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Prealgebra 2e

Review Exercises

Prealgebra 2eReview Exercises
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  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

Use a Problem Solving Strategy

Approach Word Problems with a Positive Attitude

In the following exercises, solve.

361.

How has your attitude towards solving word problems changed as a result of working through this chapter? Explain.

362.

Did the Problem Solving Strategy help you solve word problems in this chapter? Explain.

Use a Problem Solving Strategy for Word Problems

In the following exercises, solve using the problem-solving strategy for word problems. Remember to write a complete sentence to answer each question.

363.

Three-fourths of the people at a concert are children. If there are 8787 children, what is the total number of people at the concert?

364.

There are 99 saxophone players in the band. The number of saxophone players is one less than twice the number of tuba players. Find the number of tuba players.

365.

Reza was very sick and lost 15%15% of his original weight. He lost 2727 pounds. What was his original weight?

366.

Dolores bought a crib on sale for $350.$350. The sale price was 40%40% of the original price. What was the original price of the crib?

Solve Number Problems

In the following exercises, solve each number word problem.

367.

The sum of a number and three is forty-one. Find the number.

368.

Twice the difference of a number and ten is fifty-four. Find the number.

369.

One number is nine less than another. Their sum is twenty-seven. Find the numbers.

370.

The sum of two consecutive integers is 135.135. Find the numbers.

Solve Money Applications

Solve Coin Word Problems

In the following exercises, solve each coin word problem.

371.

Francie has $4.35$4.35 in dimes and quarters. The number of dimes is 55 more than the number of quarters. How many of each coin does she have?

372.

Scott has $0.39$0.39 in pennies and nickels. The number of pennies is 88 times the number of nickels. How many of each coin does he have?

373.

Paulette has $140$140 in $5$5 and $10$10 bills. The number of $10$10 bills is one less than twice the number of $5$5 bills. How many of each does she have?

374.

Lenny has $3.69$3.69 in pennies, dimes, and quarters. The number of pennies is 33 more than the number of dimes. The number of quarters is twice the number of dimes. How many of each coin does he have?

Solve Ticket and Stamp Word Problems

In the following exercises, solve each ticket or stamp word problem.

375.

A church luncheon made $842.$842. Adult tickets cost $10$10 each and children’s tickets cost $6$6 each. The number of children was 1212 more than twice the number of adults. How many of each ticket were sold?

376.

Tickets for a basketball game cost $2$2 for students and $5$5 for adults. The number of students was 33 less than 1010 times the number of adults. The total amount of money from ticket sales was $619.$619. How many of each ticket were sold?

377.

Ana spent $4.06$4.06 buying stamps. The number of $0.41$0.41 stamps she bought was 55 more than the number of $0.26$0.26 stamps. How many of each did she buy?

378.

Yumi spent $34.15$34.15 buying stamps. The number of $0.56$0.56 stamps she bought was 1010 less than 44 times the number of $0.41$0.41 stamps. How many of each did she buy?

Use Properties of Angles, Triangles, and the Pythagorean Theorem

Use Properties of Angles

In the following exercises, solve using properties of angles.

379.

What is the supplement of a 48°48° angle?

380.

What is the complement of a 61°61° angle?

381.

Two angles are complementary. The smaller angle is 24°24° less than the larger angle. Find the measures of both angles.

382.

Two angles are supplementary. The larger angle is 45°45° more than the smaller angle. Find the measures of both angles.

Use Properties of Triangles

In the following exercises, solve using properties of triangles.

383.

The measures of two angles of a triangle are 2222 and 8585 degrees. Find the measure of the third angle.

384.

One angle of a right triangle measures 41.541.5 degrees. What is the measure of the other small angle?

385.

One angle of a triangle is 30°30° more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.

386.

One angle of a triangle is twice the measure of the smallest angle. The third angle is 60°60° more than the measure of the smallest angle. Find the measures of all three angles.

In the following exercises, ΔABCΔABC is similar to ΔXYZ.ΔXYZ. Find the length of the indicated side.

Two triangles are shown. Triangle ABC is on the left. The side across from A is labeled 21, across from B is b, and across from C is 11.2. Triangle XYZ is on the right. The side across from X is labeled x, across from Y is 10, and across from Z is 8.
387.

side xx

388.

side bb

Use the Pythagorean Theorem

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

389.
A right triangle is shown. The base is labeled 10, the height is labeled 24.
390.
A right triangle is shown. The base is labeled 6, the height is labeled 8.
391.
A right triangle is shown. The height is labeled 15, the hypotenuse is labeled 17.
392.
A right triangle is shown. The height is labeled 15, the hypotenuse is labeled 25.
393.
A right triangle is shown. The height is labeled 7, the base is labeled 4.
394.
A right triangle is shown. The height is labeled 11, the base is labeled 10.

In the following exercises, solve. Approximate to the nearest tenth, if necessary.

395.

Sergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is 88 feet tall and Sergio has 1010 feet of wire. How far from the base of the antenna can he attach the wire?

An image of a house is shown. A 10-foot wire is going from the roof of the house to the ground. The wire hits the house at a height of 8 feet.
396.

Seong is building shelving in his garage. The shelves are 3636 inches wide and 1515 inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?

A rectangular shelf is shown, with a diagonal drawn in from the lower left corner to the upper right corner. The side is labeled 15 inches, the top is labeled 36 inches.
Use Properties of Rectangles, Triangles, and Trapezoids

Understand Linear, Square, Cubic Measure

In the following exercises, would you measure each item using linear, square, or cubic measure?

397.

amount of sand in a sandbag

398.

height of a tree

399.

size of a patio

400.

length of a highway

In the following exercises, find

  1. the perimeter
  2. the area of each figure
401.
Three squares are shown, in a sideways L shape.
402.
Five squares are shown, in a T-shape. There are three squares across the top and three squares down.

Use Properties of Rectangles

In the following exercises, find the perimeter area of each rectangle

403.

The length of a rectangle is 4242 meters and the width is 2828 meters.

404.

The length of a rectangle is 3636 feet and the width is 1919 feet.

405.

A sidewalk in front of Kathy’s house is in the shape of a rectangle 44 feet wide by 4545 feet long.

406.

A rectangular room is 1616 feet wide by 1212 feet long.

In the following exercises, solve.

407.

Find the length of a rectangle with perimeter of 220220 centimeters and width of 8585 centimeters.

408.

Find the width of a rectangle with perimeter 3939 and length 11.11.

409.

The area of a rectangle is 23562356 square meters. The length is 3838 meters. What is the width?

410.

The width of a rectangle is 4545 centimeters. The area is 27002700 square centimeters. What is the length?

411.

The length of a rectangle is 1212 centimeters more than the width. The perimeter is 7474 centimeters. Find the length and the width.

412.

The width of a rectangle is 33 more than twice the length. The perimeter is 9696 inches. Find the length and the width.

Use Properties of Triangles

In the following exercises, solve using the properties of triangles.

413.

Find the area of a triangle with base 1818 inches and height 1515 inches.

414.

Find the area of a triangle with base 3333 centimeters and height 2121 centimeters.

415.

A triangular road sign has base 3030 inches and height 4040 inches. What is its area?

416.

If a triangular courtyard has sides 99 feet and 1212 feet and the perimeter is 3232 feet, how long is the third side?

417.

A tile in the shape of an isosceles triangle has a base of 66 inches. If the perimeter is 2020 inches, find the length of each of the other sides.

418.

Find the length of each side of an equilateral triangle with perimeter of 8181 yards.

419.

The perimeter of a triangle is 5959 feet. One side of the triangle is 33 feet longer than the shortest side. The third side is 55 feet longer than the shortest side. Find the length of each side.

420.

One side of a triangle is three times the smallest side. The third side is 99 feet more than the shortest side. The perimeter is 3939 feet. Find the lengths of all three sides.

Use Properties of Trapezoids

In the following exercises, solve using the properties of trapezoids.

421.

The height of a trapezoid is 88 feet and the bases are 1111 and 1414 feet. What is the area?

422.

The height of a trapezoid is 55 yards and the bases are 77 and 1010 yards. What is the area?

423.

Find the area of the trapezoid with height 2525 meters and bases 32.532.5 and 21.521.5 meters.

424.

A flag is shaped like a trapezoid with height 6262 centimeters and the bases are 91.591.5 and 78.178.1 centimeters. What is the area of the flag?

Solve Geometry Applications: Circles and Irregular Figures

Use Properties of Circles

In the following exercises, solve using the properties of circles. Round answers to the nearest hundredth.

425.

A circular mosaic has radius 33 meters. Find the

  1. circumference
  2. area of the mosaic
426.

A circular fountain has radius 88 feet. Find the

  1. circumference
  2. area of the fountain
427.

Find the diameter of a circle with circumference 150.72150.72 inches.

428.

Find the radius of a circle with circumference 345.4345.4 centimeters

Find the Area of Irregular Figures

In the following exercises, find the area of each shaded region.

429.
A geometric shape is shown, formed by two rectangles. The top is labeled 8. The width of the top rectangle is labeled 3. The right side of the figure is labeled 5. The width of the bottom rectangle is labeled 3.
430.
A geometric shape is shown. It is a U-shape. The base is labeled 5, the height 6. The horizontal and vertical lines at the top are labeled 2.
431.
A geometric shape is shown. It is formed by two triangles. The shared base of the two triangles is labeled 20. The height of each triangle is labeled 15.
432.
A geometric shape is shown. It is a trapezoid with a triangle attached to the top on the right side.  The height of the trapezoid is labeled 8, the bottom base is labeled 12, and the top is labeled 9. The height of the triangle is labeled 8.
433.
A geometric shape is shown. It is a rectangle with a semi-circle attached to the top. The base of the rectangle, also the diameter of the semi-circle, is labeled 10. The height of the rectangle is labeled 16.
434.
A geometric shape is shown. It is a triangle with a semicircle attached. The base of the triangle, also the diameter of the semi-circle, is labeled 5. The height of the triangle is also labeled 5.
Solve Geometry Applications: Volume and Surface Area

Find Volume and Surface Area of Rectangular Solids

In the following exercises, find the

  1. volume
  2. surface area of the rectangular solid
435.

a rectangular solid with length 1414 centimeters, width 4.54.5 centimeters, and height 1010 centimeters

436.

a cube with sides that are 33 feet long

437.

a cube of tofu with sides 2.52.5 inches

438.

a rectangular carton with length 3232 inches, width 1818 inches, and height 1010 inches

Find Volume and Surface Area of Spheres

In the following exercises, find the

  1. volume
  2. surface area of the sphere.
439.

a sphere with radius 44 yards

440.

a sphere with radius 1212 meters

441.

a baseball with radius 1.451.45 inches

442.

a soccer ball with radius 2222 centimeters

Find Volume and Surface Area of Cylinders

In the following exercises, find the

  1. volume
  2. surface area of the cylinder
443.

a cylinder with radius 22 yards and height 66 yards

444.

a cylinder with diameter 1818 inches and height 4040 inches

445.

a juice can with diameter 88 centimeters and height 1515 centimeters

446.

a cylindrical pylon with diameter 0.80.8 feet and height 2.52.5 feet

Find Volume of Cones

In the following exercises, find the volume of the cone.

447.

a cone with height 55 meters and radius 11 meter

448.

a cone with height 2424 feet and radius 88 feet

449.

a cone-shaped water cup with diameter 2.62.6 inches and height 2.62.6 inches

450.

a cone-shaped pile of gravel with diameter 66 yards and height 55 yards

Solve a Formula for a Specific Variable

Use the Distance, Rate, and Time Formula

In the following exercises, solve using the formula for distance, rate, and time.

451.

A plane flew 44 hours at 380380 miles per hour. What distance was covered?

452.

Gus rode his bike for 112112 hours at 88 miles per hour. How far did he ride?

453.

Jack is driving from Bangor to Portland at a rate of 6868 miles per hour. The distance is 107107 miles. To the nearest tenth of an hour, how long will the trip take?

454.

Jasmine took the bus from Pittsburgh to Philadelphia. The distance is 305305 miles and the trip took 55 hours. What was the speed of the bus?

Solve a Formula for a Specific Variable

In the following exercises, use the formula d=rt.d=rt.

455.

Solve for t:t:

  1. when d=403d=403 and r=65r=65
  2. in general
456.

Solve for r:r:

  1. when d=750d=750 and t=15t=15
  2. in general

In the following exercises, use the formula A=12bh.A=12bh.

457.

Solve for b:b:

  1. when A=416A=416 and h=32h=32
  2. in general
458.

Solve for h:h:

  1. when A=48A=48 and b=8b=8
  2. in general

In the following exercises, use the formula I=Prt.I=Prt.

459.

Solve for the principal, P,P, for:

  1. I=$720I=$720, r=4%r=4%, t=3yearst=3years
  2. in general
460.

Solve for the time, tt for:

  1. I=$3630I=$3630, P=$11,000P=$11,000, r=5.5%r=5.5%
  2. in general

In the following exercises, solve.

461.

Solve the formula 6x+5y=206x+5y=20 for y:y:

  1. when x=0x=0
  2. in general
462.

Solve the formula 2x+y=152x+y=15 for y:y:

  1. when x=−5x=−5
  2. in general
463.

Solve a+b=90a+b=90 for a.a.

464.

Solve 180=a+b+c180=a+b+c for a.a.

465.

Solve the formula 4x+y=174x+y=17 for y.y.

466.

Solve the formula 3x+y=−63x+y=−6 for y.y.

467.

Solve the formula P=2L+2WP=2L+2W for W.W.

468.

Solve the formula V=LWHV=LWH for H.H.

469.

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

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