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

Review Exercises

Prealgebra 2eReview Exercises

Review Exercises

Use the Language of Algebra

Use Variables and Algebraic Symbols

In the following exercises, translate from algebra to English.

317.

3 8 3 8

318.

12 x 12 x

319.

24 ÷ 6 24 ÷ 6

320.

9 + 2 a 9 + 2 a

321.

50 47 50 47

322.

3 y < 15 3 y < 15

323.

n + 4 = 13 n + 4 = 13

324.

32 k = 7 32 k = 7

Identify Expressions and Equations

In the following exercises, determine if each is an expression or equation.

325.

5 + u = 84 5 + u = 84

326.

36 6 s 36 6 s

327.

4 y 11 4 y 11

328.

10 x = 120 10 x = 120

Simplify Expressions with Exponents

In the following exercises, write in exponential form.

329.

2 2 2 2 2 2

330.

a a a a a a a a a a

331.

x x x x x x x x x x x x

332.

10 10 10 10 10 10

In the following exercises, write in expanded form.

333.

8 4 8 4

334.

3 6 3 6

335.

y 5 y 5

336.

n 4 n 4

In the following exercises, simplify each expression.

337.

3 4 3 4

338.

10 6 10 6

339.

2 7 2 7

340.

4 3 4 3

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

341.

10 + 2 5 10 + 2 5

342.

( 10 + 2 ) 5 ( 10 + 2 ) 5

343.

( 30 + 6 ) ÷ 2 ( 30 + 6 ) ÷ 2

344.

30 + 6 ÷ 2 30 + 6 ÷ 2

345.

7 2 + 5 2 7 2 + 5 2

346.

( 7 + 5 ) 2 ( 7 + 5 ) 2

347.

4 + 3 ( 10 1 ) 4 + 3 ( 10 1 )

348.

( 4 + 3 ) ( 10 1 ) ( 4 + 3 ) ( 10 1 )

Evaluate, Simplify, and Translate Expressions

Evaluate an Expression

In the following exercises, evaluate the following expressions.

349.

9 x 5 when x = 7 9 x 5 when x = 7

350.

y 3 when y = 5 y 3 when y = 5

351.

3 a 4 b when a = 10 , b = 1 3 a 4 b when a = 10 , b = 1

352.

b h when b = 7 , h = 8 b h when b = 7 , h = 8

Identify Terms, Coefficients and Like Terms

In the following exercises, identify the terms in each expression.

353.

12 n 2 + 3 n + 1 12 n 2 + 3 n + 1

354.

4 x 3 + 11 x + 3 4 x 3 + 11 x + 3

In the following exercises, identify the coefficient of each term.

355.

6 y 6 y

356.

13 x 2 13 x 2

In the following exercises, identify the like terms.

357.

5 x 2 , 3 , 5 y 2 , 3 x , x , 4 5 x 2 , 3 , 5 y 2 , 3 x , x , 4

358.

8 , 8 r 2 , 8 r , 3 r , r 2 , 3 s 8 , 8 r 2 , 8 r , 3 r , r 2 , 3 s

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the following expressions by combining like terms.

359.

15 a + 9 a 15 a + 9 a

360.

12 y + 3 y + y 12 y + 3 y + y

361.

4 x + 7 x + 3 x 4 x + 7 x + 3 x

362.

6 + 5 c + 3 6 + 5 c + 3

363.

8 n + 2 + 4 n + 9 8 n + 2 + 4 n + 9

364.

19 p + 5 + 4 p 1 + 3 p 19 p + 5 + 4 p 1 + 3 p

365.

7 y 2 + 2 y + 11 + 3 y 2 8 7 y 2 + 2 y + 11 + 3 y 2 8

366.

13 x 2 x + 6 + 5 x 2 + 9 x 13 x 2 x + 6 + 5 x 2 + 9 x

Translate English Phrases to Algebraic Expressions

In the following exercises, translate the following phrases into algebraic expressions.

367.

the difference of xx and 66

368.

the sum of 1010 and twice aa

369.

the product of 3n3n and 99

370.

the quotient of ss and 44

371.

55 times the sum of yy and 11

372.

1010 less than the product of 55 and zz

373.

Jack bought a sandwich and a coffee. The cost of the sandwich was $3$3 more than the cost of the coffee. Call the cost of the coffee c.c. Write an expression for the cost of the sandwich.

374.

The number of poetry books on Brianna’s bookshelf is 55 less than twice the number of novels. Call the number of novels n.n. Write an expression for the number of poetry books.

Solve Equations Using the Subtraction and Addition Properties of Equality

Determine Whether a Number is a Solution of an Equation

In the following exercises, determine whether each number is a solution to the equation.

375.

y+16=40y+16=40

  1. 2424
  2. 5656
376.

d6=21d6=21

  1. 1515
  2. 2727
377.

4n+12=364n+12=36

  1. 66
  2. 1212
378.

20q10=7020q10=70

  1. 33
  2. 44
379.

15x5=10x+4515x5=10x+45

  1. 22
  2. 1010
380.

22p6=18p+8622p6=18p+86

  1. 44
  2. 2323

Model the Subtraction Property of Equality

In the following exercises, write the equation modeled by the envelopes and counters and then solve the equation using the subtraction property of equality.

381.
This image is divided into two parts: the first part shows an envelope and 3 blue counters and the next to it, the second part shows five counters.
382.
This image is divided into two parts: the first part shows an envelope and 4 blue counters and next to it, the second part shows 9 counters.

Solve Equations using the Subtraction Property of Equality

In the following exercises, solve each equation using the subtraction property of equality.

383.

c + 8 = 14 c + 8 = 14

384.

v + 8 = 150 v + 8 = 150

385.

23 = x + 12 23 = x + 12

386.

376 = n + 265 376 = n + 265

Solve Equations using the Addition Property of Equality

In the following exercises, solve each equation using the addition property of equality.

387.

y 7 = 16 y 7 = 16

388.

k 42 = 113 k 42 = 113

389.

19 = p 15 19 = p 15

390.

501 = u 399 501 = u 399

Translate English Sentences to Algebraic Equations

In the following exercises, translate each English sentence into an algebraic equation.

391.

The sum of 77 and 3333 is equal to 40.40.

392.

The difference of 1515 and 33 is equal to 12.12.

393.

The product of 44 and 88 is equal to 32.32.

394.

The quotient of 6363 and 99 is equal to 7.7.

395.

Twice the difference of nn and 33 gives 76.76.

396.

The sum of five times yy and 44 is 89.89.

Translate to an Equation and Solve

In the following exercises, translate each English sentence into an algebraic equation and then solve it.

397.

Eight more than xx is equal to 35.35.

398.

2121 less than aa is 11.11.

399.

The difference of qq and 1818 is 57.57.

400.

The sum of mm and 125125 is 240.240.

Mixed Practice

In the following exercises, solve each equation.

401.

h 15 = 27 h 15 = 27

402.

k 11 = 34 k 11 = 34

403.

z + 52 = 85 z + 52 = 85

404.

x + 93 = 114 x + 93 = 114

405.

27 = q + 19 27 = q + 19

406.

38 = p + 19 38 = p + 19

407.

31 = v 25 31 = v 25

408.

38 = u 16 38 = u 16

Find Multiples and Factors

Identify Multiples of Numbers

In the following exercises, list all the multiples less than 5050 for each of the following.

409.

3 3

410.

2 2

411.

8 8

412.

10 10

Use Common Divisibility Tests

In the following exercises, using the divisibility tests, determine whether each number is divisible by 2,by3,by5,by6,and by10.2,by3,by5,by6,and by10.

413.

96 96

414.

250 250

415.

420 420

416.

625 625

Find All the Factors of a Number

In the following exercises, find all the factors of each number.

417.

30 30

418.

70 70

419.

180 180

420.

378 378

Identify Prime and Composite Numbers

In the following exercises, identify each number as prime or composite.

421.

19 19

422.

51 51

423.

121 121

424.

219 219

Prime Factorization and the Least Common Multiple

Find the Prime Factorization of a Composite Number

In the following exercises, find the prime factorization of each number.

425.

84 84

426.

165 165

427.

350 350

428.

572 572

Find the Least Common Multiple of Two Numbers

In the following exercises, find the least common multiple of each pair of numbers.

429.

9 , 15 9 , 15

430.

12 , 20 12 , 20

431.

25 , 35 25 , 35

432.

18 , 40 18 , 40

Everyday Math

433.

Describe how you have used two topics from The Language of Algebra 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.