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Prealgebra

Review Exercises

PrealgebraReview 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

Introduction to Integers

Locate Positive and Negative Numbers on the Number Line

In the following exercises, locate and label the integer on the number line.

353.

55

354.

−5−5

355.

−3−3

356.

33

357.

−8−8

358.

−7−7

Order Positive and Negative Numbers

In the following exercises, order each of the following pairs of numbers, using << or >.>.

359.

4__84__8

360.

−6__3−6__3

361.

−5__−10−5__−10

362.

−9__−4−9__−4

363.

2__−72__−7

364.

−3__1−3__1

Find Opposites

In the following exercises, find the opposite of each number.

365.

66

366.

−2−2

367.

−4−4

368.

33

In the following exercises, simplify.

369.
  1. (8)(8)
  2. (−8)(−8)
370.
  1. (9)(9)
  2. (−9)(−9)

In the following exercises, evaluate.

371.

x,whenx,when

  1. x=32x=32
  2. x=−32x=−32
372.

n,whenn,when

  1. n=20n=20
  2. n=−20n=−20

Simplify Absolute Values

In the following exercises, simplify.

373.

|−21||−21|

374.

|−42||−42|

375.

|36||36|

376.

|15||15|

377.

|0||0|

378.

|−75||−75|

In the following exercises, evaluate.

379.

|x|whenx=−14|x|whenx=−14

380.

|r|whenr=27|r|whenr=27

381.

|y|wheny=33|y|wheny=33

382.

|−n|whenn=−4|−n|whenn=−4

In the following exercises, fill in <,>,or=<,>,or= for each of the following pairs of numbers.

383.

|−4|__4|−4|__4

384.

−2__|−2|−2__|−2|

385.

|−6|__−6|−6|__−6

386.

|−9|__|−9||−9|__|−9|

In the following exercises, simplify.

387.

(−55)and|−55|(−55)and|−55|

388.

(−48)and|−48|(−48)and|−48|

389.

|125||125|

390.

|9+7||9+7|

391.

6|−9|6|−9|

392.

|14−8||−2||14−8||−2|

393.

|93||512||93||512|

394.

5+4|153|5+4|153|

Translate Phrases to Expressions with Integers

In the following exercises, translate each of the following phrases into expressions with positive or negative numbers.

395.

the opposite of 1616

396.

the opposite of −8−8

397.

negative 33

398.

1919 minus negative 1212

399.

a temperature of 1010 below zero

400.

an elevation of 85 feet85 feet below sea level

Add Integers

Model Addition of Integers

In the following exercises, model the following to find the sum.

401.

3+73+7

402.

−2+6−2+6

403.

5+(−4)5+(−4)

404.

−3+(−6)−3+(−6)

Simplify Expressions with Integers

In the following exercises, simplify each expression.

405.

14+8214+82

406.

−33+(−67)−33+(−67)

407.

−75+25−75+25

408.

54+(−28)54+(−28)

409.

11+(−15)+311+(−15)+3

410.

−19+(−42)+12−19+(−42)+12

411.

−3+6(−1+5)−3+6(−1+5)

412.

10+4(−3+7)10+4(−3+7)

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

413.

n+4whenn+4when

  1. n=−1n=−1
  2. n=−20n=−20
414.

x+(−9)whenx+(−9)when

  1. x=3x=3
  2. x=−3x=−3
415.

(x+y)3whenx=−4,y=1(x+y)3whenx=−4,y=1

416.

(u+v)2whenu=−4,v=11(u+v)2whenu=−4,v=11

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

417.

the sum of −8 and 2the sum of −8 and 2

418.

4 more than −124 more than −12

419.

10 more than the sum of −5 and −610 more than the sum of −5 and −6

420.

the sum of3and−5,increased by 18the sum of3and−5,increased by 18

Add Integers in Applications

In the following exercises, solve.

421.

Temperature On Monday, the high temperature in Denver was −4 degrees.−4 degrees. Tuesday’s high temperature was 20 degrees20 degrees more. What was the high temperature on Tuesday?

422.

Credit Frida owed $75$75 on her credit card. Then she charged $21$21 more. What was her new balance?

Subtract Integers

Model Subtraction of Integers

In the following exercises, model the following.

423.

6161

424.

−4(−3)−4(−3)

425.

2(−5)2(−5)

426.

−14−14

Simplify Expressions with Integers

In the following exercises, simplify each expression.

427.

24162416

428.

19(−9)19(−9)

429.

−317−317

430.

−40(−11)−40(−11)

431.

−52(−17)23−52(−17)23

432.

25(−39)25(−39)

433.

(17)(38)(17)(38)

434.

32723272

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

435.

x7whenx7when

  1. x=5x=5
  2. x=−4x=−4
436.

10ywhen10ywhen

  1. y=15y=15
  2. y=−16y=−16
437.

2n2n+5whenn=−42n2n+5whenn=−4

438.

−153u2whenu=−5−153u2whenu=−5

Translate Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

439.

the difference of −12and5−12and5

440.

subtract 2323 from −50−50

Subtract Integers in Applications

In the following exercises, solve the given applications.

441.

Temperature One morning the temperature in Bangor, Maine was 18 degrees.18 degrees. By afternoon, it had dropped 20 degrees.20 degrees. What was the afternoon temperature?

442.

Temperature On January 4, the high temperature in Laredo, Texas was 78 degrees,78 degrees, and the high in Houlton, Maine was −28degrees.−28degrees. What was the difference in temperature of Laredo and Houlton?

Multiply and Divide Integers

Multiply Integers

In the following exercises, multiply.

443.

−94−94

444.

5(−7)5(−7)

445.

(−11)(−11)(−11)(−11)

446.

−16−16

Divide Integers

In the following exercises, divide.

447.

56÷(−8)56÷(−8)

448.

−120÷(−6)−120÷(−6)

449.

−96÷12−96÷12

450.

96÷(−16)96÷(−16)

451.

45÷(−1)45÷(−1)

452.

−162÷(−1)−162÷(−1)

Simplify Expressions with Integers

In the following exercises, simplify each expression.

453.

5(−9)3(−12)5(−9)3(−12)

454.

(−2)5(−2)5

455.

3434

456.

(−3)(4)(−5)(−6)(−3)(4)(−5)(−6)

457.

424(69)424(69)

458.

(815)(93)(815)(93)

459.

−2(−18)÷9−2(−18)÷9

460.

45÷(−3)1245÷(−3)12

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

461.

7x3whenx=−97x3whenx=−9

462.

162nwhenn=−8162nwhenn=−8

463.

5a+8bwhena=−2,b=−65a+8bwhena=−2,b=−6

464.

x2+5x+4whenx=−3x2+5x+4whenx=−3

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

465.

the product of −12−12 and 66

466.

the quotient of 33 and the sum of −7−7 and ss

Solve Equations using Integers; The Division Property of Equality

Determine Whether a Number is a Solution of an Equation

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

467.

5x10=−355x10=−35

  1. x=−9x=−9
  2. x=−5x=−5
  3. x=5x=5
468.

8u+24=−328u+24=−32

  1. u=−7u=−7
  2. u=−1u=−1
  3. u=7u=7

Using the Addition and Subtraction Properties of Equality

In the following exercises, solve.

469.

a+14=2a+14=2

470.

b9=−15b9=−15

471.

c+(−10)=−17c+(−10)=−17

472.

d(−6)=−26d(−6)=−26

Model the Division Property of Equality

In the following exercises, write the equation modeled by the envelopes and counters. Then solve it.

473.
This image has two columns. In the first column there are three envelopes. In the second column there are two vertical rows. The first row includes five blue circles, the second row includes four blue circles.
474.
This figure has two columns. In the first column there are  two envelopes. In the second column there are two vertical rows, each includes four blue circles.

Solve Equations Using the Division Property of Equality

In the following exercises, solve each equation using the division property of equality and check the solution.

475.

8p=728p=72

476.

−12q=48−12q=48

477.

−16r=−64−16r=−64

478.

−5s=−100−5s=−100

Translate to an Equation and Solve.

In the following exercises, translate and solve.

479.

The product of −6 andyis−42The product of −6 andyis−42

480.

The difference ofzand −13 is −18.The difference ofzand −13 is −18.

481.

Four more than mm is −48.−48.

482.

The product of −21 andnis 63.The product of −21 andnis 63.

Everyday Math
483.

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

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