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Prealgebra

Review Exercises

PrealgebraReview Exercises
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

Use the Language of Algebra

Use Variables and Algebraic Symbols

In the following exercises, translate from algebra to English.

317.

3 ⋅ 8 3 ⋅ 8

318.

12 − x 12 − x

319.

24 ÷ 6 24 ÷ 6

320.

9 + 2 a 9 + 2 a

321.

50 ≥ 47 50 ≥ 47

322.

3 y < 15 3 y < 15

323.

n + 4 = 13 n + 4 = 13

324.

32 − k = 7 32 − k = 7

Identify Expressions and Equations

In the following exercises, determine if each is an expression or equation.

325.

5 + u = 84 5 + u = 84

326.

36 − 6 s 36 − 6 s

327.

4 y − 11 4 y − 11

328.

10 x = 120 10 x = 120

Simplify Expressions with Exponents

In the following exercises, write in exponential form.

329.

2 ⋅ 2 ⋅ 2 2 ⋅ 2 ⋅ 2

330.

a ⋅ a ⋅ a ⋅ a ⋅ a a ⋅ a ⋅ a ⋅ a ⋅ a

331.

x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x

332.

10 ⋅ 10 ⋅ 10 10 ⋅ 10 ⋅ 10

In the following exercises, write in expanded form.

333.

8 4 8 4

334.

3 6 3 6

335.

y 5 y 5

336.

n 4 n 4

In the following exercises, simplify each expression.

337.

3 4 3 4

338.

10 6 10 6

339.

2 7 2 7

340.

4 3 4 3

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

341.

10 + 2 ⋅ 5 10 + 2 ⋅ 5

342.

( 10 + 2 ) ⋅ 5 ( 10 + 2 ) ⋅ 5

343.

( 30 + 6 ) ÷ 2 ( 30 + 6 ) ÷ 2

344.

30 + 6 ÷ 2 30 + 6 ÷ 2

345.

7 2 + 5 2 7 2 + 5 2

346.

( 7 + 5 ) 2 ( 7 + 5 ) 2

347.

4 + 3 ( 10 − 1 ) 4 + 3 ( 10 − 1 )

348.

( 4 + 3 ) ( 10 − 1 ) ( 4 + 3 ) ( 10 − 1 )

Evaluate, Simplify, and Translate Expressions

Evaluate an Expression

In the following exercises, evaluate the following expressions.

349.

9 x − 5 when x = 7 9 x − 5 when x = 7

350.

y 3 when y = 5 y 3 when y = 5

351.

3a−4b3a−4b when a=10,b=1a=10,b=1

352.

b h when b = 7 , h = 8 b h when b = 7 , h = 8

Identify Terms, Coefficients and Like Terms

In the following exercises, identify the terms in each expression.

353.

12 n 2 + 3 n + 1 12 n 2 + 3 n + 1

354.

4 x 3 + 11 x + 3 4 x 3 + 11 x + 3

In the following exercises, identify the coefficient of each term.

355.

6 y 6 y

356.

13 x 2 13 x 2

In the following exercises, identify the like terms.

357.

5 x 2 , 3 , 5 y 2 , 3 x , x , 4 5 x 2 , 3 , 5 y 2 , 3 x , x , 4

358.

8 , 8 r 2 , 8 r , 3 r , r 2 , 3 s 8 , 8 r 2 , 8 r , 3 r , r 2 , 3 s

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the following expressions by combining like terms.

359.

15 a + 9 a 15 a + 9 a

360.

12 y + 3 y + y 12 y + 3 y + y

361.

4 x + 7 x + 3 x 4 x + 7 x + 3 x

362.

6 + 5 c + 3 6 + 5 c + 3

363.

8 n + 2 + 4 n + 9 8 n + 2 + 4 n + 9

364.

19 p + 5 + 4 p − 1 + 3 p 19 p + 5 + 4 p − 1 + 3 p

365.

7 y 2 + 2 y + 11 + 3 y 2 − 8 7 y 2 + 2 y + 11 + 3 y 2 − 8

366.

13 x 2 − x + 6 + 5 x 2 + 9 x 13 x 2 − x + 6 + 5 x 2 + 9 x

Translate English Phrases to Algebraic Expressions

In the following exercises, translate the following phrases into algebraic expressions.

367.

the difference of xx and 66

368.

the sum of 1010 and twice aa

369.

the product of 3n3n and 99

370.

the quotient of ss and 44

371.

55 times the sum of yy and 11

372.

1010 less than the product of 55 and zz

373.

Jack bought a sandwich and a coffee. The cost of the sandwich was $3$3 more than the cost of the coffee. Call the cost of the coffee c.c. Write an expression for the cost of the sandwich.

374.

The number of poetry books on Brianna’s bookshelf is 55 less than twice the number of novels. Call the number of novels n.n. Write an expression for the number of poetry books.

Solve Equations Using the Subtraction and Addition Properties of Equality

Determine Whether a Number is a Solution of an Equation

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

375.

y+16=40y+16=40

  1. ⓐ2424
  2. ⓑ5656
376.

d−6=21d−6=21

  1. ⓐ1515
  2. ⓑ2727
377.

4n+12=364n+12=36

  1. ⓐ66
  2. ⓑ1212
378.

20q−10=7020q−10=70

  1. ⓐ33
  2. ⓑ44
379.

15x−5=10x+4515x−5=10x+45

  1. ⓐ22
  2. ⓑ1010
380.

22p−6=18p+8622p−6=18p+86

  1. ⓐ44
  2. ⓑ2323

Model the Subtraction Property of Equality

In the following exercises, write the equation modeled by the envelopes and counters and then solve the equation using the subtraction property of equality.

381.
This image is divided into two parts: the first part shows an envelope and 3 blue counters and the next to it, the second part shows five counters.
382.
This image is divided into two parts: the first part shows an envelope and 4 blue counters and next to it, the second part shows 9 counters.

Solve Equations using the Subtraction Property of Equality

In the following exercises, solve each equation using the subtraction property of equality.

383.

c + 8 = 14 c + 8 = 14

384.

v + 8 = 150 v + 8 = 150

385.

23 = x + 12 23 = x + 12

386.

376 = n + 265 376 = n + 265

Solve Equations using the Addition Property of Equality

In the following exercises, solve each equation using the addition property of equality.

387.

y − 7 = 16 y − 7 = 16

388.

k − 42 = 113 k − 42 = 113

389.

19 = p − 15 19 = p − 15

390.

501 = u − 399 501 = u − 399

Translate English Sentences to Algebraic Equations

In the following exercises, translate each English sentence into an algebraic equation.

391.

The sum of 77 and 3333 is equal to 40.40.

392.

The difference of 1515 and 33 is equal to 12.12.

393.

The product of 44 and 88 is equal to 32.32.

394.

The quotient of 6363 and 99 is equal to 7.7.

395.

Twice the difference of nn and 33 gives 76.76.

396.

The sum of five times yy and 44 is 89.89.

Translate to an Equation and Solve

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

397.

Eight more than xx is equal to 35.35.

398.

2121 less than aa is 11.11.

399.

The difference of qq and 1818 is 57.57.

400.

The sum of mm and 125125 is 240.240.

Mixed Practice

In the following exercises, solve each equation.

401.

h − 15 = 27 h − 15 = 27

402.

k − 11 = 34 k − 11 = 34

403.

z + 52 = 85 z + 52 = 85

404.

x + 93 = 114 x + 93 = 114

405.

27 = q + 19 27 = q + 19

406.

38 = p + 19 38 = p + 19

407.

31 = v − 25 31 = v − 25

408.

38 = u − 16 38 = u − 16

Find Multiples and Factors

Identify Multiples of Numbers

In the following exercises, list all the multiples less than 5050 for each of the following.

409.

3 3

410.

2 2

411.

8 8

412.

10 10

Use Common Divisibility Tests

In the following exercises, using the divisibility tests, determine whether each number is divisible by 2,by3,by5,by6,and by10.2,by3,by5,by6,and by10.

413.

96 96

414.

250 250

415.

420 420

416.

625 625

Find All the Factors of a Number

In the following exercises, find all the factors of each number.

417.

30 30

418.

70 70

419.

180 180

420.

378 378

Identify Prime and Composite Numbers

In the following exercises, identify each number as prime or composite.

421.

19 19

422.

51 51

423.

121 121

424.

219 219

Prime Factorization and the Least Common Multiple

Find the Prime Factorization of a Composite Number

In the following exercises, find the prime factorization of each number.

425.

84 84

426.

165 165

427.

350 350

428.

572 572

Find the Least Common Multiple of Two Numbers

In the following exercises, find the least common multiple of each pair of numbers.

429.

9 , 15 9 , 15

430.

12 , 20 12 , 20

431.

25 , 35 25 , 35

432.

18 , 40 18 , 40

Everyday Math
433.

Describe how you have used two topics from The Language of Algebra chapter in your life outside of your math class during the past month.

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