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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

Rational and Irrational Numbers

In the following exercises, write as the ratio of two integers.

302.

66

303.

−5−5

304.

2.92.9

305.

1.81.8

In the following exercises, determine which of the numbers is rational.

306.

0.42,0.3,2.56813…0.42,0.3,2.56813…

307.

0.75319…,0.16,1.950.75319…,0.16,1.95

In the following exercises, identify whether each given number is rational or irrational.

308.

4949 5555

309.

7272 6464

In the following exercises, list the whole numbers, integers, rational numbers, irrational numbers, real numbers for each set of numbers.

310.

−9,0,0.361....,89,16,9−9,0,0.361....,89,16,9

311.

−5,214,4,0.25,135,4−5,214,4,0.25,135,4

Commutative and Associative Properties

In the following exercises, use the commutative property to rewrite the given expression.

312.

6+4=____6+4=____

313.

−14·5=____−14·5=____

314.

3n=____3n=____

315.

a+8=____a+8=____

In the following exercises, use the associative property to rewrite the given expression.

316.

(13·5)·2=_____(13·5)·2=_____

317.

(22+7)+3=_____(22+7)+3=_____

318.

(4+9x)+x=_____(4+9x)+x=_____

319.

12(22y)=_____12(22y)=_____

In the following exercises, evaluate each expression for the given value.

320.

If y=1112,y=1112, evaluate:
y+0.7+(y)y+0.7+(y)
y+(y)+0.7y+(y)+0.7

321.

If z=53,z=53, evaluate:
z+5.39+(z)z+5.39+(z)
z+(z)+5.39z+(z)+5.39

322.

If k=65,k=65, evaluate:
49(94k)49(94k)
(49·94)k(49·94)k

323.

If m=−13,m=−13, evaluate:
25(52m)25(52m)
(25·52)m(25·52)m

In the following exercises, simplify using the commutative and associative properties.

324.

6y+37+(−6y)6y+37+(−6y)

325.

14+1115+(14)14+1115+(14)

326.

1411·359·11141411·359·1114

327.

−18·15·29−18·15·29

328.

(712+45)+15(712+45)+15

329.

(3.98d+0.75d)+1.25d(3.98d+0.75d)+1.25d

330.

−12(4m)−12(4m)

331.

30(56q)30(56q)

332.

11x+8y+16x+15y11x+8y+16x+15y

333.

52m+(−20n)+(−18m)+(−5n)52m+(−20n)+(−18m)+(−5n)

Distributive Property

In the following exercises, simplify using the distributive property.

334.

7(x+9)7(x+9)

335.

9(u4)9(u4)

336.

−3(6m1)−3(6m1)

337.

−8(−7a12)−8(−7a12)

338.

13(15n6)13(15n6)

339.

(y+10)·p(y+10)·p

340.

(a4)(6a+9)(a4)(6a+9)

341.

4(x+3)8(x7)4(x+3)8(x7)

In the following exercises, evaluate using the distributive property.

342.

If u=2,u=2, evaluate
3(8u+9)and3(8u+9)and
3·8u+3·93·8u+3·9 to show that 3(8u+9)=3·8u+3·93(8u+9)=3·8u+3·9

343.

If n=78,n=78, evaluate
8(n+14)8(n+14) and
8·n+8·148·n+8·14 to show that 8(n+14)=8·n+8·148(n+14)=8·n+8·14

344.

If d=14,d=14, evaluate
−100(0.1d+0.35)−100(0.1d+0.35) and
−100·(0.1d)+(−100)(0.35)−100·(0.1d)+(−100)(0.35) to show that −100(0.1d+0.35)=−100·(0.1d)+(−100)(0.35)−100(0.1d+0.35)=−100·(0.1d)+(−100)(0.35)

345.

If y=−18,y=−18, evaluate
(y18)(y18) and
y+18y+18 to show that (y18)=y+18(y18)=y+18

Properties of Identities, Inverses, and Zero

In the following exercises, identify whether each example is using the identity property of addition or multiplication.

346.

−35(1)=−35−35(1)=−35

347.

29+0=2929+0=29

348.

(6x+0)+4x=6x+4x(6x+0)+4x=6x+4x

349.

9·1+(3)=9+(3)9·1+(3)=9+(3)

In the following exercises, find the additive inverse.

350.

−32−32

351.

19.419.4

352.

3535

353.

715715

In the following exercises, find the multiplicative inverse.

354.

9292

355.

−5−5

356.

110110

357.

4949

In the following exercises, simplify.

358.

83·083·0

359.

0909

360.

5050

361.

0÷230÷23

362.

43+39+(−43)43+39+(−43)

363.

(n+6.75)+0.25(n+6.75)+0.25

364.

513·57·135513·57·135

365.

16·17·1216·17·12

366.

23·28·3723·28·37

367.

9(6x11)+159(6x11)+15

Systems of Measurement

In the following exercises, convert between U.S. units. Round to the nearest tenth.

368.

A floral arbor is 77 feet tall. Convert the height to inches.

369.

A picture frame is 4242 inches wide. Convert the width to feet.

370.

Kelly is 55 feet 44 inches tall. Convert her height to inches.

371.

A playground is 4545 feet wide. Convert the width to yards.

372.

The height of Mount Shasta is 14,17914,179 feet. Convert the height to miles.

373.

Shamu weighs 4.54.5 tons. Convert the weight to pounds.

374.

The play lasted 134134 hours. Convert the time to minutes.

375.

How many tablespoons are in a quart?

376.

Naomi’s baby weighed 55 pounds 1414 ounces at birth. Convert the weight to ounces.

377.

Trinh needs 3030 cups of paint for her class art project. Convert the volume to gallons.

In the following exercises, solve, and state your answer in mixed units.

378.

John caught 44 lobsters. The weights of the lobsters were 11 pound 99 ounces, 11 pound 1212 ounces, 44 pounds 22 ounces, and 22 pounds 1515 ounces. What was the total weight of the lobsters?

379.

Every day last week, Pedro recorded the amount of time he spent reading. He read for 50,25,83,45,32,60,and13550,25,83,45,32,60,and135 minutes. How much time, in hours and minutes, did Pedro spend reading?

380.

Fouad is 66 feet 22 inches tall. If he stands on a rung of a ladder 88 feet 1010 inches high, how high off the ground is the top of Fouad’s head?

381.

Dalila wants to make pillow covers. Each cover takes 3030 inches of fabric. How many yards and inches of fabric does she need for 44 pillow covers?

In the following exercises, convert between metric units.

382.

Donna is 1.71.7 meters tall. Convert her height to centimeters.

383.

Mount Everest is 8,8508,850 meters tall. Convert the height to kilometers.

384.

One cup of yogurt contains 488488 milligrams of calcium. Convert this to grams.

385.

One cup of yogurt contains 1313 grams of protein. Convert this to milligrams.

386.

Sergio weighed 2.92.9 kilograms at birth. Convert this to grams.

387.

A bottle of water contained 650650 milliliters. Convert this to liters.

In the following exercises, solve.

388.

Minh is 22 meters tall. His daughter is 8888 centimeters tall. How much taller, in meters, is Minh than his daughter?

389.

Selma had a 1-liter1-liter bottle of water. If she drank 145145 milliliters, how much water, in milliliters, was left in the bottle?

390.

One serving of cranberry juice contains 3030 grams of sugar. How many kilograms of sugar are in 3030 servings of cranberry juice?

391.

One ounce of tofu provides 22 grams of protein. How many milligrams of protein are provided by 55 ounces of tofu?

In the following exercises, convert between U.S. and metric units. Round to the nearest tenth.

392.

Majid is 6969 inches tall. Convert his height to centimeters.

393.

A college basketball court is 8484 feet long. Convert this length to meters.

394.

Caroline walked 2.52.5 kilometers. Convert this length to miles.

395.

Lucas weighs 7878 kilograms. Convert his weight to pounds.

396.

Steve’s car holds 5555 liters of gas. Convert this to gallons.

397.

A box of books weighs 2525 pounds. Convert this weight to kilograms.

In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.

398.

95°F95°F

399.

23°F23°F

400.

20°F20°F

401.

64°F64°F

In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

402.

30°C30°C

403.

−5°C−5°C

404.

−12°C−12°C

405.

24°C24°C

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