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Prealgebra 2e

Review Exercises

Prealgebra 2eReview Exercises
  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  17. Index

Review Exercises

Understand Percent

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

331.

32%32% admission rate for the university

332.

53.3%53.3% rate of college students with student loans

In the following exercises, write as a ratio and then as a percent.

333.

1313 out of 100100 architects are women.

334.

99 out of every 100100 nurses are men.

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

335.

48%48%

336.

175%175%

337.

64.1%64.1%

338.

814%814%

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

339.

6%6%

340.

23%23%

341.

128%128%

342.

4.9%

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

343.

In 2012,13.5%2012,13.5% of the United States population was age 6565 or over. (Source: www.census.gov)

344.

In 2012,6.5%2012,6.5% of the United States population was under 55 years old. (Source: www.census.gov)

345.

When a die is tossed, the probability it will land with an even number of dots on the top side is 50%.50%.

346.

A couple plans to have three children. The probability they will all be girls is 12.5%.12.5%.

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

347.

0.040.04

348.

0.150.15

349.

2.822.82

350.

33

351.

0.0030.003

352.

1.3951.395

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

353.

3434

354.

115115

355.

358358

356.

2929

357.

According to the Centers for Disease Control, 2525 of adults do not take a vitamin or supplement.

358.

According to the Centers for Disease Control, among adults who do take a vitamin or supplement, 3434 take a multivitamin.

In the following exercises, translate and solve.

359.

What number is 46%46% of 350?350?

360.

120%120% of 5555 is what number?

361.

8484 is 35%35% of what number?

362.

1515 is 8%8% of what number?

363.

200%200% of what number is 50?50?

364.

7.9%7.9% of what number is $4.74?$4.74?

365.

What percent of 120120 is 81.6?81.6?

366.

What percent of 340340 is 595?595?

Solve General Applications of Percents

In the following exercises, solve.

367.

When Aurelio and his family ate dinner at a restaurant, the bill was $83.50.$83.50. Aurelio wants to leave 20%20% of the total bill as a tip. How much should the tip be?

368.

One granola bar has 22 grams of fiber, which is 8%8% of the recommended daily amount. What is the total recommended daily amount of fiber?

369.

The nutrition label on a package of granola bars says that each granola bar has 190190 calories, and 5454 calories are from fat. What percent of the total calories is from fat?

370.

Elsa gets paid $4,600$4,600 per month. Her car payment is $253.$253. What percent of her monthly pay goes to her car payment?

In the following exercises, solve.

371.

Jorge got a raise in his hourly pay, from $19.00$19.00 to $19.76.$19.76. Find the percent increase.

372.

Last year Bernard bought a new car for $30,000.$30,000. This year the car is worth $24,000.$24,000. Find the percent decrease.

Solve Sales Tax, Commission, and Discount Applications

In the following exercises, find the sales tax the total cost.

373.

The cost of a lawn mower was $750.$750. The sales tax rate is 6%6% of the purchase price.

374.

The cost of a water heater is $577.$577. The sales tax rate is 8.75%8.75% of the purchase price.

In the following exercises, find the sales tax rate.

375.

Andy bought a piano for $4,600.$4,600. The sales tax on the purchase was $333.50.$333.50.

376.

Nahomi bought a purse for $200.$200. The sales tax on the purchase was $16.75.$16.75.

In the following exercises, find the commission.

377.

Ginny is a realtor. She receives 3%3% commission when she sells a house. How much commission will she receive for selling a house for $380,000?$380,000?

378.

Jackson receives 16.5%16.5% commission when he sells a dinette set. How much commission will he receive for selling a dinette set for $895?$895?

In the following exercises, find the rate of commission.

379.

Ruben received $675$675 commission when he sold a $4,500$4,500 painting at the art gallery where he works. What was the rate of commission?

380.

Tori received $80.75$80.75 for selling a $950$950 membership at her gym. What was her rate of commission?

In the following exercises, find the sale price.

381.

Aya bought a pair of shoes that was on sale for $30$30 off. The original price of the shoes was $75.$75.

382.

Takwanna saw a cookware set she liked on sale for $145$145 off. The original price of the cookware was $312.$312.

In the following exercises, find the amount of discount and the sale price.

383.

Nga bought a microwave for her office. The microwave was discounted 30%30% from an original price of $84.90.$84.90.

384.

Jarrett bought a tie that was discounted 65%65% from an original price of $45.$45.

In the following exercises, find the amount of discount the discount rate. (Round to the nearest tenth of a percent if needed.)

385.

Hilda bought a bedspread on sale for $37.$37. The original price of the bedspread was $50.$50.

386.

Tyler bought a phone on sale for $49.99.$49.99. The original price of the phone was $79.99.$79.99.

In the following exercises, find

  1. the amount of the mark-up
  2. the list price
387.

Manny paid $0.80$0.80 a pound for apples. He added 60%60% mark-up before selling them at his produce stand. What price did he charge for the apples?

388.

It cost Noelle $17.40$17.40 for the materials she used to make a purse. She added a 325%325% mark-up before selling it at her friend’s store. What price did she ask for the purse?

Solve Simple Interest Applications

In the following exercises, solve the simple interest problem.

389.

Find the simple interest earned after 44 years on $2,250$2,250 invested at an interest rate of 5%.5%.

390.

Find the simple interest earned after 77 years on $12,000$12,000 invested at an interest rate of 8.5%.8.5%.

391.

Find the principal invested if $660$660 interest was earned in 55 years at an interest rate of 3%.3%.

392.

Find the interest rate if $2,898$2,898 interest was earned from a principal of $23,000$23,000 invested for 33 years.

393.

Kazuo deposited $10,000$10,000 in a bank account with interest rate 4.5%.4.5%. How much interest was earned in 22 years?

394.

Brent invested $23,000$23,000 in a friend’s business. In 55 years the friend paid him the $23,000$23,000 plus $9,200$9,200 interest. What was the rate of interest?

395.

Fresia lent her son $5,000$5,000 for college expenses. Three years later he repaid her the $5,000$5,000 plus $375$375 interest. What was the rate of interest?

396.

In 66 years, a bond that paid 5.5%5.5% earned $594$594 interest. What was the principal of the bond?

Solve Proportions and their Applications

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

397.

33 is to 88 as 1212 is to 32.32.

398.

9595 miles to 33 gallons is the same as 475475 miles to 1515 gallons.

399.

11 teacher to 1818 students is the same as 2323 teachers to 414414 students.

400.

$7.35$7.35 for 1515 ounces is the same as $2.94$2.94 for 66 ounces.

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

401.

513=3078513=3078

402.

167=4823167=4823

403.

1218=6.9910.991218=6.9910.99

404.

11.69.2=37.1229.4411.69.2=37.1229.44

In the following exercises, solve each proportion.

405.

x36=59x36=59

406.

7a=−6847a=−684

407.

1.21.8=d61.21.8=d6

408.

122=m20122=m20

In the following exercises, solve the proportion problem.

409.

The children’s dosage of acetaminophen is 55 milliliters (ml) for every 2525 pounds of a child’s weight. How many milliliters of acetaminophen will be prescribed for a 6060 pound child?

410.

After a workout, Dennis takes his pulse for 1010 sec and counts 2121 beats. How many beats per minute is this?

411.

An 88 ounce serving of ice cream has 272272 calories. If Lavonne eats 1010 ounces of ice cream, how many calories does she get?

412.

Alma is going to Europe and wants to exchange $1,200$1,200 into Euros. If each dollar is 0.750.75 Euros, how many Euros will Alma get?

413.

Zack wants to drive from Omaha to Denver, a distance of 494494 miles. If his car gets 3838 miles to the gallon, how many gallons of gas will Zack need to get to Denver?

414.

Teresa is planning a party for 100100 people. Each gallon of punch will serve 1818 people. How many gallons of punch will she need?

In the following exercises, translate to a proportion.

415.

What number is 62%62% of 395?395?

416.

4242 is 70%70% of what number?

417.

What percent of 1,0001,000 is 15?15?

418.

What percent of 140140 is 210?210?

In the following exercises, translate and solve using proportions.

419.

What number is 85%85% of 900?900?

420.

6%6% of what number is $24?$24?

421.

$3.51$3.51 is 4.5%4.5% of what number?

422.

What percent of 3,1003,100 is 930?930?

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