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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 Whole Numbers

Identify Counting Numbers and Whole Numbers

In the following exercises, determine which of the following are (a) counting numbers (b) whole numbers.

453.

0,2,990,2,99

454.

0,3,250,3,25

455.

0,4,900,4,90

456.

0,1,750,1,75

Model Whole Numbers

In the following exercises, model each number using base-10base-10 blocks and then show its value using place value notation.

457.

258

458.

104

Identify the Place Value of a Digit

In the following exercises, find the place value of the given digits.

459.

472,981472,981

  1. 88
  2. 44
  3. 11
  4. 77
  5. 22
460.

12,403,29512,403,295

  1. 44
  2. 00
  3. 11
  4. 99
  5. 33

Use Place Value to Name Whole Numbers

In the following exercises, name each number in words.

461.

5,2805,280

462.

204,614204,614

463.

5,012,5825,012,582

464.

31,640,97631,640,976

Use Place Value to Write Whole Numbers

In the following exercises, write as a whole number using digits.

465.

six hundred two

466.

fifteen thousand, two hundred fifty-three

467.

three hundred forty million, nine hundred twelve thousand, sixty-one

468.

two billion, four hundred ninety-two million, seven hundred eleven thousand, two

Round Whole Numbers

In the following exercises, round to the nearest ten.

469.

412412

470.

648648

471.

3,5563,556

472.

2,7342,734

In the following exercises, round to the nearest hundred.

473.

38,97538,975

474.

26,84926,849

475.

81,48681,486

476.

75,99275,992

Add Whole Numbers

Use Addition Notation

In the following exercises, translate the following from math notation to words.

477.

4+34+3

478.

25+1825+18

479.

571+629571+629

480.

10,085+3,49210,085+3,492

Model Addition of Whole Numbers

In the following exercises, model the addition.

481.

6+76+7

482.

38+1438+14

Add Whole Numbers

In the following exercises, fill in the missing values in each chart.

483.
A table with 11 rows down and 11 rows across. The first row and first column are headers and include the numbers 0 through 9 both across and down, with a plus sign in the first cell. The numbers across in the second row down appear as follows: 0,0,  1, null, 3, 4, null, 6, 7, null, 9. The numbers across in the third row down appear as follows: 1, 1, 2, 3, 4, null, null, 7, 8, 9, null. The numbers in the fourth row down appear across as follows: 2, null, 3,4,5,6,7,8, null, 10, 11. The numbers across in the fifth row down appear as follows: 3, 3, null, 5, null, 7, 8, null, 10, null 12. The numbers across in the sixth row down appear as follows: 4, 4, 5, null, null, 8, 9,null, null, 12, null. The numbers across in the seventh row down appear as follows: 5, 5, null, 7, 8, null null, 11, null, 13, null. The numbers across in the eighth row down appear as follows:6, 6, 7, 8, null, 10, null, null, 13, null, 15. The numbers across in the ninth row down appear as follows: null, null, 9, null, null, 12, 13, null, 15, 16. The numbers across in the tenth row down appear as follows: 8,8,9,null, 11, null, null, 14, null, eleventh row down appear as follows: 9, 9, 10, 11, null, 13, 14, null, null, 17, null.
484.
This table is 5 rows and 8 columns. The top row is a header row and includes the numbers 3 through 9, one number to each cell. The rows down include 6, 7, 8, and 9. There is a plus sign in the first cell. All cells are null.

In the following exercises, add.

485.

0+190+19 19+019+0

486.

0+4800+480 480+0480+0

487.

7+67+6 6+76+7

488.

23+1823+18 18+2318+23

489.

44+3544+35

490.

63+2963+29

491.

96+5896+58

492.

375+591375+591

493.

7,281+12,5467,281+12,546

494.

5,280+16,324+9,7315,280+16,324+9,731

Translate Word Phrases to Math Notation

In the following exercises, translate each phrase into math notation and then simplify.

495.

the sum of 3030 and 1212

496.

1111 increased by 88

497.

2525 more than 3939

498.

total of 1515 and 5050

Add Whole Numbers in Applications

In the following exercises, solve.

499.

Shopping for an interview Nathan bought a new shirt, tie, and slacks to wear to a job interview. The shirt cost $24,$24, the tie cost $14,$14, and the slacks cost $38.$38. What was Nathan’s total cost?

500.

Running Jackson ran 44 miles on Monday, 1212 miles on Tuesday, 11 mile on Wednesday, 88 miles on Thursday, and 55 miles on Friday. What was the total number of miles Jackson ran?

In the following exercises, find the perimeter of each figure.

501.
An image of a rectangle that is 8 feet tall and 15 feet wide.
502.
An image of a right triangle that has a base of 12 centimeters, height of 5 centimeters, and diagonal hypotenuse of 13 centimeters.
Subtract Whole Numbers

Use Subtraction Notation

In the following exercises, translate the following from math notation to words.

503.

145145

504.

40154015

505.

351249351249

506.

5,7242,9185,7242,918

Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.

507.

184184

508.

41294129

Subtract Whole Numbers

In the following exercises, subtract and then check by adding.

509.

8585

510.

127127

511.

239239

512.

46214621

513.

82598259

514.

1108711087

515.

539217539217

516.

415296415296

517.

1,0206401,020640

518.

8,3553,9478,3553,947

519.

10,0001510,00015

520.

54,92535,64754,92535,647

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.

521.

the difference of nineteen and thirteen

522.

subtract sixty-five from one hundred

523.

seventy-four decreased by eight

524.

twenty-three less than forty-one

Subtract Whole Numbers in Applications

In the following exercises, solve.

525.

Temperature The high temperature in Peoria one day was 8686 degrees Fahrenheit and the low temperature was 2828 degrees Fahrenheit. What was the difference between the high and low temperatures?

526.

Savings Lynn wants to go on a cruise that costs $2,485.$2,485. She has $948$948 in her vacation savings account. How much more does she need to save in order to pay for the cruise?

Multiply Whole Numbers

Use Multiplication Notation

In the following exercises, translate from math notation to words.

527.

8×58×5

528.

6·146·14

529.

(10)(95)(10)(95)

530.

54(72)54(72)

Model Multiplication of Whole Numbers

In the following exercises, model the multiplication.

531.

2×42×4

532.

3×83×8

Multiply Whole Numbers

In the following exercises, fill in the missing values in each chart.

533.
A table with 10 rows down and 10 rows across. The first row and first column are headers and include the numbers 0 through 9 both across and down, with a plus sign in the first cell. The numbers across in the second row down appear as follows: 0, 0, 0, 0, 0, 0, null, 0, null, 0,0. The numbers across in the third row down appear as follows: 1, 0, 1, 2, null, 4, 5, 6, 7, null, 9.  The numbers across in the fourth row down appear as follows: 2, 0, null, 4, null, 8, 10, null, 14, 16, null. The numbers across in the fifth row down appear as follows: 3, null, 3, null, 9, null, null, 18, null, 24, null. The numbers across in the sixth row down appear as follows: 4, 0, 4, 0, 12, null, null, 24, null, null, 36.  The numbers across in the seventh row down appear as follows:5, 0, 5, 10, null, 20, null, 30, 35, 40, 45. The numbers across in the eighth row down appear as follows: 6, null, null, 12, 18, null, null, 36, 42, null, 54.  The numbers across in the ninth row down appear as follows: 7, 0, 7, null, 21, null, 35, null, null, 56, 63. The numbers in the tenth row down appear as follows: 8, 0, 8, 16, null, 32, null, 48, null, 64, null. The numbers in the eleventh row down appear across as follows: 9, null, null, 18, 27, 36, null, null, 63, 72, null.
534.
An image of a table with 8 columns and 5 rows. The cells in the first row and first column are shaded darker than the other cells. The first row has the values “x; 3; 4; 5; 6; 7; 8; 9”. The first column has the values “x;  6; 7; 8; 9”. All other cells are null.

In the following exercises, multiply.

535.

0·140·14

536.

(256)0(256)0

537.

1·991·99

538.

(4,789)1(4,789)1

539.

7·47·4 4·74·7

540.

(25)(6)(25)(6)

541.

9,261×39,261×3

542.

48·7648·76

543.

64·1064·10

544.

1,000(22)1,000(22)

545.

162×493162×493

546.

(601)(943)(601)(943)

547.

3,624×5173,624×517

548.

10,538·2210,538·22

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.

549.

the product of 1515 and 2828

550.

ninety-four times thirty-three

551.

twice 575575

552.

ten times two hundred sixty-four

Multiply Whole Numbers in Applications

In the following exercises, solve.

553.

Gardening Geniece bought 88 packs of marigolds to plant in her yard. Each pack has 66 flowers. How many marigolds did Geniece buy?

554.

Cooking Ratika is making rice for a dinner party. The number of cups of water is twice the number of cups of rice. If Ratika plans to use 44 cups of rice, how many cups of water does she need?

555.

Multiplex There are twelve theaters at the multiplex and each theater has 150150 seats. What is the total number of seats at the multiplex?

556.

Roofing Lewis needs to put new shingles on his roof. The roof is a rectangle, 3030 feet by 2424 feet. What is the area of the roof?

Divide Whole Numbers

Use Division Notation

Translate from math notation to words.

557.

54÷954÷9

558.

42/742/7

559.

728728

560.

648648

Model Division of Whole Numbers

In the following exercises, model.

561.

8÷28÷2

562.

312312

Divide Whole Numbers

In the following exercises, divide. Then check by multiplying.

563.

14÷214÷2

564.

328328

565.

52÷452÷4

566.

26262626

567.

971971

568.

0÷520÷52

569.

100÷0100÷0

570.

35553555

571.

3828÷63828÷6

572.

311,519311,519

573.

750525750525

574.

5,166÷425,166÷42

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.

575.

the quotient of 6464 and 1616

576.

the quotient of 572572 and 5252

Divide Whole Numbers in Applications

In the following exercises, solve.

577.

Ribbon One spool of ribbon is 2727 feet. Lizbeth uses 33 feet of ribbon for each gift basket that she wraps. How many gift baskets can Lizbeth wrap from one spool of ribbon?

578.

Juice One carton of fruit juice is 128128 ounces. How many 44 ounce cups can Shayla fill from one carton of juice?

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