Ratio, Proportion, and Percent

Write a Ratio as a Fraction

In this section, we will use the fraction notation. When a ratio is written in fraction form, the fraction should be simplified. If it is an improper fraction, we do not change it to a mixed number. Because a ratio compares two quantities, we would leave a ratio as instead of simplifying it to so that we can see the two parts of the ratio.

Ratios Involving Decimals

We will often work with ratios of decimals, especially when we have ratios involving money. In these cases, we can eliminate the decimals by using the Equivalent Fractions Property to convert the ratio to a fraction with whole numbers in the numerator and denominator.

For example, consider the ratio . We can write it as a fraction with decimals and then multiply the numerator and denominator by to eliminate the decimals.

Do you see a shortcut to find the equivalent fraction? Notice that and . The least common denominator of and is . By multiplying the numerator and denominator of by , we ‘moved’ the decimal two places to the right to get the equivalent fraction with no decimals. Now that we understand the math behind the process, we can find the fraction with no decimals like this:

“Move” the decimal 2 places.
Simplify.

You do not have to write out every step when you multiply the numerator and denominator by powers of ten. As long as you move both decimal places the same number of places, the ratio will remain the same.

Some ratios compare two mixed numbers. Remember that to divide mixed numbers, you first rewrite them as improper fractions.

Applications of Ratios

One real-world application of ratios that affects many people involves measuring cholesterol in blood. The ratio of total cholesterol to HDL cholesterol is one way doctors assess a person’s overall health. A ratio of less than to 1 is considered good.

Ratios of Two Measurements in Different Units

To find the ratio of two measurements, we must make sure the quantities have been measured with the same unit. If the measurements are not in the same units, we must first convert them to the same units.

We know that to simplify a fraction, we divide out common factors. Similarly in a ratio of measurements, we divide out the common unit.

Write a Rate as a Fraction

Frequently we want to compare two different types of measurements, such as miles to gallons. To make this comparison, we use a rate. Examples of rates are miles in hours, words in minutes, and dollars per ounces.

When writing a fraction as a rate, we put the first given amount with its units in the numerator and the second amount with its units in the denominator. When rates are simplified, the units remain in the numerator and denominator.

Find Unit Rates

In the last example, we calculated that Bob was driving at a rate of . This tells us that every three hours, Bob will travel miles. This is correct, but not very useful. We usually want the rate to reflect the number of miles in one hour. A rate that has a denominator of unit is referred to as a unit rate.

Unit rates are very common in our lives. For example, when we say that we are driving at a speed of miles per hour we mean that we travel miles in hour. We would write this rate as miles/hour (read miles per hour). The common abbreviation for this is mph. Note that when no number is written before a unit, it is assumed to be .

So miles/hour really means

Two rates we often use when driving can be written in different forms, as shown:

Example	Rate	Write	Abbreviate	Read
miles in hour		miles/hour	mph
miles to gallon		miles/gallon	mpg

Another example of unit rate that you may already know about is hourly pay rate. It is usually expressed as the amount of money earned for one hour of work. For example, if you are paid for each hour you work, you could write that your hourly (unit) pay rate is (read per hour.)

To convert a rate to a unit rate, we divide the numerator by the denominator. This gives us a denominator of .

Find Unit Price

Sometimes we buy common household items ‘in bulk’, where several items are packaged together and sold for one price. To compare the prices of different sized packages, we need to find the unit price. To find the unit price, divide the total price by the number of items. A unit price is a unit rate for one item.

Unit prices are very useful if you comparison shop. The better buy is the item with the lower unit price. Most grocery stores list the unit price of each item on the shelves.

Notice in the above example that we rounded the unit price to the nearest cent. Sometimes we may need to carry the division to one more place to see the difference between the unit prices.

Translate Phrases to Expressions with Fractions

Have you noticed that the examples in this section used the comparison words ratio of, to, per, in, for, on, and from? When you translate phrases that include these words, you should think either ratio or rate. If the units measure the same quantity (length, time, etc.), you have a ratio. If the units are different, you have a rate. In both cases, you write a fraction.

Glossary

Practice Makes Perfect

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

1. to	2. to
3. to	4. to
5. to	6. to
7. to	8. to
9. to	10. to
11. to	12. to
13. to	14. to
15. to	16. to
17. to	18. to
19. ounces to ounces	20. ounces to ounces
21. feet to feet	22. feet to feet
23. milligrams to milligrams	24. milligrams to milligrams
25. total cholesterol of to HDL cholesterol of	26. total cholesterol of to HDL cholesterol of
27. inches to foot	28. inches to foot

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction.

29. calories per ounces	30. calories per ounces
31. pounds per square inches	32. pounds per square inches
33. miles in hours	34. miles in hours
35. for hours	36. for hours

Find Unit Rates

In the following exercises, find the unit rate. Round to two decimal places, if necessary.

37. calories per ounces	38. calories per ounces
39. pounds per square inches	40. pounds per square inches
41. miles in hours	42. miles in hours
43. for hours	44. for hours
45. miles on gallons of gas	46. miles on gallons of gas
47. pounds in weeks	48. pounds in weeks
49. beats in minute	50. beats in minute
51. The bindery at a printing plant assembles magazines in hours. How many magazines are assembled in one hour?	52. The pressroom at a printing plant prints sections in hours. How many sections are printed per hour?

Find Unit Price

In the following exercises, find the unit price. Round to the nearest cent.

53. Soap bars at for	54. Soap bars at for
55. Women’s sports socks at pairs for	56. Men’s dress socks at pairs for
57. Snack packs of cookies at for	58. Granola bars at for
59. CD-RW discs at for	60. CDs at for
61. The grocery store has a special on macaroni and cheese. The price is for boxes. How much does each box cost?	62. The pet store has a special on cat food. The price is for cans. How much does each can cost?

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places.

63. Mouthwash, size for or size for	64. Toothpaste, ounce size for or size for
65. Breakfast cereal, ounces for or ounces for	66. Breakfast Cereal, ounces for or ounces for
67. Ketchup, regular bottle for or squeeze bottle for	68. Mayonnaise regular bottle for or squeeze bottle for
69. Cheese for lb. block or for lb. block	70. Candy for a lb. bag or for lb. of loose candy

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

71. miles per hours	72. feet per seconds
73. for lbs.	74. beats in minutes
75. 105 calories in ounces	76. minutes for dollars
77. the ratio of and	78. the ratio of and

Everyday Math

79. One elementary school in Saskatchewan has students and teachers. Write the student-to-teacher ratio as a unit rate.	80. The average Canadian produces about pounds of paper trash per year How many pounds of paper trash does the average Canadian produce each day? (Round to the nearest tenth of a pound.)
81. A popular fast food burger weighs ounces and contains calories, grams of fat, grams of carbohydrates, and grams of protein. Find the unit rate of a) calories per ounce b) grams of fat per ounce c) grams of carbohydrates per ounce d) grams of protein per ounce. Round to two decimal places.	82. A chocolate mocha coffee with whipped cream contains calories, grams of fat, grams of carbohydrates, and grams of protein. Find the unit rate of a) calories per ounce b) grams of fat per ounce c) grams of carbohydrates per ounce d) grams of protein per ounce.

Writing Exercises

83. Would you prefer the ratio of your income to your friend’s income to be or Explain your reasoning.	84. The parking lot at the airport charges for every minutes. a) How much does it cost to park for hour? b) Explain how you got your answer to part a). Was your reasoning based on the unit cost or did you use another method?
85. Kathryn ate a cup of frozen yogurt and then went for a swim. The frozen yogurt had calories. Swimming burns calories per hour. For how many minutes should Kathryn swim to burn off the calories in the frozen yogurt? Explain your reasoning.	86. Arjun had a cappuccino at his neighbourhood coffee shop. The cappuccino had calories. If Arjun walks for one hour, he burns calories. For how many minutes must Arjun walk to burn off the calories in the cappuccino? Explain your reasoning.

Answers

1.	3.	5.
7.	9.	11.
13.	15.	17.
19.	21.	23.
25.	27.	29.
31.	33.	35.
37. 11.67 calories/ounce	39. 2.73 lbs./sq. in.	41. 69.71 mph
43. $14.88/hour	45. 32 mpg	47. 2.69 lbs./week
49. 92 beats/minute	51. 8,000	53. $1.09/bar
55. $1.33/pair	57. $0.48/pack	59. $0.60/disc
61. $1.29/box	63. The 50.7-ounce size costs $0.138 per ounce. The 33.8-ounce size costs $0.142 per ounce. The 50.7-ounce size is the better buy.	65. The 18-ounce size costs $0.222 per ounce. The 14-ounce size costs $0.235 per ounce. The 18-ounce size is a better buy.
67. The regular bottle costs $0.075 per ounce. The squeeze bottle costs $0.069 per ounce. The squeeze bottle is a better buy.	69. The half-pound block costs $6.78/lb, so the 1-lb. block is a better buy.	71.
73.	75.	77.
79. 15.2 students per teacher	81. a) 72 calories/ounce       b) 3.87 grams of fat/ounce c) 5.73 grams carbs/once d) 3.33 grams protein/ounce	83. Answers will vary.
85. Answers will vary.

Attributions

This chapter has been adapted from “Ratios and Rate” in Prealgebra (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a CC BY 4.0 Licence. Adapted by Izabela Mazur. See the Copyright page for more information.

Glossary

Practice Makes Perfect

Use the Definition of Percents

In the following exercises, write each percent as a ratio.

1. In , the unemployment rate for those with only a high school degree was .	2. In , among the unemployed, were long-term unemployed.
3. The unemployment rate for those with Bachelor’s degrees was in .	4. The unemployment rate in Canada in was . In the following exercises, write as a) a ratio and b) a percent
5. out of nursing candidates received their degree at a community college.	6. out of firefighters and law enforcement officers were educated at a community college.
7. out of first-time freshmen students attend a community college.	8. out of full-time community college faculty have a master’s degree.

Convert Percents to Fractions and Decimals

In the following exercises, convert each percent to a fraction and simplify all fractions.

9.	10.
11.	12.
13.	14.
15.	16.
17.	18.
19.	20.
21.	22.
23.	24.

In the following exercises, convert each percent to a decimal.

25.	26.
27.	28.
29.	30.
31.	32.
33.	34.
35.	36.
37.	38.
39.	40.

In the following exercises, convert each percent to

a) a simplified fraction and

b) a decimal

41. In of home sales had owner financing. (Source: Bloomberg Businessweek, 5/23–29/2011)	42. In of the Canadian population was a visible minority. (Source: www12.statcan.gc.ca)
43. According to government data, in the number of cell phones in India was of the population.	44. According to the Survey of Earned Doctorates, among Canadians age or older who had doctorate degrees in are women.
45. A couple plans to have two children. The probability they will have two girls is .	46. Javier will choose one digit at random from through . The probability he will choose is .
47. According to the local weather report, the probability of thunderstorms in New York City on July is .	48. A club sells tickets to a raffle. Osbaldo bought one ticket. The probability he will win the raffle is .

Convert Decimals and Fractions to Percents

In the following exercises, convert each decimal to a percent.

49.	50.
51.	52.
53.	54.
55.	56.
57.	58.
59.	60.
61.	62.
63.	64.

In the following exercises, convert each fraction to a percent.

65.	66.
67.	68.
69.	70.
71.	72.
73.	74.
75.	76.
77.	78.
79.	80.

In the following exercises, convert each fraction to a percent.

81. of washing machines needed repair.

82. of dishwashers needed repair.

In the following exercises, convert each fraction to a percent.

83. According to the Government of Canada, in of Canadian adults were overweight or obese.

84. Statistics Canada showed that in of Canadian workers are using more than one language at work.

In the following exercises, complete the table.

85. Fraction Decimal Percent

86. Fraction Decimal Percent

87. Sales tax Felipa says she has an easy way to estimate the sales tax when she makes a purchase. The sales tax in her city is . She knows this is a little less than . a) Convert to a fraction b) Use your answer from a) to estimate the sales tax Felipa would pay on a dress.	88. Savings Ryan has of each paycheck automatically deposited in his savings account. a) Write as a fraction. b) Use your answer from a) to find the amount that goes to savings from Ryan’s paycheck.
Amelio is shopping for textbooks online. He found three sellers that are offering a book he needs for the same price, including shipping. To decide which seller to buy from he is comparing their customer satisfaction ratings. The ratings are given in the chart. Seller Rating
89. Write seller rating as a fraction and a decimal.	90. Write seller rating as a percent and a decimal.
91. Write seller rating as a percent and a decimal.	92. Which seller should Amelio buy from and why?

Writing Exercises

Answers

1.	3.	5. a) b)
7. a) b)	9.	11.
13.	15.	17.
19.	21.	23.
25. 0.05	27. 0.01	29. 0.63
31. 0.4	33. 1.15	35. 1.5
37. 0.214	39. 0.078	41. a) b)
43. a) b)	45. a) b)	47. a) b)
49. 1%	51. 18%	53. 135%
55. 300%	57. 0.9%	59. 8.75%
61. 150%	63. 225.4%	65. 25%
67. 37.5%	69. 175%	71. 680%
73. 41.7%	75.	77. 42.9%
79. 55.6%	81. 25%	83. 64%
85. Fraction Decimal Percent	87. a) b)	89.
91. 80%; 0.8	93. .	95. The Szetos sold their home for five times what they paid 30 years ago.

Attributions

This chapter has been adapted from “Understand Percent” in Prealgebra (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a CC BY 4.0 Licence. Adapted by Izabela Mazur. See the Copyright page for more information.

Use the Definition of Proportion

When two ratios or rates are equal, the equation relating them is called a proportion.

The equation is a proportion because the two fractions are equal. The proportion is read is to as is to

If we compare quantities with units, we have to be sure we are comparing them in the right order. For example, in the proportion we compare the number of students to the number of teachers. We put students in the numerators and teachers in the denominators.

Look at the proportions and . From our work with equivalent fractions we know these equations are true. But how do we know if an equation is a proportion with equivalent fractions if it contains fractions with larger numbers?

To determine if a proportion is true, we find the cross products of each proportion. To find the cross products, we multiply each denominator with the opposite numerator (diagonally across the equal sign). The results are called a cross products because of the cross formed. The cross products of a proportion are equal.

Cross products can be used to test whether a proportion is true. To test whether an equation makes a proportion, we find the cross products. If they are the equal, we have a proportion.

Solve Proportions

To solve a proportion containing a variable, we remember that the proportion is an equation. All of the techniques we have used so far to solve equations still apply. In the next example, we will solve a proportion by multiplying by the Least Common Denominator (LCD) using the Multiplication Property of Equality.

When the variable is in a denominator, we’ll use the fact that the cross products of a proportion are equal to solve the proportions.

We can find the cross products of the proportion and then set them equal. Then we solve the resulting equation using our familiar techniques.

Solve Applications Using Proportions

The strategy for solving applications that we have used earlier in this chapter, also works for proportions, since proportions are equations. When we set up the proportion, we must make sure the units are correct—the units in the numerators match and the units in the denominators match.

Write Percent Equations As Proportions

Previously, we solved percent equations by applying the properties of equality we have used to solve equations throughout this text. Some people prefer to solve percent equations by using the proportion method. The proportion method for solving percent problems involves a percent proportion. A percent proportion is an equation where a percent is equal to an equivalent ratio.

For example, and we can simplify . Since the equation shows a percent equal to an equivalent ratio, we call it a percent proportion. Using the vocabulary we used earlier:

If we restate the problem in the words of a proportion, it may be easier to set up the proportion:

We could also say:

First we will practice translating into a percent proportion. Later, we’ll solve the proportion.

Translate and Solve Percent Proportions

Now that we have written percent equations as proportions, we are ready to solve the equations.

In the next example, the percent is more than , which is more than one whole. So the unknown number will be more than the base.

Percents with decimals and money are also used in proportions.

Glossary

Practice Makes Perfect

Use the Definition of Proportion

In the following exercises, write each sentence as a proportion.

1. is to as is to .	2. is to as is to .
3. is to as is to .	4. is to as is to .
5. wins in games is the same as wins in games.	6. wins in games is the same as wins in games.
7. campers to counsellor is the same as campers to counsellors.	8. campers to counselor is the same as campers to counselors.
9. for ounces is the same as for ounces.	10. for ounces is the same as for ounces.
11. for pounds is the same as for pounds.	12. for pounds is the same as for pounds.

In the following exercises, determine whether each equation is a proportion.

13.	14.
15.	16.
17.	18.
19.	20.

Solve Proportions

In the following exercises, solve each proportion.

21.	22.
23.	24.
25.	26.
27.	28.
29.	30.
31.	32.
33.	34.
35.	36.

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

37. Pediatricians prescribe millilitre s (ml) of acetaminophen for every pounds of a child’s weight. How many millilitres of acetaminophen will the doctor prescribe for Jocelyn, who weighs pounds?	38. Brianna, who weighs kg, just received her shots and needs a pain killer. The pain killer is prescribed for children at milligrams (mg) for every kilogram (kg) of the child’s weight. How many milligrams will the doctor prescribe?
39. At the gym, Carol takes her pulse for sec and counts beats. How many beats per minute is this? Has Carol met her target heart rate of beats per minute?	40. Kevin wants to keep his heart rate at beats per minute while training. During his workout he counts beats in seconds. How many beats per minute is this? Has Kevin met his target heart rate?
41. A new energy drink advertises calories for ounces. How many calories are in ounces of the drink?	42. One ounce can of soda has calories. If Josiah drinks the big ounce size from the local mini-mart, how many calories does he get?
43. Karen eats cup of oatmeal that counts for points on her weight loss program. Her husband, Joe, can have points of oatmeal for breakfast. How much oatmeal can he have?	44. An oatmeal cookie recipe calls for cup of butter to make dozen cookies. Hilda needs to make dozen cookies for the bake sale. How many cups of butter will she need?
45. Janice is traveling to the US and will change Canadian dollars into US dollars. At the current exchange rate, Canadian is equal to US. How many Canadian dollars will she get for her trip?	46. Todd is traveling to Mexico and needs to exchange into Mexican pesos. If each dollar is worth pesos, how many pesos will he get for his trip?
47. Steve changed into Euros. How many Euros did he receive per Canadian dollar?	48. Martha changed Canadian into Australian dollars. How many Australian dollars did she receive per US dollar?
49. At the laundromat, Lucy changed into quarters. How many quarters did she get?	50. When she arrived at a casino, Gerty changed into nickels. How many nickels did she get?
51. Jesse’s car gets miles per gallon of gas. If Toronto is miles away, how many gallons of gas are needed to get there and then home? If gas is per gallon, what is the total cost of the gas for the trip?	52. Danny wants to drive to Banff to see his grandfather. Banff is miles from Danny’s home and his car gets miles per gallon. How many gallons of gas will Danny need to get to and from Banff? If gas is per gallon, what is the total cost for the gas to drive to see his grandfather?
53. Hugh leaves early one morning to drive from his home in White Rock to go to Edmonton, miles away. After hours, he has gone miles. At that rate, how long will the whole drive take?	54. Kelly leaves her home in Seattle to drive to Spokane, a distance of miles. After hours, she has gone miles. At that rate, how long will the whole drive take?
55. Phil wants to fertilize his lawn. Each bag of fertilizer covers about square feet of lawn. Phil’s lawn is approximately square feet. How many bags of fertilizer will he have to buy?	56. April wants to paint the exterior of her house. One gallon of paint covers about square feet, and the exterior of the house measures approximately square feet. How many gallons of paint will she have to buy?

Write Percent Equations as Proportions

In the following exercises, translate to a proportion.

57. What number is of	58. What number is of
59. What number is of	60. What number is of
61. is of what number?	62. is of what number?
63. is of what number?	64. is of what number?
64. is of what number?	65. What percent of is
66. What percent of is	67. What percent of is
68. What percent of is

Translate and Solve Percent Proportions

In the following exercises, translate and solve using proportions.

69. What number is of	70. What number is of
71. of is what number?	72. of is what number?
73. of is what number?	74. of is what number?
75. What is of	76. What is of
77. of what number is	78. of what number is
79. is of what number?	80. is of what number?
81. What percent of is	82. What percent of is
83. What percent of is	84. What percent of is

Everyday Math

85. Mixing a concentrate Sam bought a large bottle of concentrated cleaning solution at the warehouse store. He must mix the concentrate with water to make a solution for washing his windows. The directions tell him to mix ounces of concentrate with ounces of water. If he puts ounces of concentrate in a bucket, how many ounces of water should he add? How many ounces of the solution will he have altogether?

86. Mixing a concentrate Travis is going to wash his car. The directions on the bottle of car wash concentrate say to mix ounces of concentrate with ounces of water. If Travis puts ounces of concentrate in a bucket, how much water must he mix with the concentrate?

Writing Exercises

87. To solve “what number is of do you prefer to use an equation like you did in the section on Decimal Operations or a proportion like you did in this section? Explain your reason.

88. To solve “what percent of is do you prefer to use an equation like you did in the section on Decimal Operations or a proportion like you did in this section? Explain your reason.

Answers

1.	3.	5.
7.	9.	11.
13. yes	15. no	17. no
19. yes	21. 49	23. 47
25. 9	27. -11	29. 7
31. 2	33. 0.6	35. 4
37. 9 ml	39. 114, no	41. 159 cal
43.	45. $175.00	47. 0.65
49. 48 quarters	51. 19, $58.71	53. 11.1 hours
55. 4 bags	57.	59.
61.	63.	65.
67.	69. 117	70. 165
71. 16.56	73. 45.5	75. 1464
77. $45	79. $164	81. 25%
83. 12.5%	85. 20, 32	87. Answers will vary.

Attributions

This chapter has been adapted from “Solve Proportions and their Applications” in Prealgebra (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a CC BY 4.0 Licence. Adapted by Izabela Mazur. See the Copyright page for more information.

Translate and Solve Basic Percent Equations

In the last section, we solved percent problems by setting them up as proportions. That is the best method available when you did not have the tools of algebra. Now, in this section we will translate word sentences into algebraic equations, and then solve the percent equations.

We’ll look at a common application of percent—tips to a server at a restaurant—to see how to set up a basic percent application.

When Kim and her friends went on a road trip to Vancouver, they ate lunch at Marta’s Cafe Tower. The bill came to . They wanted to leave a tip. What amount would the tip be?

To solve this, we want to find what amount is of . The is called the base. The amount of the tip would be , or See (Figure 1). To find the amount of the tip, we multiplied the percent by the base.

A tip for an restaurant bill comes out to .

In the next examples, we will find the amount. We must be sure to change the given percent to a decimal when we translate the words into an equation.

In the next examples, we are asked to find the base.

In the next examples, we will solve for the percent.

Solve Applications of Percent

Many applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we’ll translate to a basic percent equation, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it.

We will update the strategy we used in our earlier applications to include equations now. Notice that we will translate a sentence into an equation.

Now that we have the strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications. Be sure to ask yourself if your final answer makes sense—since many of the applications we’ll solve involve everyday situations, you can rely on your own experience.

Find Percent Increase and Percent Decrease

People in the media often talk about how much an amount has increased or decreased over a certain period of time. They usually express this increase or decrease as a percent.

To find the percent increase, first we find the amount of increase, which is the difference between the new amount and the original amount. Then we find what percent the amount of increase is of the original amount.

Finding the percent decrease is very similar to finding the percent increase, but now the amount of decrease is the difference between the original amount and the final amount. Then we find what percent the amount of decrease is of the original amount.

Key Concepts

• Solve an application.
  1. Identify what you are asked to find and choose a variable to represent it.
  2. Write a sentence that gives the information to find it.
  3. Translate the sentence into an equation.
  4. Solve the equation using good algebra techniques.
  5. Write a complete sentence that answers the question.
  6. Check the answer in the problem and make sure it makes sense.
• Find percent increase.
  1. Find the amount of increase:
     
  2. Find the percent increase as a percent of the original amount.
• Find percent decrease.
  1. Find the amount of decrease.
     
  2. Find the percent decrease as a percent of the original amount.

Glossary

Practice Makes Perfect

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

1. What number is of	2. What number is of
3. What number is of	4. What number is of
5. of is what number?	6. of is what number?
7. of is what number?	8. of is what number?
9. is of what number?	10. is of what number?
11. is of what number?	12. is of what number?
13. of what number is	14. of what number is
15. of what number is	16. of what number is
17. What percent of is	18. What percent of is
19. What percent of is	20. What percent of is
21. is what percent of	22. is what percent of
23. is what percent of	24. is what percent of

Solve Applications of Percents

In the following exercises, solve the applications of percents.

25. Geneva treated her parents to dinner at their favorite restaurant. The bill was . She wants to leave of the total bill as a tip. How much should the tip be?	26. When Hiro and his co-workers had lunch at a restaurant the bill was . They want to leave of the total bill as a tip. How much should the tip be?
27. Trong has of each paycheck automatically deposited to his savings account. His last paycheck was . How much money was deposited to Trong’s savings account?	28. Cherise deposits of each paycheck into her retirement account. Her last paycheck was . How much did Cherise deposit into her retirement account?
29. One serving of oatmeal has grams of fiber, which is of the recommended daily amount. What is the total recommended daily amount of fiber?	30. One serving of trail mix has grams of carbohydrates, which is of the recommended daily amount. What is the total recommended daily amount of carbohydrates?
31. A bacon cheeseburger at a popular fast food restaurant contains milligrams (mg) of sodium, which is of the recommended daily amount. What is the total recommended daily amount of sodium?	32. A grilled chicken salad at a popular fast food restaurant contains milligrams (mg) of sodium, which is of the recommended daily amount. What is the total recommended daily amount of sodium?
33. The nutrition fact sheet at a fast food restaurant says the fish sandwich has calories, and calories are from fat. What percent of the total calories is from fat?	34. The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has calories, and calories are from fat. What percent of the total calories is from fat?
35. Emma gets paid per month. She pays a month for rent. What percent of her monthly pay goes to rent?	36. Dimple gets paid per month. She pays a month for rent. What percent of her monthly pay goes to rent?

Find Percent Increase and Percent Decrease

In the following exercises, find the percent increase or percent decrease.

37. Tamanika got a raise in her hourly pay, from to . Find the percent increase.	38. Ayodele got a raise in her hourly pay, from to . Find the percent increase.
39. According to Statistics Canada, annual international graduate student fees in Canada rose from about in to about in . Find the percent increase.	40. The price of a share of one stock rose from to . Find the percent increase.
41. According to Time magazine annual global seafood consumption rose from pounds per person in to pounds per person today. Find the percent increase. (Round to the nearest tenth of a percent.)	42. In one month, the median home price in the Northeast rose from to . Find the percent increase. (Round to the nearest tenth of a percent.)
43. A grocery store reduced the price of a loaf of bread from to . Find the percent decrease.	44. The price of a share of one stock fell from to . Find the percent decrease.
45. Hernando’s salary was last year. This year his salary was cut to . Find the percent decrease.	46. From to , the population of Detroit fell from about to about . Find the percent decrease. (Round to the nearest tenth of a percent.)
47. In one month, the median home price in the West fell from to . Find the percent decrease. (Round to the nearest tenth of a percent.)	48. Sales of video games and consoles fell from million to million in one year. Find the percent decrease. (Round to the nearest tenth of a percent.)

Everyday Math

49. Tipping At the campus coffee cart, a medium coffee costs . MaryAnne brings with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave?

50. Late Fees Alison was late paying her credit card bill of . She was charged a late fee. What was the amount of the late fee?

Writing Exercises

51. Without solving the problem is of what number”, think about what the solution might be. Should it be a number that is greater than or less than Explain your reasoning.	52. Without solving the problem “What is of think about what the solution might be. Should it be a number that is greater than or less than Explain your reasoning.
53. After returning from vacation, Alex said he should have packed fewer shorts and more shirts. Explain what Alex meant.	54. Because of road construction in one city, commuters were advised to plan their Monday morning commute to take of their usual commuting time. Explain what this means.

Answers

1. 54	3. 26.88	5. 162.5
7. 18,000	9. 112	11. 108
13. $35	15. $940	17. 30%
19. 36%	21. 150%	23. 175%
25. $11.88	27. $259.80	29. 24.2 grams
31. 2,407 grams	33. 45%	35. 25%
37. 13.2%	39. 15%	41. 72.7%
43. 2.5%	45. 11%	47. 5.5%
49. 21.2%	51. The original number should be greater than 44.80% is less than 100%, so when 80% is converted to a decimal and multiplied to the base in the percent equation, the resulting amount of 44 is less. 44 is only the larger number in cases where the percent is greater than 100%.	53. Alex should have packed half as many shorts and twice as many shirts.

Attributions

This chapter has been adapted from “Solve General Applications of Percent” in Prealgebra (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a CC BY 4.0 Licence. Adapted by Izabela Mazur. See the Copyright page for more information.