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Prealgebra 2e

Review Exercises

Prealgebra 2eReview Exercises
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Table of contents
  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. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. 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

Solve Equations using the Subtraction and Addition Properties of Equality

In the following exercises, determine whether the given number is a solution to the equation.

255.

x + 16 = 31 , x = 15 x + 16 = 31 , x = 15

256.

w − 8 = 5 , w = 3 w − 8 = 5 , w = 3

257.

−9 n = 45 , n = 54 −9 n = 45 , n = 54

258.

4 a = 72 , a = 18 4 a = 72 , a = 18

In the following exercises, solve the equation using the Subtraction Property of Equality.

259.

x + 7 = 19 x + 7 = 19

260.

y + 2 = −6 y + 2 = −6

261.

a + 1 3 = 5 3 a + 1 3 = 5 3

262.

n + 3.6 = 5.1 n + 3.6 = 5.1

In the following exercises, solve the equation using the Addition Property of Equality.

263.

u − 7 = 10 u − 7 = 10

264.

x − 9 = −4 x − 9 = −4

265.

c − 3 11 = 9 11 c − 3 11 = 9 11

266.

p − 4.8 = 14 p − 4.8 = 14

In the following exercises, solve the equation.

267.

n − 12 = 32 n − 12 = 32

268.

y + 16 = −9 y + 16 = −9

269.

f + 2 3 = 4 f + 2 3 = 4

270.

d − 3.9 = 8.2 d − 3.9 = 8.2

271.

y + 8 − 15 = −3 y + 8 − 15 = −3

272.

7 x + 10 − 6 x + 3 = 5 7 x + 10 − 6 x + 3 = 5

273.

6 ( n − 1 ) − 5 n = −14 6 ( n − 1 ) − 5 n = −14

274.

8 ( 3 p + 5 ) − 23 ( p − 1 ) = 35 8 ( 3 p + 5 ) − 23 ( p − 1 ) = 35

In the following exercises, translate each English sentence into an algebraic equation and then solve it.

275.

The sum of −6−6 and mm is 25.25.

276.

Four less than nn is 13.13.

In the following exercises, translate into an algebraic equation and solve.

277.

Rochelle’s daughter is 1111 years old. Her son is 33 years younger. How old is her son?

278.

Tan weighs 146146 pounds. Minh weighs 1515 pounds more than Tan. How much does Minh weigh?

279.

Peter paid $9.75$9.75 to go to the movies, which was $46.25$46.25 less than he paid to go to a concert. How much did he pay for the concert?

280.

Elissa earned $152.84$152.84 this week, which was $21.65$21.65 more than she earned last week. How much did she earn last week?

Solve Equations using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation using the Division Property of Equality.

281.

8 x = 72 8 x = 72

282.

13 a = −65 13 a = −65

283.

0.25 p = 5.25 0.25 p = 5.25

284.

− y = 4 − y = 4

In the following exercises, solve each equation using the Multiplication Property of Equality.

285.

n 6 = 18 n 6 = 18

286.

y −10 = 30 y −10 = 30

287.

36 = 3 4 x 36 = 3 4 x

288.

5 8 u = 15 16 5 8 u = 15 16

In the following exercises, solve each equation.

289.

−18 m = −72 −18 m = −72

290.

c 9 = 36 c 9 = 36

291.

0.45 x = 6.75 0.45 x = 6.75

292.

11 12 = 2 3 y 11 12 = 2 3 y

293.

5 r − 3 r + 9 r = 35 − 2 5 r − 3 r + 9 r = 35 − 2

294.

24 x + 8 x − 11 x = −7 −14 24 x + 8 x − 11 x = −7 −14

Solve Equations with Variables and Constants on Both Sides

In the following exercises, solve the equations with constants on both sides.

295.

8 p + 7 = 47 8 p + 7 = 47

296.

10 w − 5 = 65 10 w − 5 = 65

297.

3 x + 19 = −47 3 x + 19 = −47

298.

32 = −4 − 9 n 32 = −4 − 9 n

In the following exercises, solve the equations with variables on both sides.

299.

7 y = 6 y − 13 7 y = 6 y − 13

300.

5 a + 21 = 2 a 5 a + 21 = 2 a

301.

k = −6 k − 35 k = −6 k − 35

302.

4 x − 3 8 = 3 x 4 x − 3 8 = 3 x

In the following exercises, solve the equations with constants and variables on both sides.

303.

12 x − 9 = 3 x + 45 12 x − 9 = 3 x + 45

304.

5 n − 20 = −7 n − 80 5 n − 20 = −7 n − 80

305.

4 u + 16 = −19 − u 4 u + 16 = −19 − u

306.

5 8 c − 4 = 3 8 c + 4 5 8 c − 4 = 3 8 c + 4

In the following exercises, solve each linear equation using the general strategy.

307.

6 ( x + 6 ) = 24 6 ( x + 6 ) = 24

308.

9 ( 2 p − 5 ) = 72 9 ( 2 p − 5 ) = 72

309.

− ( s + 4 ) = 18 − ( s + 4 ) = 18

310.

8 + 3 ( n − 9 ) = 17 8 + 3 ( n − 9 ) = 17

311.

23 − 3 ( y − 7 ) = 8 23 − 3 ( y − 7 ) = 8

312.

1 3 ( 6 m + 21 ) = m − 7 1 3 ( 6 m + 21 ) = m − 7

313.

8 ( r − 2 ) = 6 ( r + 10 ) 8 ( r − 2 ) = 6 ( r + 10 )

314.

5 + 7 ( 2 − 5 x ) = 2 ( 9 x + 1 ) − ( 13 x − 57 ) 5 + 7 ( 2 − 5 x ) = 2 ( 9 x + 1 ) − ( 13 x − 57 )

315.

4 ( 3.5 y + 0.25 ) = 365 4 ( 3.5 y + 0.25 ) = 365

316.

0.25 ( q − 8 ) = 0.1 ( q + 7 ) 0.25 ( q − 8 ) = 0.1 ( q + 7 )

Solve Equations with Fraction or Decimal Coefficients

In the following exercises, solve each equation by clearing the fractions.

317.

2 5 n − 1 10 = 7 10 2 5 n − 1 10 = 7 10

318.

1 3 x + 1 5 x = 8 1 3 x + 1 5 x = 8

319.

3 4 a − 1 3 = 1 2 a + 5 6 3 4 a − 1 3 = 1 2 a + 5 6

320.

1 2 ( k + 3 ) = 1 3 ( k + 16 ) 1 2 ( k + 3 ) = 1 3 ( k + 16 )

In the following exercises, solve each equation by clearing the decimals.

321.

0.8 x − 0.3 = 0.7 x + 0.2 0.8 x − 0.3 = 0.7 x + 0.2

322.

0.36 u + 2.55 = 0.41 u + 6.8 0.36 u + 2.55 = 0.41 u + 6.8

323.

0.6 p − 1.9 = 0.78 p + 1.7 0.6 p − 1.9 = 0.78 p + 1.7

324.

0.10 d + 0.05 ( d − 4 ) = 2.05 0.10 d + 0.05 ( d − 4 ) = 2.05

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