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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

Use the Rectangular Coordinate System

Plot Points in a Rectangular Coordinate System

In the following exercises, plot each point in a rectangular coordinate system.

277.

( 1 , 3 ) , ( 3 , 1 ) ( 1 , 3 ) , ( 3 , 1 )

278.

( 2 , 5 ) , ( 5 , 2 ) ( 2 , 5 ) , ( 5 , 2 )

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.

279.
  1. ⓐ (−1,−5)(−1,−5)
  2. ⓑ (−3,4)(−3,4)
  3. ⓒ (2,−3)(2,−3)
  4. ⓓ (1,52)(1,52)
280.
  1. ⓐ (3,−2)(3,−2)
  2. ⓑ (−4,−1)(−4,−1)
  3. ⓒ (−5,4)(−5,4)
  4. ⓓ (2,103)(2,103)

Identify Points on a Graph

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.

281.
The graph shows the x y-coordinate plane. The axes run from -7 to 7. “a” is plotted at 5, 3, “b” at 2, -1, “c” at -3,-2, and “d” at -1,4.
282.
The graph shows the x y-coordinate plane. The axes run from -7 to 7. “a” is plotted at -2, 2, “b” at 3, 5, “c” at 4,-1, and “d” at -1,3.
283.
The graph shows the x y-coordinate plane. The axes run from -7 to 7. “a” is plotted at 2, 0, “b” at 0, -5, “c” at -4,0, and “d” at 0,3.
284.
The graph shows the x y-coordinate plane. The axes run from -7 to 7. “a” is plotted at 0, 4, “b” at 5, 0, “c” at 0,-1, and “d” at -3,0.

Verify Solutions to an Equation in Two Variables

In the following exercises, find the ordered pairs that are solutions to the given equation.

285.

5 x + y = 10 5 x + y = 10

  1. ⓐ (5,1)(5,1)
  2. ⓑ (2,0)(2,0)
  3. ⓒ (4,−10)(4,−10)
286.

y = 6 x − 2 y = 6 x − 2

  1. ⓐ (1,4)(1,4)
  2. ⓑ (13,0)(13,0)
  3. ⓒ (6,−2)(6,−2)

Complete a Table of Solutions to a Linear Equation in Two Variables

In the following exercises, complete the table to find solutions to each linear equation.

287.

y = 4 x − 1 y = 4 x − 1

xx yy (x,y)(x,y)
00
11
−2−2
288.

y = − 1 2 x + 3 y = − 1 2 x + 3

xx yy (x,y)(x,y)
00
11
−2−2
289.

x + 2 y = 5 x + 2 y = 5

xx yy (x,y)(x,y)
00
11
−1−1
290.

3 x − 2 y = 6 3 x − 2 y = 6

xx yy (x,y)(x,y)
00
00
−2−2

Find Solutions to a Linear Equation in Two Variables

In the following exercises, find three solutions to each linear equation.

291.

x + y = 3 x + y = 3

292.

x + y = −4 x + y = −4

293.

y = 3 x + 1 y = 3 x + 1

294.

y = − x − 1 y = − x − 1

Graphing Linear Equations

Recognize the Relation Between the Solutions of an Equation and its Graph

In each of the following exercises, an equation and its graph is shown. For each ordered pair, decide

  1. ⓐ if the ordered pair is a solution to the equation.
  2. ⓑ if the point is on the line.
295.

y=−x+4y=−x+4

The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0, 4” and “ordered pair 4, 0”.
  1. (0,4)(0,4)
  2. (−1,3)(−1,3)
  3. (2,2)(2,2)
  4. (−2,6)(−2,6)
296.

y=23x−1y=23x−1

The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0, -1” and “ordered pair 3, 1”.
  1. (0,−1)(0,−1)
  2. (3,1)(3,1)
  3. (−3,−3)(−3,−3)
  4. (6,4)(6,4)

Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

297.

y = 4 x − 3 y = 4 x − 3

298.

y = −3 x y = −3 x

299.

2 x + y = 7 2 x + y = 7

Graph Vertical and Horizontal lines

In the following exercises, graph the vertical or horizontal lines.

300.

y = −2 y = −2

301.

x = 3 x = 3

Graphing with Intercepts

Identify the Intercepts on a Graph

In the following exercises, find the x-x- and y-intercepts.y-intercepts.

302.
The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0, 4” and “ordered pair -4, 0”.
303.
The graph shows the x y-coordinate plane. The x-axis runs from -1 to 6. The y-axis runs from -4 to 2. A line passes through the points “ordered pair 5, 1” and “ordered pair 0, -3”.

Find the Intercepts from an Equation of a Line

In the following exercises, find the intercepts.

304.

x + y = 5 x + y = 5

305.

x − y = −1 x − y = −1

306.

y = 3 4 x − 12 y = 3 4 x − 12

307.

y = 3 x y = 3 x

Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

308.

− x + 3 y = 3 − x + 3 y = 3

309.

x + y = −2 x + y = −2

Choose the Most Convenient Method to Graph a Line

In the following exercises, identify the most convenient method to graph each line.

310.

x = 5 x = 5

311.

y = −3 y = −3

312.

2 x + y = 5 2 x + y = 5

313.

x − y = 2 x − y = 2

314.

y = 1 2 x + 2 y = 1 2 x + 2

315.

y = 3 4 x − 1 y = 3 4 x − 1

Understand Slope of a Line

Use Geoboards to Model Slope

In the following exercises, find the slope modeled on each geoboard.

316.
The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 1 row 4 and the point in column 4 row 2.
317.
The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 1 row 5 and the point in column 4 row 1.
318.
The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 1 row 3 and the point in column 4 row 4.
319.
The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 1 row 2 and the point in column 4 row 4.

In the following exercises, model each slope. Draw a picture to show your results.

320.

1 3 1 3

321.

3 2 3 2

322.

− 2 3 − 2 3

323.

− 1 2 − 1 2

Find the Slope of a Line from its Graph

In the following exercises, find the slope of each line shown.

324.
The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0, 0” and “ordered pair 2, -6”.
325.
The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair 0, 4” and “ordered pair -4, 0”.
326.
The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair -4, -4” and “ordered pair 5, -1”.
327.
The graph shows the x y-coordinate plane. The axes run from -7 to 7. A line passes through the points “ordered pair -3, 6” and “ordered pair 5, 2”.

Find the Slope of Horizontal and Vertical Lines

In the following exercises, find the slope of each line.

328.

y = 2 y = 2

329.

x = 5 x = 5

330.

x = −3 x = −3

331.

y = −1 y = −1

Use the Slope Formula to find the Slope of a Line between Two Points

In the following exercises, use the slope formula to find the slope of the line between each pair of points.

332.

( 2 , 1 ) , ( 4 , 5 ) ( 2 , 1 ) , ( 4 , 5 )

333.

( −1 , −1 ) , ( 0 , −5 ) ( −1 , −1 ) , ( 0 , −5 )

334.

( 3 , 5 ) , ( 4 , −1 ) ( 3 , 5 ) , ( 4 , −1 )

335.

( −5 , −2 ) , ( 3 , 2 ) ( −5 , −2 ) , ( 3 , 2 )

Graph a Line Given a Point and the Slope

In the following exercises, graph the line given a point and the slope.

336.

( 2 , −2 ) ; m = 5 2 ( 2 , −2 ) ; m = 5 2

337.

( −3 , 4 ) ; m = − 1 3 ( −3 , 4 ) ; m = − 1 3

Solve Slope Applications

In the following exercise, solve the slope application.

338.

A roof has rise 1010 feet and run 1515 feet. What is its slope?


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