How to find the sum of percentages

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How to find the sum of percentages

Download Article   Co-authored by Jake Adams

Last Updated: July 9, 2022 References Approved

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This article was co-authored by Jake Adams. Jake Adams is an academic tutor and the owner of Simplifi EDU, a Santa Monica, California based online tutoring business offering learning resources and online tutors for academic subjects K-College, SAT & ACT prep, and college admissions applications. With over 14 years of professional tutoring experience, Jake is dedicated to providing his clients the very best online tutoring experience and access to a network of excellent undergraduate and graduate-level tutors from top colleges all over the nation. Jake holds a BS in International Business and Marketing from Pepperdine University.

There are 12 references cited in this article, which can be found at the bottom of the page.

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Knowing how to calculate percentages will help you not only score well on a math test but in the real world as well. You can work out percentages to calculate how much to tip at restaurants, find the percent change of a price, or even determine statistics of your favorite sports team. While the language may initially seem confusing, calculating percentages can actually be quite easy.[1] X Expert Source

Jake Adams
Academic Tutor & Test Prep Specialist Expert Interview.  24 July 2020. Go to source  We'll walk you through the main types of percentage problems you'll see in math homework and business, and we'll give you everyday examples of percentage calculations.

Steps

Resources And Tools Calculate Percentages Practice ProblemsCalculate Percentages Practice Problems Answer Key Use wikiHow's Percentage Calculator

Method 1Method 1 of 6:Calculating Percentage

1Put the two values into a fraction. The smaller part goes on top of the fraction (numerator), and the value of the whole goes on the bottom (denominator).[2] X Expert Source

Grace Imson, MA
Math Instructor, City College of San Francisco Expert Interview.  1 November 2019. Go to source  For instance, let's say we have a jar containing 1199 red marbles and 485 blue marbles, making it 1684 marbles in total.[3] X Research source Go to source  If were looking to find the percentage of blue marbles, that is our "part." The "whole" is the total number of marbles (1684). Therefore the fraction is 485/1684 (part/whole).[4] X Expert Source

Jake Adams
Academic Tutor & Test Prep Specialist Expert Interview.  20 May 2020. Go to source

  • When you're setting up two proportions, it's easiest to set them both up as the part over the whole on either side of the equation.[5] X Expert Source

Jake Adams
Academic Tutor & Test Prep Specialist Expert Interview.  24 July 2020. Go to source

2Convert the fraction into a decimal. Percentages are best calculated from the decimal form.[6] X Expert Source

Grace Imson, MA
Math Instructor, City College of San Francisco Expert Interview.  1 November 2019. Go to source  For the marbles example, to turn 485/1684 into a decimal, divide 485 by 1684 using a calculator or pencil and paper. This comes to 0.288.[7] X Research source Go to source

3Convert the decimal into a percent. Multiply the result obtained in the step above by 100.[8] X Expert Source

Grace Imson, MA
Math Instructor, City College of San Francisco Expert Interview.  1 November 2019. Go to source  For the marbles example, 0.288 multiplied by 100 equals 28.8%.[9] X Research source Go to source

A simple way to multiply a decimal by 100 is to move the decimal to the right two digits.
 The percent symbol is then just tacked on at the end, like a unit of measurement would be.

4Bonus Example 1: Jerry, an electrician, worked 7 months out of the year. What percent of the year did he work?[10] X Research source Go to source

  • There are 12 months total in a year, so Jerry worked 7/12 months.
  • Then, convert the fraction to a decimal: 7/12 = 0.58
  • Next, convert the fraction to a percent: 0.58 x 100% = 58%
  • Jerry the electrician worked 58% of the year.

5Bonus Example 2: Donovan took a math test and got 35 correct and 10 incorrect answers. What was the percentage of correct answers?

  • 35 correct answers + 10 incorrect answers = 45 answers total
  • We can set this problem up as the fraction 35/45.
  • 35/45 = 0.78
  • 0.78 x 100 = 78%
  • Donovan got 78% of the answers correct on his test.

Method 2Method 2 of 6:What Is X Percent of Y?

1Use this method when youre given a percentage and a "whole." Set the numbers youre given into the percent formula P/100 = Part/Whole. Say you borrowed money from a friend who is going to charge you daily interest. The amount borrowed was initially $15 and the interest rate is 3% per day. Then, 3% would be P in the formula, and $15 would be the "whole" amount.[11] X Research source Go to source  Plug the numbers into the formula to get 3/100 = X/15.[12] X Expert Source

Jake Adams
Academic Tutor & Test Prep Specialist Expert Interview.  20 May 2020. Go to source

  • Remember, part over whole equals part over whole.[13] X Expert Source

Jake Adams
Academic Tutor & Test Prep Specialist Expert Interview.  20 May 2020. Go to source

2Convert the percentage into a decimal. Divide the percentage by 100%, or you can multiply by 0.01 (theyre the exact same).  3%/100% = 3/100 = 0.03. Youd be left with 0.03=X/15.[14] X Research source Go to source

  • You can translate any percentage into a decimal by dividing by 100. For example, 26% = 26/100 = .26[15] X Expert Source

Jake Adams
Academic Tutor & Test Prep Specialist Expert Interview.  24 July 2020. Go to source

You can also simply move the decimal to the left two places.

3Cross multiply to solve for X. It helps to reword your problem with the new value(s) now in the form of "X of Y is Z." X is the decimal form of your percent, "of" means to multiply, Y is the whole amount, and Z is the answer. So, 0.03 x $15 is $0.45.[16] X Research source Go to source

  • In this example, $0.45 is the amount of interest accrued each day that you do not pay your friend back.
  • If you need to further calculate the total due after 1 day, you would add the amount you borrowed to the amount of the interest times the number of days. So $15 + ($0.45 x 1 day) = $15.45.

4Bonus Example 1: A baseball pitcher won 80% of the games he pitched. If he pitched 35 ballgames, how many games did he win?[17] X Research source Go to source

  • We can reword this problem as "What is 80% of 35?"
  • Plug the values into the formula P/100 = Part/Whole
  • 80/100 = X/35
  • 0.8 = X/35
  • 35 x 0.8 = X
  • X = 28
  • The pitcher won 28 games.

5Bonus Example 2: A metal bar weighs 8.15 ounces. 93% of the bar is silver. How many ounces of silver are in the bar?[18] X Research source Go to source

  • We can reword this problem as "What is 93% of 8.15?"
  • Plug the values into the formula P/100 = Part/Whole
  • 93/100 = X/8.15
  • 0.93 = X/8.15
  • 0.93 x 8.15 = X
  • X = 7.58
  • There are 7.58 ounces of silver.

Method 3Method 3 of 6:P Percent of What Number Is Y?

1Use this method to solve for a missing "whole" when youre given a percentage and a "part." Set the numbers youre given into the percent formula P/100 = Part/Whole, which we can write as P/100 = X/Y. For example, imagine youre given the problem "45% of what number is 12?" Plug the numbers into the equation like this: 45/100 = 12/Y.

  • A shortcut: notice you can manipulate the percent equation to get this formula below.
  • Part/Percent (in decimal form) = Whole
  • Keep reading for a full walk-through if youre not sure how to get there.

2Convert the percentage into a decimal. Divide the percentage by 100, or just move the decimal place over 2 places to the left.  45%/100% = 45/100 = 0.45. Youll end up with 0.45 = 12/Y.[19] X Research source Go to source

3Cross multiply to move Y into the numerator. That means youll move from 0.45 = 12/Y to 0.45 x Y = 12. Now you can solve for your missing variable Y. In your head, you can reword this to "45 percent of Y is 12." Remember "of" means "multiply."

4Divide the part by the percentage (in decimal form) to get your answer. For the main example, solve for Y by dividing both sides by 0.45. Youll get Y = 12/0.45, which equals 26.67. For these types of problems, check your work by making sure that the answer is bigger than the original part you were given.

5Check out these additional examples below.

  • Bonus Example 1: This year, Acme Computers made approximately 72% of its sales online. There were 1,380 online purchases. Rounding up to the nearest whole number, how many total sales did Acme Computers make this year?
  • Plug the values into the formula P/100 = Part/Whole
  • 72/100 = 1,380 online sales/Y total sales
  • 72/100 = 1,380/Y
  • 0.72 = 1,380/Y
  • 0.72 x Y = 1,380
  • 1,380/0.72 = Y
  • Y = 1916.66
  • Acme Computers made 1917 total sales this year.
  • Bonus Example 2: 39% of what number is 89?
  • Plug the values into the formula P/100 = Part/Whole
  • 39/100 = 89/Y
  • 0.39 = 89/Y
  • 0.39 x Y = 89
  • 89/0.39 = Y
  • Y = 228.2

Method 4Method 4 of 6:Calculating Percent Increase

1Subtract the original amount from the new, bigger amount. Imagine your small company makes $44,000 in one year. The next year, you make $49,750. To start calculating the percent change in revenue, find the difference between $49,750 and $44,000: $49,750 - $44,000 = $5,750. Youll treat $5,750 as the "part" of the "whole" (which is your original number).[20] X Research source Go to source

2Divide the difference of the numbers by the original amount. You might recognize this as the first step in a basic percentage calculationyoure setting up a fraction with the "part" over the "whole." For the small business example, divide $5,750 by $44,000: $5,750 / $44,000 = 0.13.[21] X Research source Go to source

3Multiply the decimal by 100% to get the percentage. You could also move the decimal place over twice to the rightits the same thing! In this case, wed have 0.13 x 100% = 13%.[22] X Research source Go to source

4Bonus Example 1: A game cost $13.99 last month, but this month it costs $15.75. Calculate the percent increase of the price.

  • New Amount - Original Amount = Difference
  • $15.75 - $13.99 = $1.76
  • (Difference / Original Amount) x 100% = Percent Increase
  • ($1.76 / $13.99) x 100% = 12.5%
  • The price of the game went up by 12.5%.

5Bonus Example 2: A sweater company buys sweaters from a factory for $22. Then, they put their brand on the sweaters and sell them for $55. Whats the percentage of their markup (the difference in cost)?

  • New Amount - Original Amount = Difference
  • $55 - $22 = $33
  • (Difference / Original Amount) x 100% = Percent Increase
  • ($33 / $55) x 100% = 60%
  • The company has a 60% markup on sweaters.

Method 5Method 5 of 6:Calculating Percent Decrease

1Subtract the new amount from the original, bigger amount. For example, imagine youre looking to invest in the stock market. A certain stock sold at $67 per share in one month. Now, the price has dropped to $52 per share. Subtract $52 from $67: $67 - $52 = $15. That $15 difference is the "part" of the "whole" ($67).

2Divide the difference by the original amount. This is the basic percentage calculationyoure essentially putting the "part" over the "whole" in fraction form. For the stock example, divide $67 by $15: $15 / $67 = 0.22.[23] X Research source Go to source

3Multiply the decimal by 100% to get the percentage. For a quick way to do this, move the decimal place over twice to the right. In this case, wed have 0.22 x 100% = 22%.[24] X Research source Go to source

4Bonus Example 1: Jane worked 42 hours a week in April. In May, she worked 39 hours a week. What was the percent change in her hours between the two months?

  • Original Amount - New Amount = Difference
  • 42 - 39 = 3
  • (Difference / Original Amount) x 100% = Percent Increase
  • (3 / 42) x 100% = 7%
  • Janes hours decreased by 7%.

5Bonus Example 2: Company A starts out with 563 employees. After layoffs, theyre left with 542 employees. Whats the percent change in the number of employees?

  • Original Amount - New Amount = Difference
  • 563 - 542 = 21
  • (Difference / Original Amount) x 100% = Percent Increase
  • (21 / 563) x 100% = 3.7%
  • Company A decreased their number of employees by 3.7%.

Method 6Method 6 of 6:Percentage in Real Life

1Calculate a restaurant tip in your head. You can calculate restaurant tips with tricks that involve moving the decimal place over for the total cost of your bill. Here are quick strategies to work out tip percentages without a calculator:[25] X Research source Go to source

  • Calculating a 10% tip: Simply move the decimal place over once to the left.
  • Example: If your bill is $54, a 10% tip would be $5.4.
  • Calculating a 15% tip: Find 10% by moving the decimal place over to the left. Then, divide that number in half to get 5% of the bill. Then, add the 10% and 5% values together.
  • Example: For a $54 bill, 10% is $5.4. Half of $5.4 is $2.7. Finally, $5.4 + $2.7 = $8.1.
  • Calculating a 20% tip: Double the total bill, then move the decimal place over once to the left.
  • Example: For a $54 bill, double that is $108. If you move the decimal one place to the left, you'll get $10.80.

2Calculate your savings from a price discount. Write down the original price and the discount percentage. Then, subtract the discount percentage from 100. For instance, if you want to buy a shirt thats 30% off, 100% - 30% is 70%. That means youll pay 70% of the original price. Now youre ready to walk through this easy calculation:[26] X Research source Go to source [27] X Research source Go to source

  • Move the decimal two places to the left. In this example, 70%/100% = 70/100 = 7/10 = 0.7.[28] X Research source Go to source
  • Multiply the original price by the new decimal. If the shirt you want is $20, multiply $20 by 0.7. This comes to $14, meaning the shirt is now on sale for $14.[29] X Research source Go to source
  • Calculate your savings. Simply subtract the sale price from the original price ($20 - $14 = $6 saved)!

3Calculate the total cost with sales tax. To calculate the cost of an item plus tax, start by converting the sales tax to a decimal. Next, add that number to 1 (think of 1 as 100% of the cost of the original item). For example, if sales tax is 8%, youd do 0.08 + 1 = 1.08. Then, multiply the price of your item by 1.08. If your item costs $20, the item plus 8% tax would be $20 x 1.08, which equals $21.6.[30] X Research source Go to source

  • Bonus Example: Mark is buying a sweater that costs $15. Sales tax is 9%. How much will he pay at checkout?
  • Convert 9% to a decimal: 0.09
  • Add the decimal to 1: 0.09 + 1 = 1.09
  • Multiple that value by the original price: $15 x 1.09 = $16.35
  • Mark will pay $16.35 at checkout.

Percentage Calculator Try it yourself! Enter a part (X) and a whole (Y). X / Y * 100 = P Part (X) Whole (Y) = Percentage (P)

Community Q&A

  • Question How do you calculate the percentage of a number?

Jake Adams Academic Tutor & Test Prep Specialist Expert Answer Set up the equation so that each side is a part over the whole. That way your piece of missing information with be either the part or the whole on either side. For instance, if you want to know 38% of 52, the equation would be 38/100 = x/52, where x is the number you're solving for.

  • Question How can you calculate a percentage using a calculator?

wikiHow Staff Editor Staff Answer One of the quickest ways to calculate a percentage with a calculator is to convert the percentage into a decimal and multiply it by the number youre trying to find the percentage of. For example, if you want to find 60% of 285, enter 285 x .6 into your calculator to get 171. To figure out what percentage a number represents out of a whole, divide the smaller number by the larger one and convert the resulting decimal number into a percent. For example, 171 ÷ 285 = 0.6 = 60%.

  • Question How do you calculate a percentage in Excel?

wikiHow Staff Editor Staff Answer To calculate a basic percentage in Excel, use the Percent Style button under the Home Tab>Number Group and apply it to the column where youd like to display the percent (e.g., column D). Use the formula C2/B2 in column D to calculate the what percentage of the number in column B is represented by the number in column C. For example, if column A specifies your product, column B might represent the total produced and column C might be the total shipped. If B is 75 and C is 69, enter C2/B2 in column D to get 92%.

  • Question How do I calculate 9% of $456.39?

Community Answer Convert the percent to a decimal like so: 0.09. Then multiply that decimal by 456.39.

  • Question I know that 1325 is 12.2% of the total. How do I calculate the total?

Donagan Top Answerer Divide 1325 by 0.122.

  • Question My child got 447 marks in 450, so what percentage did he get?

Community Answer He got a little over 99.333...%. Divide 447 by 450. The answer was a decimal which is then converted into a percent by moving the decimal point two places to the right.

  • Question I saved 185.73 an income is 2456.85 a year. How do I calculate the percentage I saved?

Community Answer Divide 185.73 by 2456.85. The answer was a decimal which is then converted into a percent by moving the decimal point two places to the right. You've saved 7.559%

  • Question What is the percentage of $177.78 of $444.45?

Donagan Top Answerer Divide the first number by the second number, and multiply by 100.

  • Question How can I calculate the percent change between two numbers?

Community Answer To calculate the percentage increase, work out the difference (increase) between the two numbers you are comparing. Then divide the increase by the original number and multiply the answer by 100. If your answer is a negative number, then this is a percentage decrease.

  • Question How do I add a percentage of a number to the number?

Community Answer First you need to calculate what number the percentage is equal to. Do this by converting the percentage to a decimal and then multiplying the decimal by the original number. Now you can add this answer to the original number.

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Tips

  • x% of y is the same as y% of x. For example, 10% of 30 = 3 = 30% of 10.[31] X Research source Go to source

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References

  1. Jake Adams. Academic Tutor & Test Prep Specialist. Expert Interview. 24 July 2020.
  2. Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
  3. https://txwes.edu/media/twu/content-assets/images/academics/academic-success-center/Quick-Guide-to-Percentages-and-Decimals.pdf
  4. Jake Adams. Academic Tutor & Test Prep Specialist. Expert Interview. 20 May 2020.
  5. Jake Adams. Academic Tutor & Test Prep Specialist. Expert Interview. 24 July 2020.
  6. Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
  7. https://www.whatcom.edu/home/showpublisheddocument/1760/635548017079270000/
  8. Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
  9. https://www.whatcom.edu/home/showpublisheddocument/1760/635548017079270000More References (22)
  10. https://www.cnm.edu/depts/tutoring/tlc/res/accuplacer/8_Math_550_Percent_Word_Problems__2_.pdf
  11. https://www.mathsisfun.com/percentage-calculator.html
  12. Jake Adams. Academic Tutor & Test Prep Specialist. Expert Interview. 20 May 2020.
  13. Jake Adams. Academic Tutor & Test Prep Specialist. Expert Interview. 20 May 2020.
  14. https://www.mathsisfun.com/percentage-calculator.html
  15. Jake Adams. Academic Tutor & Test Prep Specialist. Expert Interview. 24 July 2020.
  16. https://www.mathsisfun.com/percentage-calculator.html
  17. https://www.cnm.edu/depts/tutoring/tlc/res/accuplacer/8_Math_550_Percent_Word_Problems__2_.pdf
  18. https://www.cnm.edu/depts/tutoring/tlc/res/accuplacer/8_Math_550_Percent_Word_Problems__2_.pdf
  19. https://www.mathsisfun.com/percentage-calculator.html
  20. https://www.onemathematicalcat.org/algebra_book/online_problems/calc_percent_inc_dec.htm
  21. https://www.onemathematicalcat.org/algebra_book/online_problems/calc_percent_inc_dec.htm
  22. https://www.onemathematicalcat.org/algebra_book/online_problems/calc_percent_inc_dec.htm
  23. https://www.onemathematicalcat.org/algebra_book/online_problems/calc_percent_inc_dec.htm
  24. https://www.onemathematicalcat.org/algebra_book/online_problems/calc_percent_inc_dec.htm
  25. https://sciencing.com/easy-ways-calculate-percentages-8362422.html
  26. https://www.mathgoodies.com/lessons/percent/sale_price
  27. https://www.mathgoodies.com/lessons/percent/sale_price
  28. https://www.mathgoodies.com/lessons/percent/sale_price
  29. https://www.mathgoodies.com/lessons/percent/sale_price
  30. https://edu.gcfglobal.org/en/percents/percentages-in-real-life/1/
  31. https://www.mathsisfun.com/percentage-calculator.html

About This Article

Co-authored by: Jake Adams Academic Tutor & Test Prep Specialist This article was co-authored by Jake Adams. Jake Adams is an academic tutor and the owner of Simplifi EDU, a Santa Monica, California based online tutoring business offering learning resources and online tutors for academic subjects K-College, SAT & ACT prep, and college admissions applications. With over 14 years of professional tutoring experience, Jake is dedicated to providing his clients the very best online tutoring experience and access to a network of excellent undergraduate and graduate-level tutors from top colleges all over the nation. Jake holds a BS in International Business and Marketing from Pepperdine University.  This article has been viewed 8,145,269 times.   Co-authors:  134 Updated: July 9, 2022 Views:8,145,269 Article Rating:60% - 15 votes Categories: Featured Articles | Mathematics Article SummaryX

To calculate percentages, start by writing the number you want to turn into a percentage over the total value so you end up with a fraction. Then, turn the fraction into a decimal by dividing the top number by the bottom number. Finally, multiply the decimal by 100 to find the percentage. To learn how to calculate a discount using a percentage, scroll down!In other languagesItaliano:Calcolare le Percentuali Español:calcular porcentajes Deutsch:Prozente berechnen Português:Calcular Porcentagens Français:calculer des pourcentages Русский:находить проценты Nederlands:Procenten berekenen 中文:计算百分数 Bahasa Indonesia:Menghitung Persentase 日本語:パーセンテージを計算する ไทย:คำนวณเป็นเปอร์เซ็นต์ हिन्दी:प्रतिशत की गणना करें العربية:حساب النسب المئوية 한국어:백분율 계산법 Tiếng Việt:Tính Phần trăm Türkçe:Yüzde Nasıl Hesaplanır فارسی:درصد را محاسبه کنیم

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Aug 8, 2016 "This article is the easiest way to understand how to calculate a percentage. Clearly set out in different colors, big numbers, and relates to everyday situations we come across. The best on the net.  It also solved my level of frustration!"

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Mar 15, 2017 "Being honest, I didn't think of percentages being mega easy. All I knew was 50%=1/2, 25%=1/4 and 75%=3/4. Really helps, so if you have a friend who doesn't know, tell them about wikiHow and how useful it is."   Rated this article:

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Shannon Lock

Shannon Lock

Oct 13, 2017 "Really helpful! When you haven't had to do sums like that for awhile, it is easy to forget. This was such a simple and easy-to-read reminder! "   Rated this article:

Moriah Awaseb

Moriah Awaseb

Aug 9, 2018 "it helped with a lot of tricks on percentage and more ways on calculate it. It just showed me more, that we did not learn at school. "   Rated this article:

Bhanu Prakash

Bhanu Prakash

Mar 16, 2017 "I have come to know how to calculate the percentage. Not only this, I have also got so many solutions for other questions like this."

Cecilia Govea

Cecilia Govea

Jun 5, 2017 "I didn't remember how to take percentage off. Once I saw that you convert the number to a decimal and multiply, I felt it was easy."   Rated this article:

Julie Hardy

Julie Hardy

Jun 4, 2017 "The information helped me figure out the percent increase of the 100% Assessed Value on my home this year vs. last year. Thank you!"   Rated this article:

Anonymous

Anonymous

Oct 24, 2016 "I followed the directions and looked at all the examples like the answers to people's questions, which helped a lot. Thank you."

Anonymous

Anonymous

May 28, 2017 "This helped me because before I didn't know how to get a answer, but now I know how to get a percentage of a number. Thanks!"   Rated this article:

Navin Tamu

Navin Tamu

Aug 22, 2017 "Being a hotelier, I need to calculate tax and rates. I had a bit of confusion, I think it's really helpful to me."   Rated this article:

School Daze

School Daze

Apr 17, 2017 "This method was a quick and easy way to calculate my research results. Sometimes I have to go back to the basics."

Aya Lapiz

Aya Lapiz

Jul 22, 2019 "This made me understand percentage and decimals way easier. My mum's example took a long time to understand."

Alexander R-M.

Alexander R-M.

Aug 16, 2017 "I went from not having a clue how to calculate a percentage to being able to do it in less than 10 minutes. "   Rated this article:

Vidya Naveen

Vidya Naveen

Jan 3, 2017 "We get to know each and everything step by step. There won't be any doubt regarding the topic. Thanks."     More reader stories Hide reader stories

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