Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Prealgebra 2e

Review Exercises

Prealgebra 2eReview Exercises

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.

5 5

354.

−5 −5

355.

−3 −3

356.

3 3

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 __ 8 4 __ 8

360.

−6 __ 3 −6 __ 3

361.

−5 __ −10 −5 __ −10

362.

−9 __ −4 −9 __ −4

363.

2 __ −7 2 __ −7

364.

−3 __ 1 −3 __ 1

Find Opposites

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

365.

6 6

366.

−2 −2

367.

−4 −4

368.

3 3

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 | when x = −14 | x | when x = −14

380.

| r | when r = 27 | r | when r = 27

381.

| y | when y = 33 | y | when y = 33

382.

| −n | when n = −4 | −n | when n = −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.

| 12 5 | | 12 5 |

390.

| 9 + 7 | | 9 + 7 |

391.

6 | −9 | 6 | −9 |

392.

| 14 −8 | | −2 | | 14 −8 | | −2 |

393.

| 9 3 | | 5 12 | | 9 3 | | 5 12 |

394.

5 + 4 | 15 3 | 5 + 4 | 15 3 |

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 + 7 3 + 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 + 82 14 + 82

406.

−33 + ( −67 ) −33 + ( −67 )

407.

−75 + 25 −75 + 25

408.

54 + ( −28 ) 54 + ( −28 )

409.

11 + ( −15 ) + 3 11 + ( −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 ) 3 when x = −4 , y = 1 ( x + y ) 3 when x = −4 , y = 1

416.

( u + v ) 2 when u = −4 , v = 11 ( u + v ) 2 when u = −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 2 the sum of −8 and 2

418.

4 more than −12 4 more than −12

419.

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

420.

the sum of 3 and −5 , increased by 18 the sum of 3 and −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.

6 1 6 1

424.

−4 ( −3 ) −4 ( −3 )

425.

2 ( −5 ) 2 ( −5 )

426.

−1 4 −1 4

Simplify Expressions with Integers

In the following exercises, simplify each expression.

427.

24 16 24 16

428.

19 ( −9 ) 19 ( −9 )

429.

−31 7 −31 7

430.

−40 ( −11 ) −40 ( −11 )

431.

−52 ( −17 ) 23 −52 ( −17 ) 23

432.

25 ( −3 9 ) 25 ( −3 9 )

433.

( 1 7 ) ( 3 8 ) ( 1 7 ) ( 3 8 )

434.

3 2 7 2 3 2 7 2

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.

2 n 2 n + 5 when n = −4 2 n 2 n + 5 when n = −4

438.

−15 3 u 2 when u = −5 −15 3 u 2 when u = −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.

−9 4 −9 4

444.

5 ( −7 ) 5 ( −7 )

445.

( −11 ) ( −11 ) ( −11 ) ( −11 )

446.

−1 6 −1 6

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.

3 4 3 4

456.

( −3 ) ( 4 ) ( −5 ) ( −6 ) ( −3 ) ( 4 ) ( −5 ) ( −6 )

457.

42 4 ( 6 9 ) 42 4 ( 6 9 )

458.

( 8 15 ) ( 9 3 ) ( 8 15 ) ( 9 3 )

459.

−2 ( −18 ) ÷ 9 −2 ( −18 ) ÷ 9

460.

45 ÷ ( −3 ) 12 45 ÷ ( −3 ) 12

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

461.

7 x 3 when x = −9 7 x 3 when x = −9

462.

16 2 n when n = −8 16 2 n when n = −8

463.

5 a + 8 b when a = −2 , b = −6 5 a + 8 b when a = −2 , b = −6

464.

x 2 + 5 x + 4 when x = −3 x 2 + 5 x + 4 when x = −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 = 2 a + 14 = 2

470.

b 9 = −15 b 9 = −15

471.

c + ( −10 ) = −17 c + ( −10 ) = −17

472.

d ( −6 ) = −26 d ( −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.

8 p = 72 8 p = 72

476.

−12 q = 48 −12 q = 48

477.

−16 r = −64 −16 r = −64

478.

−5 s = −100 −5 s = −100

Translate to an Equation and Solve.

In the following exercises, translate and solve.

479.

The product of −6 and y is −42 The product of −6 and y is −42

480.

The difference of z and −13 is −18. The difference of z and −13 is −18.

481.

Four more than mm is −48.−48.

482.

The product of −21 and n is 63. The product of −21 and n is 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.

Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/prealgebra-2e/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/prealgebra-2e/pages/1-introduction
Citation information

© Jan 23, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.