p>\n
\na. 7% sales tax or \\(\\frac{1}{20}\\) sales tax
\nBy using the method of converting fraction into Percent and comparing ,
\nWe can rewrite \\(\\frac{1}{20}\\) as\u00a0 0.05 in decimal form,
\nTo get get the percent , multiply 100 to 0.05, then we get 5%.
\nSo, \\(\\frac{1}{20}\\) can be write as 5%,
\nFinally, by comparing two values 7% sales tax is greater than 5% sales tax<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{1}{3}\\) as\u00a0 0.33 in decimal form
\nFinally, by comparing two values 0.37 cup of flour is greater than 0.33 cup of flour.<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{5}{8}\\) by dividing 5 by 8, we have\u00a0 0.625 in decimal form
\nFinally, by comparing two values 0.625 inch wrench is greater than 0.375 inch wrench.<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite fraction\\(\\frac{63}{5}\\) by dividing 63 by 5, we have 12.6 in decimal form
\nFinally, by comparing two values 12.6 dollars are greater than 12.56 dollars<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite fraction \\(\\frac{35}{6}\\) \u00a0by dividing 35 by 6, we have 5.83 in decimal form
\nFinally, by comparing two values 5.83 fluid ounces is greater than 5.6 fluid ounces<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-6.1-2.png\")
<\/p>\n\n
\nLet the numbers be 6,\u00a0 21, 0.95, \\(\\frac{83}{45}\\), 78%
\nIn order to put them in an ascending order we have to calculate the fraction, percent, decimal in their respective form, So Fraction \\(\\frac{83}{45}\\) can be rewrite as 1.84 in decimal form
\nThen 78% can be rewrite as 0.78 in decimal form,
\nAs we can see 0.78 is less than 0.95 , 0.95 is less than \\(\\frac{83}{45}\\),\\(\\frac{83}{45}\\) is less than 6, 6 is less than 21,
\nFinally, we have the ascending order as 78%, 0.95, \\(\\frac{83}{45}\\), 6, 21.<\/p>\n
\nQuestion 1.
\n39%
\nAnswer: 0.39<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.15.png\")
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\nSo, 39% in decimal form is 0.39<\/p>\n
\n12. 6 %
\nAnswer: 0.126<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.16.png\")
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\nSo, 12.6% in decimal form is 0.126<\/p>\n
\n0.05
\nAnswer: 5%<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.17.png\")
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol.
\nSo, 0.05 can be rewrite as 5%<\/p>\n
\n1.25
\nAnswer:\u00a0 125%<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.18.png\")
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol.
\nSo, 1.25 can be rewrite as 125%<\/p>\n
\nQuestion 5.
\n\\(\\frac{5}{8}\\)
\nAnswer: 0.625 or 62.5%<\/p>\n
\nTo get the percent or decimal from\u00a0 fraction \\(\\frac{5}{8}\\) we have to divide 5 by 8 ,
\nThen, we get 0.625,
\nTo get the percent of 0.625 multiply by 100 , it will be 62.5%
\nSo, \\(\\frac{5}{8}\\) can be written as\u00a0 0.625 or 62.5%<\/p>\n
\n\\(\\frac{1}{6}\\)
\nAnswer: 0.166 or 16.6%<\/p>\n
\nTo get the percent or decimal from\u00a0 fraction \\(\\frac{1}{6}\\) we have to divide 1 by 6 ,
\nThen, we get 0.166,
\nTo get the percent of 0.166 multiply by 100 , it will be 16.6%
\nSo, \\(\\frac{1}{6}\\) can be written as\u00a0 0.166 or 16.6%<\/p>\n
\n\\(\\frac{11}{3}\\)
\nAnswer:\u00a0 3.66 or 366%<\/p>\n
\nTo get the percent or decimal from\u00a0 fraction \\(\\frac{11}{3}\\) we have to divide 11 by 3 ,
\nThen, we get 3.66,
\nTo get the percent of 3.66 multiply by 100 , it will be 366%
\nSo, \\(\\frac{11}{3}\\) can be written as\u00a0 3.66 or 366%<\/p>\n
\n\\(\\frac{3}{1000}\\)
\nAnswer: 0.003 or 0.3%<\/p>\n
\nTo get the percent or decimal from\u00a0 fraction \\(\\frac{3}{1000}\\) we have to divide 3 by 1000 ,
\nThen, we get 0.003,
\nTo get the percent of 0.003 multiply by 100 , it will be 0.3%
\nSo, \\(\\frac{3}{1000}\\) can be written as\u00a0 0.003 or 0.3%<\/p>\n
\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n
\nQuestion 9.
\n46%
\nAnswer: 0.46<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.19.png\")
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\nSo, 46% in decimal form is 0.46<\/p>\n
\n\\(66 . \\overline{6} \\%\\)
\nAnswer: \\(0 .66 \\overline{6}\\)<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.20.png\")
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\nSo, \\(66 . \\overline{6} \\%\\) in decimal form is \\(0 .66 \\overline{6}\\)<\/p>\n
\n0.18
\nAnswer: 18%<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.21.png\")
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol.
\nSo, 0.18 can be rewrite as 18%<\/p>\n
\n\\(2 . \\overline{3}\\)
\nAnswer: \\(233 . \\overline{3} \\%\\)<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.22.png\")
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol.
\nSo, \\(2 . \\overline{3}\\) can be rewrite as \\(233 . \\overline{3} \\%\\)<\/p>\n
\nQuestion 13.
\n\\(\\frac{7}{10}\\)
\nAnswer: decimal = 0.7, percent = 70%<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{7}{10}\\) as\u00a0 0.7 in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then 0.7 can be rewrite as 70%
\nSo, \\(\\frac{7}{10}\\) in decimal = 0.7, percent = 70%<\/p>\n
\n\\(\\frac{5}{9}\\)
\nAnswer: decimal = \\(0 .\\overline{5}\\), percent = \\(55 . \\overline{5} \\%\\)<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{5}{9}\\) as\u00a0 \\(0 .\\overline{5}\\)\u00a0in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then \\(0 .\\overline{5}\\) can be rewrite as \\(55 . \\overline{5} \\%\\)
\nSo, \\(\\frac{5}{9}\\) in decimal = \\(0 .\\overline{5}\\), percent = \\(55 . \\overline{5} \\%\\)<\/p>\n
\n\\(\\frac{7}{2000}\\)
\nAnswer: decimal = 0.0035, percent = 0.35%<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{7}{2000}\\) as\u00a0 0.0035 in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then 0.0035 can be rewrite as 0.35%
\nSo, \\(\\frac{7}{2000}\\) in decimal = 0.0035, percent = 0.35%<\/p>\n
\n\\(\\frac{17}{15}\\)
\nAnswer: decimal = \\(1.1 \\overline{3}\\) , percent = \\(113 . \\overline{3} \\%\\)<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{17}{15}\\) as \\(1.1 \\overline{3}\\) in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then \\(1.1 \\overline{3}\\) can be rewrite as \\(113 . \\overline{3} \\%\\)
\nSo, \\(\\frac{17}{15}\\) in decimal = \\(1.1 \\overline{3}\\), percent = \\(113 . \\overline{3} \\%\\)<\/p>\n
\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n
\nAn astronaut spends 53% of the day working, 0.1 of the day eating, \\(\\frac{3}{10}\\) of the day sleeping, and the rest of the day exercising. Order the events by duration from least to greatest. Justify your answer.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-6.1-3.png\")
\nAnswer:\u00a0 An astronaut spends the day 7% by exercising, 10% by eating, 30% by sleeping, 53% by working.<\/p>\n
\nAn astronaut spends 53% of the day working,
\n0.1 of the day eating, in terms of percent we can write it as 10%,
\n\\(\\frac{3}{10}\\) of the day sleeping, in decimals we ca rewrite as 0.3 and in percent it will be 30%,
\nLet us say that the whole day be 100% , The sum of the works he is doing in percent we get,
\n53% + 10% + 30% = 93%, and
\nGiven that the rest of the day exercising, so 100% – 93% = 7%, A whole day is completed with these works.
\nTo put them in Order the events by duration from least to greatest, we have , 7%, 10%, 30%, 53%.
\nAn astronaut spends the day 7% by exercising, 10% by eating, 30% by sleeping, 53% by working.<\/p>\n
\nDIG DEEPER!<\/strong>
\nA band plays one concert in Arizona, one concert in California, and one concert in Georgia. In California, the band earned \\(\\frac{3}{2}\\) the profit that they earned in Arizona. Of the total profit earned by the band, 32% is earned in Arizona. How many times more money did the band earn at the most profitable concert than at the least profitable concert? Justify your answer.
\nAnswer:<\/p>\n<\/a>Fractions, Decimals, and Percents Homework & Practice 6.1<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-6.1-4.png\")
\nAnswer: The model height of the Figure skater is 4.5inches and The Actual length of pipe is 75 feet .<\/p>\n
\nGiven , to use the scale oof 1 : 15 , Let the model height\u00a0 be x
\nThe model height of Figure skater is \\(\\frac{1}{15}\\) = \\(\\frac{x}{67.5}\\)
\n15x = 67.5
\nx = \\(\\frac{67.5}{15}\\)
\nx = 4.5
\nSo , The model height of the Figure skater is 4.5inches<\/p>\n
\nThe Actual length of pipe is \\(\\frac{1}{15}\\) = \\(\\frac{5}{y}\\)
\ny = 15 \u00d7 5 = 75
\nSo , The Actual length of pipe is 75 feet .<\/p>\n
\nQuestion 3.
\n2(3p – 6) + 4p
\nAnswer: p = 1.2<\/p>\n
\nLet us say that whole expression is equal to 0
\n2(3p – 6) + 4p = 0
\n[2(3p) – 2(6)] + 4p = 0
\n6p – 12 + 4p = 0
\n10p – 12 = 0
\np = 12\/10 = 1.2
\nSo, p = 1.2<\/p>\n
\n5n – 3(4n + 1)
\nAnswer: n = -0.42<\/p>\n
\nLet us say that whole expression is equal to 0
\n5n – 3(4n + 1) = 0
\n5n – [ 3(4n) + 3(1) ] = 0
\n5n – 12n – 3 = 0
\n– 3 – 7n = 0
\n7n = – 3
\nn = -3\/7 = -0.42
\nSo, n = -0.42<\/p>\n
\nWhat is the solution of 2n – 4 > – 12?
\nA. n < – 10
\nB. n < – 4
\nC. n > – 2
\nD. n > – 4
\nAnswer:\u00a0 D . n > -4<\/p>\n
\nGiven, 2n – 4 > – 12
\nadd 4 in both sides,
\n2n – 4 + 4 > – 12 + 4
\n2n > – 8
\ndivide both sides by 2
\n2n\/2 > -8\/2
\nn > – 4 .<\/p>\n
\nCOMPARING NUMBERS IN DIFFERENT FORMS<\/strong> Determine which number is greater. Explain your method. (See Exploration 1, p. 235.)
\nQuestion 6.
\n4\\(\\frac{2}{5}\\) tons or 4.3 tons
\nAnswer: 4\\(\\frac{2}{5}\\) tons is greater than 4.3 tons<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite fraction \\(\\frac{22}{5}\\) \u00a0by dividing 22 by 5, we have 4.4 in decimal form
\nFinally, by comparing two values 4\\(\\frac{2}{5}\\) tons is greater than 4.3 tons<\/p>\n
\n82% success rate or \\(\\frac{5}{6}\\) success rate
\nAnswer: \\(\\frac{5}{6}\\) success rate is greater than 82% success rate<\/p>\n
\nBy using the method of converting fraction into Percent and comparing ,
\nWe can rewrite \\(\\frac{5}{6}\\) \u00a0as\u00a0 0.833 in decimal form,
\nTo get get the percent , multiply 100 to 0.833, then we get 83.3%.
\nSo, \\(\\frac{5}{6}\\) \u00a0can be write as 83.3%,
\nFinally, by comparing two values \\(\\frac{5}{6}\\) success rate is greater than 82% success rate<\/p>\n
\nQuestion 8.
\n26%
\nAnswer: 0.26<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.23.png\")
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\nSo, 26% in decimal form is 0.26<\/p>\n
\n0.63
\nAnswer: 63%<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.25.png\")
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol.
\nSo, 0.63 can be rewrite as 63%<\/p>\n
\n9%
\nAnswer: 0.09<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.26.png\")
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\nSo, 9% in decimal form is 0.09<\/p>\n
\n0.6
\nAnswer: 60%<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.27.png\")
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol.
\nSo, 0.6 can be rewrite as 60%<\/p>\n
\n44.7%
\nAnswer: 0.447<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.28.png\")
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\nSo, 44.7% in decimal form is 0.447<\/p>\n
\n55%
\nAnswer: 0.55<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.29.png\")
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\nSo, 55% in decimal form is 0.55<\/p>\n
\n\\(39 . \\overline{2} \\%\\)
\nAnswer: \\(0.39 \\overline{2}\\)<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.30.png\")
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\nSo, \\(39 . \\overline{2} \\%\\) in decimal form is \\(0.39 \\overline{2}\\)<\/p>\n
\n3.554
\nAnswer: 355.4%<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.31.png\")
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol.
\nSo, 3.554 \u00a0can be rewrite as 355.4%<\/p>\n
\n123%
\nAnswer: 1.23<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.32.png\")
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\nSo, 123% in decimal form is 1.23<\/p>\n
\n0.041
\nAnswer: 4.1%<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.33.png\")
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol.
\nSo, 0.041 can be rewrite as 4.1%<\/p>\n
\n0.122
\nAnswer: 12.2%<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.34.png\")
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol.
\nSo, 0.122 can be rewrite as 12.2%<\/p>\n
\n\\(49 . \\overline{92} \\%\\)
\nAnswer: \\(0.49 \\overline{92}\\)<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.35.png\")
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\nSo, \\(49 . \\overline{92} \\%\\) in decimal form is \\(0.49 \\overline{92}\\)<\/p>\n
\nYOU BE THE TEACHER<\/strong>
\nYour friend writes \\(49 . \\overline{8} \\%\\) as a decimal. Is your friend correct? Explain your reasoning.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-6.1-5.png\")
\nAnswer: He wrote the decimal for \\(4. \\overline{8} \\%\\) instead of \\(49 . \\overline{8} \\%\\)<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.24.png\")
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\nSo, \\(49 . \\overline{8} \\%\\) \u00a0in decimal form is \\(0.49 \\overline{8}\\)<\/p>\n
\nQuestion 21.
\n\\(\\frac{29}{100}\\)
\nAnswer: decimal = 0.29, percent = 29%<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{29}{100}\\) as\u00a0 0.29 in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then 0.29 can be rewrite as 29%
\nSo, \\(\\frac{29}{100}\\) in decimal = 0.29, percent = 29%<\/p>\n
\n\\(\\frac{3}{4}\\)
\nAnswer: decimal = 0.75, percent = 75%<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite\\(\\frac{3}{4}\\) as\u00a0 0.75 in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then 0.75 can be rewrite as 75%
\nSo, \\(\\frac{3}{4}\\) in decimal = 0.75, percent = 75%<\/p>\n
\n\\(\\frac{7}{8}\\)
\nAnswer: decimal = 0.875, percent = 87.5%<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{7}{8}\\) as\u00a0 0.875 in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then 0.875 can be rewrite as 87.5%
\nSo, \\(\\frac{7}{8}\\) in decimal = 0.875, percent = 87.5%<\/p>\n
\n\\(\\frac{2}{3}\\)
\nAnswer: decimal = \\(0. \\overline{6}\\), percent = \\(66. \\overline{6} \\%\\)<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{2}{3}\\) as \\(0. \\overline{6}\\) in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then\\(0. \\overline{6}\\) can be rewrite as \\(66. \\overline{6} \\%\\)
\nSo, \\(\\frac{2}{3}\\) in decimal =\\(0. \\overline{6}\\), percent = \\(66. \\overline{6} \\%\\)<\/p>\n
\n\\(\\frac{7}{9}\\)
\nAnswer: decimal = 0.77, percent = 77.7%<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite\\(\\frac{7}{9}\\) as\u00a0 0.77 in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then 0.77 can be rewrite as 77.7%
\nSo, \\(\\frac{7}{9}\\) in decimal = 0.77, percent = 77.7%<\/p>\n
\n\\(\\frac{12}{5}\\)
\nAnswer: decimal = 2.4, percent = 240%<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{12}{5}\\) as\u00a0 2.4 in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then 2.4 can be rewrite as 240%
\nSo, \\(\\frac{12}{5}\\) in decimal =2.4, percent = 240%<\/p>\n
\n\\(\\frac{9}{2}\\)
\nAnswer: decimal = 4.5, percent = 450%<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite\\(\\frac{9}{2}\\) as 4.5 in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then 4.5 can be rewrite as 450%
\nSo, \\(\\frac{9}{2}\\) in decimal = 4.5, percent = 450%<\/p>\n
\n\\(\\frac{1}{1000}\\)
\nAnswer: decimal = 0.0010, percent = 0.10%<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{1}{1000}\\) as\u00a0 0.0010 in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then 0.0010 can be rewrite as 0.10%
\nSo, \\(\\frac{1}{1000}\\) in decimal = 0.0010, percent = 0.10%<\/p>\n
\n\\(\\frac{17}{6}\\)
\nAnswer: decimal = \\(2.8 \\overline{3}\\), percent = \\(283 . \\overline{3} \\%\\)<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{17}{6}\\) as \\(2.8 \\overline{3}\\) in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then\\(2.8 \\overline{3}\\) can be rewrite as \\(283 . \\overline{3} \\%\\)
\nSo, \\(\\frac{17}{6}\\) in decimal = \\(2.8 \\overline{3}\\), percent = \\(283 . \\overline{3} \\%\\)<\/p>\n
\n\\(\\frac{3}{11}\\)
\nAnswer: decimal = 0.27, percent = 27%<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{3}{11}\\) as\u00a0 0.27 in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then 0.27 can be rewrite as 27%
\nSo, \\(\\frac{3}{11}\\) in decimal = 0.27, percent = 27%<\/p>\n
\n\\(\\frac{1}{750}\\)
\nAnswer: decimal = \\(0.001 \\overline{3}\\), percent =\\(0.1 \\overline{3} \\%\\)<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{1}{750}\\) as\u00a0 \\(0.001 \\overline{3}\\) in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then \\(0.001 \\overline{3}\\) can be rewrite as \\(0.1 \\overline{3} \\%\\)
\nSo, \\(\\frac{1}{750}\\) in decimal = \\(0.001 \\overline{3}\\), percent = \\(0.1 \\overline{3} \\%\\)<\/p>\n
\n\\(\\frac{22}{9}\\)
\nAnswer: decimal = \\(2. \\overline{4}\\), percent = \\(244 . \\overline{4} \\%\\)<\/p>\n
\nBy using the method of converting fraction into decimal and comparing ,
\nWe can rewrite \\(\\frac{22}{9}\\) as\u00a0 \\(2. \\overline{4}\\) in decimal form,
\nTo write decimal into percent we should multiply the number by 100, which moves the decimal point two places to the right and add a percent symbol , then \\(2. \\overline{4}\\) can be rewrite as \\(244 . \\overline{4} \\%\\)
\nSo, \\(\\frac{22}{9}\\) in decimal = \\(2. \\overline{4}\\), percent = \\(244 . \\overline{4} \\%\\)<\/p>\n
\nQuestion 33.
\n66.1%, 0.66, \\(\\frac{2}{3}\\), 0.667
\nAnswer: 0.66, 66.1%, \\(\\frac{2}{3}\\), 0.667<\/p>\n
\nIn order to put them in an ascending order we have to calculate the fraction, percent, decimal in their respective form, So Fraction \\(\\frac{2}{3}\\) can be rewrite as \\(0. \\overline{6}\\) in decimal form
\nThen 66.1% can be rewrite as 0.661 in decimal form,
\nAs we can see 0.66 is less than 66.1% , 66.1% is less than \\(\\frac{2}{3}\\), \\(\\frac{2}{3}\\) \u00a0is less than 0.667,
\nFinally, we have the ascending order as 0.66, 66.1%, \\(\\frac{2}{3}\\), 0.667.<\/p>\n
\n\\(\\frac{2}{9}\\), 21%, \\(0.2 \\overline{1}\\), \\(\\frac{11}{50}\\)
\nAnswer: 21%, \\(0.2 \\overline{1}\\), \\(\\frac{11}{50}\\), \\(\\frac{2}{9}\\)<\/p>\n
\nIn order to put them in an ascending order we have to calculate the fraction, percent, decimal in their respective form, So Fraction \\(\\frac{11}{50}\\) can be rewrite as 0.22 in decimal form,
\n\\(\\frac{2}{9}\\) can be rewrite as \\(0.22 \\overline{2}\\)in decimal form,
\nThen 21% can be rewrite as 0.21 in decimal form,
\nAs we can see 21% \u00a0is less than \\(0.2 \\overline{1}\\) ,\\(0.2 \\overline{1}\\) is less than \\(\\frac{11}{50}\\), \u00a0\\(\\frac{11}{50}\\)\u00a0 is less than \\(\\frac{2}{9}\\),
\nFinally, we have the ascending order as 21%, \\(0.2 \\overline{1}\\), \\(\\frac{11}{50}\\), \\(\\frac{2}{9}\\)<\/p>\n
\nQuestion 35.
\n\\(\\frac{7}{9}\\)
\nAnswer: decimal = 0.777 , it is in the graph at the point A<\/p>\n
\nBy using the method of converting fraction into decimal ,
\nWe can rewrite \\(\\frac{7}{9}\\) as 0.777 in decimal form,
\nSo, looking at the graph given, it is at point A.<\/p>\n
\n0.812
\nAnswer:\u00a0 it is at the point C in the given graph.<\/p>\n
\n\\(\\frac{5}{6}\\)
\nAnswer: decimal = 0.833 , it is in the graph at the point D<\/p>\n
\nBy using the method of converting fraction into decimal ,
\nWe can rewrite \\(\\frac{5}{6}\\) as 0.833 in decimal form,
\nSo, looking at the graph given, it is at point D.<\/p>\n
\n79.5%
\nAnswer: 0.795, it is in the graph at the point B<\/p>\n
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\nSo, 79.5% in decimal form is 0.795
\n0.795 is in the graph given , at the point B vb<\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-6.1-6.png\")
<\/p>\n
\nPROBLEM SOLVING<\/strong>
\nThe table shows the portion of students in each grade that participate in School Spirit Week. Order the grades by portion of participation from least to greatest.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-6.1-7.png\")
\nAnswer: The grades by portion of participation from least to greatest are 7 , 6 , 8.<\/p>\n
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left. So, 65% in decimal form is 0.65.
\nBy using the method of converting fraction into Percent\u00a0 ,
\nWe can rewrite \\(\\frac{5}{6}\\) as 0.6 in decimal form,
\nThen grade 6 = 0.64 , grade 7 = 0.6 , grade 8 = 0.65 ,
\nSo, The grades by portion of participation from least to greatest are 7 , 6 , 8.<\/p>\n
\nMODELING REAL LIFE<\/strong>
\nThe table shows the portion of gold medals that were won by the United States in five summer Olympic games. In what year did the United States win the least portion of gold medals? the greatest portion? Justify your answers.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-6.1-8.png\")
\nAnswer: The United States win the least portion of gold medals in the year 2004 and the greatest portion of gold medals won in the year 2012<\/p>\n
\nBy using the method of converting fraction into Percent and comparing ,
\nWe can rewrite \\(\\frac{36}{301}\\)\u00a0 as\u00a0 0.119 in decimal form,
\n\\(\\frac{23}{150}\\) as 0.153 in decimal form,
\n\\(\\frac{46}{307}\\) as 0.149 in decimal form,
\nTo write percent into decimal we have to remove percent symbol and divide by 100, which moves the decimal point two places to the left.
\n\\(12. \\overline{3} \\%\\) as \\(0.12 \\overline{3}\\) in decimal form.
\nSo, according to their years and portions of gold medals we have ,
\nyear 2000 – \\(0.12 \\overline{3}\\),
\nyear 2004 – 0.119,
\nyear 2008 – \\(0. \\overline{12}\\),
\nyear 2012 – 0.153,
\nyear 2016 – 0.149,
\nFinally, The United States win the least portion of gold medals in the year 2004 and the greatest portion of gold medals won in the year 2012.<\/p>\n
\nPROBLEM SOLVING<\/strong>
\nYou, your friend, and your cousin have a basketball competition where each person attempts the same number of shots. You make 70% of your shots, your friend makes of her shots, \\(\\frac{7}{9}\\) and your cousin makes \\(0.7 \\overline{2}\\) of his shots. How many times more shots are made by the first place finisher than the third place finisher?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-6.1-9.png\")
\nAnswer: The first place finisher made 0.077 more shorts than the third place finisher.<\/p>\n
\nThe shorts made by 1st person are 70%, that is 0.7 in decimal,
\nThe shorts made by 2nd person are \\(\\frac{7}{9}\\) rewriting as 0.777 in decimal,
\nThe shorts made by 3rd person are \\(0.7 \\overline{2}\\)
\nThe shorts made by\u00a0 the first place finisher is\u00a0 0.777 and by the Third place finisher is 0.7,
\nTo know how many more shorts are made by first place finisher than third place finisher is the difference between 0.777 and 0.7 , that is 0.777 – 0.7 = 0.077.
\nSo, the first place finisher made 0.077 more shorts than the third place finisher.<\/p>\n
\nDIG DEEPER!<\/strong>
\nThree different mixtures contain small amounts of acetic acid. Mixture A is 0.036 acetic acid, Mixture B is 4.2% acetic acid, and Mixture C is \\(\\frac{1}{22}\\) acetic acid. Explain how to use this information to determine which mixture contains the greatest amount of acetic acid.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-6.1-10.png\")
\nAnswer: 0.045 , Mixture C has more amount of acetic acid as compared to Mixture A and Mixture B.<\/p>\n
\nMixture A is 0.036 acetic acid,
\nMixture B is 4.2% acetic acid, in decimal we can write it as 0.042,
\nMixture C is \\(\\frac{1}{22}\\) acetic acid, rewriting as 0.045 in decimal form,
\nSo, 0.036 is less than 0.042 , 0.042 is less than 0.045,
\nFinally,\u00a0 0.045 Mixture c has the more amount of acetic acid as compared to Mixture A and Mixture B.<\/p>\n
\nMODELING REAL LIFE<\/strong>
\nOver 44% of the 30 students in a class read a book last month. What are the possible numbers of students in the class who read a book last month? Justify your answer.
\nAnswer: 13 number of students in the class read the book last month.<\/p>\n
\nGiven, 44% of 30 students
\n=(44%) \u00d7 30
\n= \\(\\frac{44}{100}\\) \u00d7 30
\n= \\(\\frac{44 \u00d7 30}{100}\\)
\n= \\(\\frac{1320}{100}\\)
\n=13.2
\nSo, 13 number of students in the class read the book last month.<\/p>\n
\nNUMBER SENSE<\/strong>
\nFill in the blanks using each of the numbers 0 – 7 exactly once, so that the percent, decimal, and fraction below are ordered from least to greatest. Justify your answer.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-6-Percents-6.1-11.png\")
\nAnswer:\u00a0 The percent, decimal, and fraction are ordered from least to greatest are 12.3%, 0.57, \\(\\frac{4}{6}\\) by using 0 – 7 numbers only once .<\/p>\n
\nGiven , using each of the numbers 0 – 7 exactly once,
\nEstimating on the numbes
\nUsing numbers 1 , 2 , 3 for percent gives 12.3% as shown and can be writen as 0.123
\nUsing numbers 0 , 5 , 7 for decimal gives 0.57 as shown
\nUsing numbers 4 and 6 for fraction gives \\(\\frac{4}{6}\\) and can be writen as 0.66
\nThe order from least to greatest is 0.123 , 0.57 , 0.66 .
\nSo , The percent, decimal, and fraction are ordered from least to greatest are 12.3%, 0.57, \\(\\frac{4}{6}\\)<\/p>\n<\/a>Lesson 6.2 The Percent Proportion<\/h3>\n
\nWork with a partner.
\na. Complete each model. Explain what each model represents.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-6-Percents-6.2-1.png\")
\nb. Use the models in part (a) to answer each question.<\/p>\n\n
\nd. Write a question different from those in part (b) that can be answered using one of the models in part(a). Trade questions with another group and find the solution.
\nAnswer: All the answers are given below the explanation.<\/p>\n
\na. ![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.36.png\")
\nThis model represents the number 30 which is divided in to two equal halves ,which can be represented in percent and numbers,
\nthat is 50% of 30 is 15.
\n50 percent \u00d7 30 =
\n(50:100) \u00d7 30 =
\n(50 \u00d7 30):100 =
\n1500:100 = 15<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.37.png\")
\nThis model represents the number 75 which is divided in to five equal halves, which can be represented in percent and numbers ,That is
\n20% of 75 is 15,
\n40% of 75 is 30,
\n60% of 75 is 45,
\n80% of 75 is 60.<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.38.png\")
\nThis model represents the number 96 which is divided in to four equal halves, which can be represented in percent and numbers ,That is
\n33\\(\\frac{1}{3}\\%\\) of 96 is 24,
\n66\\(\\frac{2}{3}\\%\\) of 96 is 48,
\n100% of 96 is 72.<\/p>\n
\nFrom the figure 2 of part (a) we know, 15 is the number which is 20% of 75,
\nFrom the figure 3 of part (a) we know, 96 is the number which is 133\\(\\frac{1}{3}\\%\\) of 96.<\/p>\n
\nSince the divided equal parts are equally represents the whole number given ,So that the ratios of the parts can be easily combined in to the whole number .
\nThus, the proportion can be used to calculate the percent of each ratio and have the unchanged output .
\nFor example, <\/p>\n
\nWhat number is 80% of 75?<\/p>\n
\nQuestion 1.
\nWhat percent of 5 is 3?
\nAnswer: 60%<\/p>\n
\n3 : 5 \u00d7 100 =
\n(3 \u00d7 100): 5
\n300 : 5 = 60
\nSo, 5 is 60% of 3.<\/p>\n
\n24 is what percent of 20?
\nAnswer: 120%<\/p>\n
\n24 : 20 \u00d7 100 =
\n(24 \u00d7 100) : 20 =
\n2400 : 20 = 120
\nSo, 24 is the 120% of 20.<\/p>\n
\nQuestion 3.
\nWhat number is 80% of 60?
\nAnswer:\u00a0 48<\/p>\n
\n80 % \u00d7 60 =
\n(80 :100) \u00d7 60 =
\n(80 \u00d7 60) :100 =
\n4800 : 100 = 48
\nSo, 48 is 80% of 60.<\/p>\n
\n10% of 40.5 is what number?
\nAnswer: 4.05<\/p>\n
\n10 % \u00d7 40.5 =
\n(10 : 100) \u00d7 40.5 =
\n(10 \u00d7 40.5) : 100 =
\n4.05 : 100 = 4.05
\nSo, 4.05 is the 10% of 40.5<\/p>\n
\nQuestion 5.
\n0.1% of what number is 4?
\nAnswer: 4,000<\/p>\n
\nLet the number be X
\n0.1% \u00d7 X = 4
\nX = 4 \u00f7 0.1%
\n= 4 \u00f7 (0.1 \u00f7 100)
\n= (100 \u00d7 4 ) \u00f7 0.1
\n= 400 \u00f7 0.1
\n=4,000
\nSo, 4 is the 0.1% of 4,000.<\/p>\n
\n\\(\\frac{1}{2}\\) is 25% of what number?
\nAnswer:\u00a0 2<\/p>\n
\nTo make calculation easier we can rewrite \\(\\frac{1}{2}\\) as 0.5
\nlet the number be X
\n25% \u00d7 X = 0.5
\nX = 0.5 \u00f7 25%
\n= 0.5 \u00f7 (25 \u00f7 100)
\n= (100 \u00d7 0.5 ) \u00f7 25
\n= 50 \u00f7 25
\n=2
\nSo, 0.5 is the 25% of 2.<\/p>\n
\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n
\nUSING THE PERCENT PROPORTION<\/strong>
\nWrite and solve a proportion to determine what percent of 120 is 54.
\nAnswer:\u00a0 45%<\/p>\n
\nBy using percent proportion, we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{54}{120}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{54 \u00d7 100}{120}\\) = p
\np = \\(\\frac{5400}{120}\\)
\np = 45%
\nso, 54 is the 45% of 120.<\/p>\n
\nCHOOSE TOOLS<\/strong>
\nUse a model to find 60% of 30.
\nAnswer: 18<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.39.png\")
\n60% \u00d7 30
\n= (60 : 100) \u00d7 30
\n= (60 \u00d7 30) : 100
\n= 1800 : 100
\n= 18
\nSo, 60% of 30 is 18.<\/p>\n
\nWHICH ONE DOESN\u2019T BELONG?<\/strong>
\nWhich proportion at the left does not belong with the other three? Explain your reasoning.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-6-Percents-6.2-2.png\")
\nAnswer: second proportion doesn’t belong to other three<\/p>\n
\nsecond proportion: 15\/50 = p \/100
\np = (15 \u00d7 100) \u00f750
\np = 150 \u00f7 5
\np = 30
\nHere we got 30% , as the p values of the other three proportions are 50%
\nSo, second proportion does not fit in to the other three proportions.<\/p>\n
\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n
\nAn arctic woolly-bear caterpillar lives for 7 years and spends 90% of its life frozen. How many days of its life is the arctic woolly-bear frozen?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-6-Percents-6.2-3.png\")
\nAnswer: The arctic woolly-bear frozen for 6.3 years in their life time.<\/p>\n
\nGiven, An arctic woolly-bear caterpillar lives for 7 years and spends 90% of its life frozen
\nWe have, 90% \u00d7 7
\n= (90 : 100 ) \u00d7 7
\n= (90 \u00d7 7) : 100
\n= 630 : 100
\n= 6.3 years
\nSo, The arctic woolly-bear frozen for 6.3 years in their life time.<\/p>\n
\nDIG DEEPER!<\/strong>
\nThe table shows the numbers of pictures you upload to a social media website for 5 days in a row. How many total pictures do you upload during the week when 32% of the total pictures are uploaded on Saturday and Sunday?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-6-Percents-6.2-4.png\")
\nAnswer: The total pictures uploaded during the week are 53.<\/p>\n
\nGiven,\u00a0 32% of the total pictures are uploaded on Saturday and Sunday
\nAnd adding the photos that we uploaded during the 5 days are 2 + 2 + 4 + 1 + 8 = 17
\nLet the number we should find be X
\n32% \u00d7 X = 17
\nX = 17 \u00f7 32%
\n= 17 \u00f7 (32 \u00f7 100)
\n= (100 \u00d7 17 ) \u00f7 32
\n= 1700 \u00f7 32
\n= 53.12
\nSo, 17 is the 32% of 53.
\nFinally we have, The total pictures uploaded during the week are 53.<\/p>\n<\/a>The Percent Proportion Homework & Practice 6.2<\/h3>\n
\nQuestion 1.
\n\\(\\frac{42}{100}\\)
\nAnswer: decimal = 0.42 , percent = 42%<\/p>\n
\nTo get the percent or decimal from fraction \\(\\frac{42}{100}\\) we have to divide 42 by 100 ,
\nThen, we get 0.42,
\nTo get the percent of 0.42 multiply by 100 , it will be 42%
\nSo, \\(\\frac{42}{100}\\) can be written as\u00a0 0.42 or 42%<\/p>\n
\n\\(\\frac{7}{1000}\\)
\nAnswer: decimal = 0.007 , percent = 0.7%<\/p>\n
\nTo get the percent or decimal from\u00a0 fraction \\(\\frac{7}{1000}\\) we have to divide 7 by 1000 ,
\nThen, we get 0.007,
\nTo get the percent of 0.007 multiply by 100 , it will be 0.7%
\nSo, \\(\\frac{7}{1000}\\) can be written as\u00a0 0.007 or 0.7%<\/p>\n
\n\\(\\frac{13}{9}\\)
\nAnswer: decimal = 1.444 , percent = 144.4%<\/p>\n
\nTo get the percent or decimal from \\(\\frac{13}{9}\\) \u00a0fraction we have to divide 13 by 9 ,
\nThen, we get 1.444,
\nTo get the percent of 1.444 multiply by 100 , it will be 144.4%
\nSo, \\(\\frac{13}{9}\\)\u00a0can be written as\u00a0 1.444 or 144.4%<\/p>\n
\n\\(\\frac{41}{66}\\)
\nAnswer: decimal = \\(0.62 \\overline{12}\\) , percent = \\(62. \\overline{12} \\%\\)<\/p>\n
\nTo get the percent or decimal from\u00a0 fraction \\(\\frac{41}{66}\\) we have to divide 41 by 66 ,
\nThen, we get \\(0.62 \\overline{12}\\),
\nTo get the percent of \\(0.62 \\overline{12}\\) multiply by 100 , it will be \\(62. \\overline{12} \\%\\)
\nSo, \\(\\frac{41}{66}\\) can be written as\u00a0 \\(0.62 \\overline{12}\\) or \\(62. \\overline{12} \\%\\)<\/p>\n
\nQuestion 5.
\na \u00f7 5
\nAnswer: -3<\/p>\n
\nGiven , a = – 15
\nThen , – 15 \u00f7 5
\n= \\(\\frac{-15}{5}\\)
\n= – 3.
\nso, a \u00f7 5 = – 3.<\/p>\n
\n\\(\\frac{b+14}{a}\\)
\nAnswer: \\(\\frac{9}{-15}\\)<\/p>\n
\nGiven , a = -15 , b = -5 , by substituting the given values in the expression, we get
\n= \\(\\frac{(- 5)+14}{-15}\\)
\n= \\(\\frac{9}{-15}\\)
\nSo, \\(\\frac{b+14}{a}\\) = \\(\\frac{9}{-15}\\)<\/p>\n
\n\\(\\frac{b^{2}}{a+5}\\)
\nAnswer: \\(\\frac{25}{-10}\\)<\/p>\n
\nGiven , a = -15 , b = -5, by substituting the given values in the expression, we get
\n= \\(\\frac{(-5)^{2}}{(-15)+5}\\)
\n= \\(\\frac{25}{-10}\\)
\nSo, \\(\\frac{b^{2}}{a+5}\\) = \\(\\frac{25}{-10}\\)<\/p>\n
\nA. x = – 5
\nB. x = – 0.2
\nC. x = 0.2
\nD. x = 5
\nAnswer: C . x = 0.2<\/p>\n
\nGiven, 9x = 1.8
\nx = \\(\\frac{1.8}{9}\\)
\nx = 0.2.<\/p>\n
\nQuestion 9.
\nWhat number is 20% of 80?
\nAnswer: 16<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.41.png\")
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\)\u00a0 = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{80}\\) = \\(\\frac{20}{100}\\)
\n\\(\\frac{a}{80}\\) = \\(\\frac{1}{5}\\)
\na = \\(\\frac{80}{5}\\)
\na = 16.
\nSo, 16 is 20% of 80.<\/p>\n
\n10 is what percent of 40?
\nAnswer: 25%<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.42.png\")
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{10}{40}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{1}{4}\\)\u00a0 = \\(\\frac{p}{100}\\)
\np = \\(\\frac{100}{4}\\)
\np = 25
\nSo, 10 is 25% of 40.<\/p>\n
\n15 is 30% of what number?
\nAnswer: 50<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.40.png\")
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\)\u00a0 = \\(\\frac{p}{100}\\)
\n\\(\\frac{15}{w}\\)\u00a0 = \\(\\frac{30}{100}\\)
\nby cross multiplication we get,
\n30 \u00d7 w = 15 \u00d7 100
\nw\u00a0 = \\(\\frac{1500}{30}\\)
\nw = \\(\\frac{150}{30}\\)
\nw = 50.
\nSo, 15 is 30% of 50.<\/p>\n
\nWhat number is 120% of 70?
\nAnswer: 84<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.44.png\")
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{70}\\)\u00a0 = \\(\\frac{120}{100}\\)
\n\\(\\frac{a}{70}\\)\u00a0 = \\(\\frac{6}{5}\\)
\na = \\(\\frac{70 \u00d7 6}{5}\\)
\na = \\(\\frac{420}{5}\\)
\na = 84
\nSo, 84 is 120% of 70.<\/p>\n
\n20 is what percent of 50?
\nAnswer: 40%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{20}{50}\\)\u00a0 = \\(\\frac{p}{100}\\)
\np = \\(\\frac{20 \u00d7 100}{50}\\)
\np = \\(\\frac{200}{5}\\)
\np = 40
\nSo, 20 is 40% of 50.<\/p>\n
\n48 is 75% of what number?
\nAnswer: 64<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.43.png\")
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\)\u00a0 = \\(\\frac{p}{100}\\)
\n\\(\\frac{48}{w}\\)\u00a0 = \\(\\frac{75}{100}\\)
\nw =\\(\\frac{48 \u00d7 100}{75}\\)
\nw = \\(\\frac{4800}{75}\\)
\nw = 64
\nSo, 48 is 75% of 64.<\/p>\n
\nQuestion 15.
\nWhat percent of 25 is 12?
\nAnswer: 48%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\)\u00a0 = \\(\\frac{p}{100}\\)
\n\\(\\frac{12}{25}\\)\u00a0 = \\(\\frac{p}{100}\\)
\np = \\(\\frac{12 \u00d7 100}{25}\\)
\np = \\(\\frac{1200}{25}\\)
\np = 48
\nSo, 12 is 48% of 25.<\/p>\n
\n14 is what percent of 56?
\nAnswer: 25%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{14}{56}\\)\u00a0 = \\(\\frac{p}{100}\\)
\np = \\(\\frac{14 \u00d7 100}{56}\\)
\np = \\(\\frac{1400}{56}\\)
\np = 25
\nSo, 14 is 25% of 56.<\/p>\n
\n25% of what number is 9?
\nAnswer: 36<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{9}{w}\\) = \\(\\frac{25}{100}\\)
\n\\(\\frac{9}{w}\\) = \\(\\frac{1}{4}\\)
\nw = 9 \u00d7 4
\nw = 36.
\nSo, 9 is 25% of 36.<\/p>\n
\n36 is 0.9% of what number?
\nAnswer: 4,000<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\)\u00a0 = \\(\\frac{p}{100}\\)
\n\\(\\frac{36}{w}\\) = \\(\\frac{0.9}{100}\\)
\nw = \\(\\frac{36 \u00d7 100}{0.9}\\)
\nw = \\(\\frac{3600}{0.9}\\)
\nw = \\(\\frac{36,000}{9}\\)
\nw = 4,000
\nSo, 36 is 0.9% of 4,000.<\/p>\n
\n75% of 124 is what number?
\nAnswer: 93<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{124}\\) = \\(\\frac{75}{100}\\)
\na = \\(\\frac{75 \u00d7 124}{100}\\)
\na\u00a0 = \\(\\frac{9,300}{100}\\)
\na = 93
\nSo, 93 is 75% of 124.<\/p>\n
\n110% of 90 is what number?
\nAnswer: 99<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\)\u00a0 = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{90}\\)\u00a0 = \\(\\frac{110}{100}\\)
\na = \\(\\frac{110 \u00d7 90}{100}\\)
\na = \\(\\frac{9900}{100}\\)
\na = 99
\nSo, 99 is 110% of 90.<\/p>\n
\nWhat number is 0.4% of 40?
\nAnswer: 0.16<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\)\u00a0 = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{40}\\)\u00a0 = \\(\\frac{0.4}{100}\\)
\na = \\(\\frac{0.4 \u00d7 40}{100}\\)
\na = \\(\\frac{16}{100}\\)
\na = 0.16
\nSo, 0.16 is 0.4% of 40.<\/p>\n
\n72 is what percent of 45?
\nAnswer:\u00a0 160%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{72}{45}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{72 \u00d7 100}{45}\\)
\np = \\(\\frac{7200}{45}\\)
\np = 160
\nSo, 72 is 160% of 45.<\/p>\n
\nYOU BE THE TEACHER<\/strong>
\nYour friend uses the percent proportion to answer the question below. Is your friend correct? Explain your reasoning.
\n\u201c40%of what number is 34?\u201d
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-6-Percents-6.2-5.png\")
\nAnswer:\u00a0 yes, he used the correct percent proportion.<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{34}{w}\\) = \\(\\frac{40}{100}\\)
\nw = \\(\\frac{34 \u00d7 100}{40}\\)
\nw = \\(\\frac{3400}{40}\\)
\nw = 85
\nSo, 34 is 40% of 85.<\/p>\n
\nMODELING REAL LIFE<\/strong>
\nOf 140 seventh-grade students, 15% earn the Presidential Youth Fitness Award. How many students earn the award?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-6-Percents-6.2-6.png\")
\nAnswer: 21 students earn the Presidential Youth Fitness Award.<\/p>\n
\nGiven, Of 140 seventh-grade students, 15% earn the Presidential Youth Fitness Award.
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{140}\\) = \\(\\frac{15}{100}\\)
\na = \\(\\frac{15 \u00d7 140}{100}\\)
\na = \\(\\frac{2100}{100}\\)
\na = 21
\nSo, 21 is 15% of 140.
\nTotally ,21 students earn the Presidential Youth Fitness Award.<\/p>\n
\nMODELING REAL LIFE<\/strong>
\nA salesperson receives a 3% commission on sales. The salesperson receives $180 in commission. What is the amount of sales?
\nAnswer: The total amount of sale is $6,000.<\/p>\n
\nGiven, A salesperson receives a 3% commission on sales, The salesperson receives $180 in commission.
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{180}{w}\\) = \\(\\frac{3}{100}\\)
\nw = \\(\\frac{180 \u00d7 100}{3}\\)
\nw = \\(\\frac{18,000}{3}\\)
\nw = 6,000
\nSo, $180 is 3% of $6,000.
\nTotal amount of sale is $6,000.<\/p>\n
\nQuestion 26.
\n0.5 is what percent of 20?
\nAnswer: 2.5%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{0.5}{20}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{0.5 \u00d7 100}{20}\\)
\np = 0.5 \u00d7 5
\np = 2.5
\nSo, 0.5 is 2.5% of 20.<\/p>\n
\n14.2 is 35.5% of what number?
\nAnswer: 40<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{14.2}{w}\\) = \\(\\frac{35.5}{100}\\)
\nw = \\(\\frac{14.2 \u00d7 100}{35.5}\\)
\nw = \\(\\frac{142 \u00d7 10}{35.5}\\)
\nw = 40
\nSo, 14.2 is 35.5% of 40.<\/p>\n
\n\\(\\frac{3}{4}\\) is 60% of what number?
\nAnswer: 1.25<\/p>\n
\n\\(\\frac{3}{4}\\) can be rewrite as 0.75 in decimal,
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{0.75}{w}\\) = \\(\\frac{60}{100}\\)
\nw = \\(\\frac{0.75 \u00d7 100}{60}\\)
\nw = \\(\\frac{75}{60}\\)
\nw = 1.25
\nSo, 0.75 is 60% of 1.25.<\/p>\n
\nWhat number is 25% of \\(\\frac{7}{8}\\)?
\nAnswer: 0.218<\/p>\n
\n\\(\\frac{7}{8}\\) can be rewrite as 0.875 in decimal,
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{0.875}\\) = \\(\\frac{25}{100}\\)
\na = \\(\\frac{0.875 \u00d7 25}{100}\\)
\na = \\(\\frac{21.87}{100}\\)
\na = 0.218
\nSo, 0.218 is 25% of 0.875.<\/p>\n
\nMODELING REAL LIFE<\/strong>
\nYou are assigned 32 math exercises for homework. You complete 75% of the exercises before dinner. How many exercises do you have left to do after dinner?
\nAnswer: 24 exercises are left .<\/p>\n
\nYou are assigned 32 math exercises for homework. You complete 75% of the exercises before dinner.
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{32}\\) = \\(\\frac{75}{100}\\)
\na = \\(\\frac{32 \u00d7 75}{100}\\)
\na = \\(\\frac{2,400}{100}\\)
\na = 24
\nSo, 24 is 75% of 32.
\nTotally, 24 exercise are left .<\/p>\n
\nMODELING REAL LIFE<\/strong>
\nYour friend earns $10.50 per hour, which is 125% of her hourly wage last year. How much did your friend earn per hour last year?
\nAnswer: Friend earned $8.4 per hour last year<\/p>\n
\nYour friend earns $10.50 per hour, which is 125% of her hourly wage last year,
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{10.5}{w}\\) = \\(\\frac{125}{100}\\)
\nw = \\(\\frac{10.5 \u00d7 100}{125}\\)
\nw = \\(\\frac{1050}{125}\\)
\nw = 8.4
\nSo, 8.4 is 125% of 10.5.<\/p>\n
\nMODELING REAL LIFE<\/strong>
\nThe bar graph shows the numbers of reserved campsites at a campground for one week. What percent of the reservations were for Friday or Saturday?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-6-Percents-6.2-7.png\")
\nAnswer: The percent of reservations For Friday is 74.2% and for Saturday is\u00a0 85%<\/p>\n
\nAs per the graph shown, The reservations made for the week are 35 ,
\nFriday reservations are 26, so
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{26}{35}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{26 \u00d7 100}{35}\\)
\np = \\(\\frac{2600}{35}\\)
\np = 74.2
\nSo, 26 is 74.2% of 35.<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{30}{35}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{30 \u00d7 100}{35}\\)
\np = \\(\\frac{3,000}{35}\\)
\np = 85
\nSo, 30 is 85% of 35.<\/p>\n
\nPROBLEM SOLVING<\/strong>
\nYour friend displays the results of a survey that asks several people to vote on a new school mascot.
\na. What is missing from the bar graph?
\nb. What percent of the votes does the least popular mascot receive? Explain your reasoning.
\nc. There are 124 votes total. How many votes does tiger receive?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-6-Percents-6.2-8.png\")
\nAnswer: a. The numerical values for the votes are missing from the graph<\/p>\n
\nDIG DEEPER!<\/strong>
\nA quarterback completes 18 of 33 passes during the first three quarters of a football game. He completes every pass in the fourth quarter and 62.5% of his passes for the entire game. How many passes does the quarterback throw in the fourth quarter? Justify your answer.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-6-Percents-6.2-9.png\")
\nAnswer: Quarterback throw 20.6 passes in the fourth quarter<\/p>\n
\nA quarterback completes 18 of 33 passes during the first three quarters of a football game,
\nHe completes every pass in the fourth quarter and 62.5% of his passes for the entire game.
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{33}\\) = \\(\\frac{62.5}{100}\\)
\na = \\(\\frac{33 \u00d7 62.5}{100}\\)
\na = \\(\\frac{2,062.5}{100}\\)
\na = 20.6
\nSo, 20.6 is 62.5% of 33.<\/p>\n
\nREASONING<\/strong>
\n20% of a number is x. What is 100% of the number? Assume x > 0.
\nAnswer: 5x<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\nsubstitute a = x and p = 20
\n\\(\\frac{x}{w}\\) = \\(\\frac{20}{100}\\)
\nby cross multiplication , we get
\nw \u00d7 20 = x \u00d7 100
\n20w = 100x
\nDivide both sides by 20,
\n\\(\\frac{20w}{20}\\) = \\(\\frac{100x}{20}\\)
\nw = 5x
\nSo, 100% of the number is 5x.<\/p>\n
\nSTRUCTURE<\/strong>
\nAnswer each question. Assume x > 0.
\na. What percent of 8x is 5x?
\nb. What is 65% of 80x?
\nAnswer: a. 62.5% , b. 52x<\/p>\n
\na. percent of 8x is 5x
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{5x}{8x}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{5}{8}\\) = \\(\\frac{p}{100}\\)
\nby cross multiplying
\n8p = 500
\np = \\(\\frac{500}{8}\\)
\np = 62.5
\nSo, 5x is 62.5% of 8x.<\/p>\n
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{8x}\\) = \\(\\frac{65}{100}\\)
\na = \\(\\frac{8x \u00d7 65}{100}\\)
\na = \\(\\frac{520x}{100}\\)
\na = 52x
\nSo, 52x is 65% of 80x.<\/p>\n<\/a>Lesson 6.3 The Percent Equation<\/h3>\n
\nWork with a partner.
\na. The circle graph shows the number of votes received by each candidate during a school election. So far, only half of the students have voted. Find the percent of students who voted for each candidate. Explain your method.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents-6.3-1.png\")
\nc. The circle graph shows the final results of the election after every student voted. Use the equation you wrote in part(b) to find the number of students who voted for each candidate.
\nd. Use a different method to check your answers in part(c). Which method do you prefer? Explain.
\nAnswer:
\na. The percent of students who voted for each candidate are
\nFor Person A = 20% ,
\nFor Person B = 25%
\nFor Person C = 15%
\nFor Person D = 40%<\/p>\n
\nFor Person A = 30
\nFor Person B = 24
\nFor Person C = 24
\nFor Person D = 42<\/p>\n
\na. Given, The circle graph shows the number of votes received by each candidate during a school election. So far, only half of the students have voted.
\nThe number of votes received till now are 12 + 15 + 9 + 24 = 60,
\nTo know the percent of students who voted for each candidate we have ,
\nFor person A, w = 60 , a = 12 , p = ?
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{12}{60}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{12 \u00d7 100}{60}\\)
\np = \\(\\frac{1200}{60}\\)
\np = 20
\nSo, 12 is 20% of 60.
\nThe percent of\u00a0 students who voted for person A is 20%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{15}{60}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{15 \u00d7 100}{60}\\)
\np = \\(\\frac{1500}{60}\\)
\np = 25
\nSo, 15 is 25% of 60.
\nThe percent of\u00a0 students who voted for person B is 25%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{9}{60}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{9 \u00d7 100}{60}\\)
\np = \\(\\frac{900}{60}\\)
\np = 15
\nSo, 9 is 15% of 60.
\nThe percent of\u00a0 students who voted for person C is 15%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{24}{60}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{24 \u00d7 100}{60}\\)
\np = \\(\\frac{2400}{60}\\)
\np = 40
\nSo, 24 is 40% of 60.
\nThe percent of\u00a0 students who voted for person D is 40%<\/p>\n
\nwhere as a = part , w= whole , p = percent ,
\nTo solve for a , we can write it as a = \\(\\frac{w \u00d7 p}{100}\\)<\/p>\n
\nas shown in part (a)\u00a0 half of the students are 60 ,
\nThe half of the students voted in all the students are 60 and total strength of students are 60 + 60 = 120
\nTo calculate the number of voting acquired by each candidate we have,
\nFor person A , w\u00a0 = 120 , p = 25 , a = ?
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{120}\\) = \\(\\frac{25}{100}\\)
\na = \\(\\frac{120 \u00d7 25}{100}\\)
\na = \\(\\frac{120}{4}\\)
\na = 30
\nSo, 30 is 25% of 120.
\nThe number of students who voted for person A after final results are 30<\/p>\n
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{120}\\) = \\(\\frac{20}{100}\\)
\na = \\(\\frac{120 \u00d7 20}{100}\\)
\na = \\(\\frac{120}{5}\\)
\na = 24
\nSo, 24 is 20% of 120.
\nThe number of students who voted for person B after final results are 24<\/p>\n
\nBy using percent proportion , we have
\nsame as for person B ,
\nSo, 24 is 20% of 120.
\nThe number of students who voted for person C after final results are 24<\/p>\n
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{120}\\) = \\(\\frac{35}{100}\\)
\na = \\(\\frac{120 \u00d7 35}{100}\\)
\na = \\(\\frac{4,200}{100}\\)
\na = 42
\nSo, 42 is 35% of 120.
\nThe number of students who voted for person D after final results are 42.<\/p>\n
\nFor person A , 25 % \u00d7 120 =
\n(25 : 100) \u00d7 120 =
\n(25 \u00d7 120) : 100 =
\n3,000 : 100 = 30
\nSo, 30 is the 25% of 120.<\/p>\n
\n(20 : 100) \u00d7 120 =
\n(20 \u00d7 120) : 100 =
\n2,400 : 100 = 24
\nSo, 24 is the 20% of 120.<\/p>\n
\nSo, 24 is the 20% of 120.<\/p>\n
\n(35 : 100) \u00d7 120 =
\n(35 \u00d7 120) : 100 =
\n4,200 : 100 = 42
\nSo, 42 is the 35% of 120.
\nAll the answers are verified with ratio proportion method.<\/p>\n
\nQuestion 1.
\nWhat number is 10% of 20?
\nAnswer:\u00a0 2<\/p>\n
\n10 % \u00d7 20 =
\n(10 : 100) \u00d7 20 =
\n(10 \u00d7 20) : 100 =
\n200 : 100 = 2
\nSo, 2 is the 10% of 20.<\/p>\n
\nWhat number is 150% of 40?
\nAnswer: 60<\/p>\n
\n150 % \u00d7 40 =
\n(150 : 100) \u00d7 40 =
\n(150 \u00d7 40) : 100 =
\n6,000 : 100 = 60
\nSo, 60 is the 150% of 40.<\/p>\n
\nQuestion 3.
\n3 is what percent of 600?
\nAnswer: 0.5%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{3}{600}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{3 \u00d7 100}{600}\\)
\np = \\(\\frac{300}{600}\\)
\np = \\(\\frac{1}{2}\\)
\np = 0.5
\nSo, 3 is 0.5% of 600.<\/p>\n
\n18 is what percent of 20?
\nAnswer:<\/p>\n
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{18}{20}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{18 \u00d7 100}{20}\\)
\np = \\(\\frac{1800}{20}\\)
\np = \\(\\frac{180}{2}\\)
\np = 90
\nSo, 18 is 90% of 20.<\/p>\n
\nQuestion 5.
\n8 is 80% of what number?
\nAnswer: 10<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{8}{w}\\) = \\(\\frac{80}{100}\\)
\nw = \\(\\frac{8 \u00d7 100}{80}\\)
\nw = \\(\\frac{800}{80}\\)
\nw = 10
\nSo, 8 is 80% of 10.<\/p>\n
\n90 is 180% of what number?
\nAnswer: 50<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{90}{w}\\) = \\(\\frac{180}{100}\\)
\nw = \\(\\frac{90 \u00d7 100}{180}\\)
\nw = \\(\\frac{9,000}{180}\\)
\nw = 50
\nSo, 90 is 180% of 50.<\/p>\n
\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n
\nVOCABULARY<\/strong>
\nWrite the percent equation in words.
\nAnswer:
\nPercent Equation:
\nIn this equation, the whole is the number of which we are taking a percentage and the part is the value that results from taking the percent of the whole. This means that in any percent problem, there are three basic values to be concerned about: the percent, the whole, and the resulting part.
\nwe can represent percent = p , whole = w , part = a
\nSo, we have the percent equation as,
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\).<\/p>\n
\nQuestion 8.
\n14 is what percent of 70?
\nAnswer: 20%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{14}{70}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{14 \u00d7 100}{70}\\)
\np = \\(\\frac{1400}{70}\\)
\np = 20
\nSo, 14 is 20% of 70.<\/p>\n
\nWhat number is 36% of 85?
\nAnswer: 30.6<\/p>\n
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{85}\\) = \\(\\frac{36}{100}\\)
\na = \\(\\frac{85 \u00d7 36}{100}\\)
\na = \\(\\frac{3,060}{100}\\)
\na = 30.6
\nSo, 30.6 is 36% of 85.<\/p>\n
\n9 is 12% of what number?
\nAnswer: 75<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{9}{w}\\) = \\(\\frac{12}{100}\\)
\nw = \\(\\frac{9 \u00d7 100}{12}\\)
\nw = \\(\\frac{900}{12}\\)
\nw = 75
\nSo, 9 is 12% of 75.<\/p>\n
\n108 is what percent of 72?
\nAnswer: 150%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{108}{72}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{108 \u00d7 100}{72}\\)
\np = \\(\\frac{10,800}{72}\\)
\np = 150
\nSo, 108 is 150% of 72.<\/p>\n
\nDIFFERENT WORDS, SAME QUESTION<\/strong>
\nWhich is different? Find \u201cboth\u201d answers.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents-6.3-2.png\")
\nAnswer: 55 is 20% of what number ? , is different\u00a0 from other three questions.<\/p>\n
\nGiven , 20% of 55 , we have to find the part of whole number
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{55}\\) = \\(\\frac{20}{100}\\)
\na = \\(\\frac{55 \u00d7 20}{100}\\)
\na = \\(\\frac{1,100}{100}\\)
\na = 11
\nSo, 11 is 20% of 55.<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{55}{w}\\) = \\(\\frac{20}{100}\\)
\nw = \\(\\frac{55 \u00d7 100}{20}\\)
\nw = \\(\\frac{5500}{20}\\)
\nw = 275
\nSo, 55 is 20% of 275.
\nHence , 55 is 20% of what number ? , is different\u00a0 from other three questions.<\/p>\n
\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n
\nDIG DEEPER!<\/strong>
\nA school offers band and chorus classes. The table shows the percents of the 1200 students in the school who are enrolled in band, chorus, or neither class. How many students are enrolled in both classes? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents-6.3-3.png\")
\nAnswer: The total number of students enrolled for both classes\u00a0 are 744.<\/p>\n
\nGiven, The table shows the percent of the 1200 students in the school who are enrolled in band, chorus, or neither class.
\nFor Band , w = 1200 , p = 34 , a = ?
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{1200}\\) = \\(\\frac{34}{100}\\)
\na = \\(\\frac{1200 \u00d7 34}{100}\\)
\na = 12 \u00d7 34
\na = 408
\nSo, 408 is 34% of 1200.
\nThe number of students enrolled for the Band are 408.<\/p>\n
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{1200}\\) = \\(\\frac{28}{100}\\)
\na = \\(\\frac{1200 \u00d7 28}{100}\\)
\na = 12 \u00d7 28
\na = 336
\nSo, 336 is 28% of 1200.
\nThe number of students enrolled for the chorus are 336.<\/p>\n
\nWater Tank A has a capacity of 550 gallons and is 66% full. Water Tank B is 53% full. The ratio of the capacity of Water Tank A to Water Tank B is 11:15.
\na. How much water is in each tank?
\nb. What percent of the total volume of both tanks is filled with water?
\nAnswer:
\na. The water tank A is filled with 363 gallons of water.
\nThe water tank B is filled with 397.5 gallons of water.<\/p>\n
\na.\u00a0 Given , Water Tank A has a capacity of 550 gallons and is 66% full.
\nw = 550 gallons , p = 66% , a = ?
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{550}\\) = \\(\\frac{66}{100}\\)
\na = \\(\\frac{550 \u00d7 66}{100}\\)
\na = 550 \u00d7 0.66
\na = 363
\nSo, 363 is 66% of 550.
\nThe water tank A is filled with 363 gallons of water.<\/p>\n
\nThe ratio of the capacity of Water Tank A to Water Tank B is 11:15.
\nThe capacity of Water Tank A is 550 gallons
\nLet the capacity of tank B is x gallons
\n\\(\\frac{550}{x}\\) = \\(\\frac{11}{15}\\)
\nx = \\(\\frac{550 \u00d7 15}{11}\\)
\nx =\u00a0 \\(\\frac{8,250}{11}\\)
\nx = 750.
\nThe capacity of the water Tank B is 750 gallons,
\nTo know the amount of water filled in the tank we have,
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{750}\\) = \\(\\frac{53}{100}\\)
\na = \\(\\frac{750 \u00d7 53}{100}\\)
\na = 7.5 \u00d7 53
\na = 397.5
\nSo, 397.5 is 53% of 750.
\nThe water tank B is filled with 397.5 gallons of water.<\/p>\n
\nThe total capacity of Water tank A and Water tank B = 550 + 750 = 1,300 gallons
\nThe total amount of water filled in both tanks are 363 + 397.5 =\u00a0 760.5 gallons
\nSo, w = 1,300 , a = 760.5 , p = ?
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{760.5}{1,300}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{760.5 \u00d7 100}{1,300}\\)
\np = \\(\\frac{760.5}{13}\\)
\np = 58.5
\nSo, 760.5 is 58.5% of 1,300.
\nThe percent of the total volume of both tanks is filled with water is 58.5%.<\/p>\n<\/a>The Percent Equation Homework & Practice 6.3<\/h3>\n
\nQuestion 1.
\n30% of what number is 9?
\nAnswer: 30<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{9}{w}\\) = \\(\\frac{30}{100}\\)
\nw = \\(\\frac{9 \u00d7 100}{30}\\)
\nw = \\(\\frac{900}{30}\\)
\nw = 30
\nSo, 9 is 30% of 30.<\/p>\n
\n42 is what percent of 80?
\nAnswer:\u00a0 52.5%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{42}{80}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{42 \u00d7 100}{80}\\)
\np = \\(\\frac{420}{8}\\)
\np = 52.5
\nSo, 42 is 52.5% of 80.<\/p>\n
\nWhat percent of 36 is 20?
\nAnswer:<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{20}{36}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{20 \u00d7 100}{36}\\)
\np = \\(\\frac{2,000}{36}\\)
\np = 5.55
\nSo, 20 is55.5% of 36.<\/p>\n
\nWhat number is 120% of 80?
\nAnswer: 96<\/p>\n
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{80}\\) = \\(\\frac{120}{100}\\)
\na = \\(\\frac{80 \u00d7 120}{100}\\)
\na =\u00a0 8 \u00d7 12
\na = 96
\nSo, 96 is 120% of 80.<\/p>\n
\nQuestion 5.
\n– 4 and 10
\nAnswer: The distance between the two numbers\u00a0 – 4 and 10\u00a0 on a number line is 14 .<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.45.png\")
\nFor the number line above we have divided each segment in to equal parts ,
\nSo, The distance between the two numbers\u00a0 – 4 and 10\u00a0 on a number line is 14 .<\/p>\n
\n–\\(\\frac{2}{3}\\) and \\(\\frac{4}{3}\\)
\nAnswer: The distance between the two numbers –\\(\\frac{2}{3}\\) and \\(\\frac{4}{3}\\) on a number line is 6 .<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.46.png\")
\nFor the number line above we have divided each segment in to equal parts ,
\nSo, The distance between the two numbers –\\(\\frac{2}{3}\\) and \\(\\frac{4}{3}\\) on a number line is 6 .<\/p>\n
\n– 5\\(\\frac{2}{3}\\) and – 1 \\(\\frac{3}{10}\\)
\nAnswer: The distance between the two numbers\u00a0 – 5\\(\\frac{2}{3}\\) and – 1 \\(\\frac{3}{10}\\) on a number line is 6.<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.47.png\")
\nGiven , – 5\\(\\frac{2}{3}\\) and – 1 \\(\\frac{3}{10}\\)
\ncan be written as \\(\\frac{-13}{3}\\) and\u00a0 \\(\\frac{-7}{10}\\)
\nconverting into decimal form we get , -4.3 and -0.7
\nFor the number line above we have divided each segment in to equal parts ,
\nSo, The distance between the two numbers\u00a0 – 5\\(\\frac{2}{3}\\) and – 1 \\(\\frac{3}{10}\\) on a number line is 6.<\/p>\n
\n– 4.3 and 7.5
\nAnswer: The distance between the two numbers\u00a0 – 4.3 and 7.5\u00a0 on a number line is 8 .<\/p>\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents.48.png\")
\nFor the number line above we have divided each segment in to equal parts ,
\nSo, The distance between the two numbers\u00a0 – 4.3 and 7.5\u00a0 on a number line is 8 .<\/p>\n
\nThere are 160 people in a grade. The ratio of boys to girls is 3 to 5. Which proportion can you use to find the number x of boys?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents-6.3-4.png\")
\nAnswer:\u00a0 A. \\(\\frac{3}{8}\\) = \\(\\frac{x}{160}\\)<\/p>\n
\nGiven, The ratio of boys to girls is\\(\\frac{3}{5}\\)
\nThe ratio of boys to the grade is \\(\\frac{3}{8}\\)
\nto find the number of x boys, we have to
\n\\(\\frac{3}{8}\\) = \\(\\frac{x}{160}\\)
\nx = \\(\\frac{3 \u00d7 160}{8}\\)
\nx = \\(\\frac{480}{8}\\)
\nx = 60.
\nSo, A =\u00a0 \\(\\frac{3}{8}\\) = \\(\\frac{x}{160}\\) is the correct answer.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents-6.3-5.png\")
\nQuestion 10.
\nCandidate A
\nAnswer: The percent of students who voted for the candidate A is\u00a0 36%<\/p>\n
\nGiven, the circle graph shows the number of votes received by each candidate during a school election.
\nThe total number of students voted are 54 + 60 + 36 = 150
\nFor candidate A we have , w = 150 , a = 54 , p = ?
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{54}{150}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{54 \u00d7 100}{150}\\)
\np = \\(\\frac{540}{15}\\)
\np = 36
\nSo, 54 is 36% of 150.
\nThe percent of students who voted for the candidate A is 36%.<\/p>\n
\nCandidate B
\nAnswer: The percent of students who voted for the candidate B is 40%.<\/p>\n
\nFor candidate B we have , w = 150 , a = 60 , p = ?
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{60}{150}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{60 \u00d7 100}{150}\\)
\np = \\(\\frac{600}{15}\\)
\np = 40
\nSo, 60 is 40% of 150.
\nThe percent of students who voted for the candidate B is 40%.<\/p>\n
\nCandidate C
\nAnswer: The percent of students who voted for the candidate C is 24%.<\/p>\n
\nFor candidate C we have , w = 150 , a = 36 , p = ?
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{36}{150}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{36 \u00d7 100}{150}\\)
\np = \\(\\frac{360}{15}\\)
\np = 24
\nSo, 36 is 24% of 150.
\nThe percent of students who voted for the candidate C is 24%.<\/p>\n
\nQuestion 13.
\n20% of 150 is what number?
\nAnswer:\u00a0 30<\/p>\n
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{150}\\) = \\(\\frac{20}{100}\\)
\na = \\(\\frac{150 \u00d7 20}{100}\\)
\na = 15 \u00d7 2
\na = 30
\nSo, 30 is 20% of 150.<\/p>\n
\n45 is what percent of 60?
\nAnswer: 75%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{45}{60}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{45 \u00d7 100}{60}\\)
\np = \\(\\frac{4,500}{60}\\)
\np = 75
\nSo, 45 is 75% of 60.<\/p>\n
\n35% of what number is 35?
\nAnswer: 35 is 35% of 100.<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{35}{w}\\) = \\(\\frac{35}{100}\\)
\nw = \\(\\frac{35 \u00d7 100}{35}\\)
\nw = \\(\\frac{3500}{35}\\)
\nw = 100
\nSo, 35 is 35% of 100.<\/p>\n
\n0.8% of 150 is what number?
\nAnswer: 1.2 .<\/p>\n
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{150}\\) = \\(\\frac{0.8}{100}\\)
\na = \\(\\frac{150 \u00d7 0.8}{100}\\)
\na = \\(\\frac{120}{100}\\)
\na = 1.2
\nSo, 1.2 is 0.8% of 150.<\/p>\n
\n29 is what percent of 20?
\nAnswer: 145%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{29}{20}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{29 \u00d7 100}{20}\\)
\np = \\(\\frac{2,900}{20}\\)
\np = \\(\\frac{2,90}{2}\\)
\np = 145
\nSo, 29 is 145% of 20.<\/p>\n
\n0.5% of what number is 12?
\nAnswer:<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{12}{w}\\) = \\(\\frac{0.5}{100}\\)
\nw = \\(\\frac{12 \u00d7 100}{0.5}\\)
\nw = \\(\\frac{1200}{0.5}\\)
\nw = 2,400.
\nSo, 12 is 0.5% of 2,400.<\/p>\n
\nWhat percent of 300 is 51?
\nAnswer: 17%<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{51}{300}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{51 \u00d7 100}{300}\\)
\np = \\(\\frac{51}{3}\\)
\np = 17
\nSo, 51 is 17% of 300.<\/p>\n
\n120% of what number is 102?
\nAnswer: 85<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{102}{w}\\) = \\(\\frac{120}{100}\\)
\nw = \\(\\frac{102 \u00d7 100}{120}\\)
\nw = \\(\\frac{1020}{12}\\)
\nw = 85
\nSo, 102 is 120% of 85.<\/p>\n
\nQuestion 21.
\nWhat number is 35% of 20?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents-6.3-6.png\")
\nAnswer: yes , He is correct .<\/p>\n
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{20}\\) = \\(\\frac{35}{100}\\)
\na = \\(\\frac{20 \u00d7 35}{100}\\)
\na = \\(\\frac{700}{100}\\)
\na = 7
\nSo, 7 is 35% of 20.<\/p>\n
\n30 is 60% of what number?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents-6.3-7.png\")
\nAnswer: 30 is 60% of 50.<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{30}{w}\\) = \\(\\frac{60}{100}\\)
\nw = \\(\\frac{30 \u00d7 100}{60}\\)
\nw = \\(\\frac{300}{6}\\)
\nw = 50
\nSo, 30 is 60% of 50.<\/p>\n
\nMODELING REAL LIFE<\/strong>
\nA salesperson receives a 2.5% commission on sales. What commission does the salesperson receive for $8000 in sales?
\nAnswer: He receives $200 for commission of the sale.<\/p>\n
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{8000}\\) = \\(\\frac{2.5}{100}\\)
\na = \\(\\frac{8000 \u00d7 2.5}{100}\\)
\na = 80 \u00d7 2.5
\na = $200
\nSo, $200 is 2.5% of $8000.
\nHe receives $200 for commission of the sale.<\/p>\n
\nMODELING REAL LIFE<\/strong>
\nYour school raised 125% of its fundraising goal. The school raised $6750. What was the goal?
\nAnswer: The fundraising goal of the school is $5,400.<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{6750}{w}\\) = \\(\\frac{125}{100}\\)
\nw = \\(\\frac{6750 \u00d7 100}{125}\\)
\nw =54 \u00d7 100
\nw = $5,400
\nSo, $6750 is 125% of $5,400.
\nThe fundraising goal of the school is $5,400.<\/p>\n
\nMODELING REAL LIFE<\/strong>
\nThe sales tax on the model rocket shown is $1.92. What is the percent of sales tax?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents-6.3-8.png\")
\nAnswer: The percent of sales tax on the rocket model\u00a0 is 8%.<\/p>\n
\nGiven, The sales tax on the model rocket shown is $1.92.
\nThe tax on the rocket is $24 , we have ,
\nw = 24 , a = 1.92 , p = ?
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{1.92}{24}\\) = \\(\\frac{p}{100}\\)
\np = \\(\\frac{1.92 \u00d7 100}{24}\\)
\np = \\(\\frac{192}{24}\\)
\np = 8
\nSo, $1.92 is 8% of $24.
\nThe percent of sales tax on the rocket model\u00a0 is 8%.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents-6.3-9.png\")
\nQuestion 26.
\nx is 25% of 104. What was Rutledge\u2019s age?
\nAnswer: The age of Rutledge is 26.<\/p>\n
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{104}\\) = \\(\\frac{25}{100}\\)
\na = \\(\\frac{104 \u00d7 25}{100}\\)
\na = \\(\\frac{104}{4}\\)
\na = 26
\nx = 26.
\nSo, 26 is 25% of 104.<\/p>\n
\n7 is 10% of y. What was Franklin\u2019s age?
\nAnswer: The Franklin\u2019s age is 70.<\/p>\n
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{7}{w}\\) = \\(\\frac{10}{100}\\)
\nw = \\(\\frac{7 \u00d7 100}{10}\\)
\nw = \\(\\frac{700}{10}\\)
\nw = 70
\ny = 70.
\nSo, 7 is 10% of 70.
\nThe Franklin\u2019s age is 70.<\/p>\n
\nn is 80% of y. How many signers were there?
\nAnswer: There are n = 56 members signers.<\/p>\n
\ny = 70 , p = 80 ,
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{70}\\) = \\(\\frac{80}{100}\\)
\na = \\(\\frac{70 \u00d7 80}{100}\\)
\na = 7 \u00d7 8
\na =56
\nn = 56
\nSo, 56 is 80% of 70.
\nThere are n = 56 members signers.<\/p>\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-6-Percents-6.3-10.png\")
<\/p>\n
\nLOGIC<\/strong>
\nHow can you tell whether a percent of a number will be greater than, less than, or equal to the number? Give examples to support your answer.
\nAnswer: The percent of a number is less than 100% , Then the percent of the number will be less than the number.
\nThe percent of a number is 100% , Then the percent of the number will be equal the number.
\nThe percent of a number is greater than 100% , Then the percent of the number will be greater than the number.<\/p>\n
\nIf the percent of a number is less than 100% , Then the percent of the number will be less than the number.
\nFor example , 80% of 50
\n= 0.8 \u00d7 50
\n= 40
\n80% < 100% ,\u00a0 so 40 < 50.<\/p>\n
\nFor example , 100% of 50
\n= 1 \u00d7 50
\n= 50.
\n100% = 100% , So, 50 = 50.<\/p>\n
\nFor example , 120% of 50
\n= 1.2 \u00d7 50
\n= 60.
\n120% > 100% , So, 60 > 50.<\/p>\n
\nPROBLEM SOLVING<\/strong>
\nIn a survey, a group of students is asked their favorite sport. Eighteen students choose \u201cother\u201d sports.
\na. How many students participate in the survey?
\nb. How many choose football?
\nAnswer:\u00a0 a. The number of students participated\u00a0 are 80.
\nb. The number of students chose football are 30.<\/p>\n
\na. 18 students chose ” other” sports So, a = 18 ,
\nThe percent of the “other” sport = 100% – (40% + 37.5%) = 22.5%
\nBy using proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{18}{w}\\) = \\(\\frac{22.5}{100}\\)
\nw = \\(\\frac{18 \u00d7 100}{22.5}\\)
\nw = \\(\\frac{1800}{22.5}\\)
\nw =\u00a0 80
\nSo, 18 is 22.5% of 80.
\nThe number of students participated\u00a0 are 80.<\/p>\n
\nThe percent of the students who chose football is 37.5%
\nBy using percent proportion , we have
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{a}{80}\\) = \\(\\frac{37.5}{100}\\)
\na = \\(\\frac{80 \u00d7 37.5}{100}\\)
\na = \\(\\frac{3,000}{100}\\)
\na = 30
\nSo, 30 is 37.5% of 80.
\nThe number of students chose football are 30.<\/p>\n
\nTRUE OR FALSE?<\/strong>
\nTell whether the statement is true or false. Explain your reasoning.
\nIf W is 25% of Z, then Z : W is 75 : 25.
\nAnswer: The statement is False.<\/p>\n
\nGiven , W is 25% of Z
\n\\(\\frac{a}{w}\\) = \\(\\frac{p}{100}\\)
\n\\(\\frac{W}{Z}\\) = \\(\\frac{25}{100}\\)
\nSo, \\(\\frac{Z}{W}\\) = \\(\\frac{100}{25}\\)
\nBut given that Z : W is 75 : 25
\nSo, The statement is False.<\/p>\n
\nDIG DEEPER!<\/strong>
\nAt a restaurant, the amount of your bill before taxes and tip is $19.83. A 6% sales tax is applied to your bill, and you leave a tip equal to 19% of the original amount. Use mental math to estimate the total amount of money you pay. Explain your reasoning. (Hint: Use 10% of the original amount.)
\nAnswer: The total amount of the money to be paid is $22.18.<\/p>\n
\nGiven ,The amount of your bill before taxes and tip is $19.83.
\nA 6% sales tax is applied to your bill, and you leave a tip equal to 19% of the original amount.
\nbill before the tax = $19.83
\nsales tax = 6%
\nSo, $19.83 – 6%
\n= $19.83 – 0.06
\n= $18.64
\nTip = 19%
\nSo, $18.64 + 19%
\n= $18.64 + 0.19
\n= $22.18
\nThe total amount of the money to be paid is $22.18.<\/p>\n
\nREASONING<\/strong>