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All Textbook Solutions for Intermediate Algebra
Why do you need a common denominator to add or subtract fractions? Explain.How do you find the LCD of 2 fractions?Explain how you find the reciprocal of a fraction.Explain how you find the reciprocal of a negative number.Round 6.582 to the nearest (a) hundredth (b) tenth (c) whole number.Round 15.2175 to the nearest (a) thousandth (b) hundredth (c) tenth.Add or subtract: (a) 4.811.69 (b) 9.5810 .Add or subtract: (a) 5.12318.47 (b) 37.4250 .Multiply: 4.5(6.107) .Multiply: 10.79(8.12) .Multiply 2.58 by (a) 10 (b) 100 (c) 1000.Multiply 14.2 by (a) 10 (b) 100 (c) 1000.Divide: 23.492(0.04) .Divide: 4.11(0.12) .Write: (a) 0.234 as a fraction (b) 78 as a decimal.Write: (a) 0.024 as a fraction (b) 38 as a decimal.Convert each: (a) percent to a decimal: 9%, 87%, and 3.9%. (b) decimal to a percent: 0.17, 1.75, and 0.0825.Convert each: (a) percent to a decimal: 3%, 91%, and 8.3%. (b) decimal to a percent: 0.41, 2.25, and 0.0925.Simplify: (a) 36 (b) 169 (c) 225 .Simplify: (a) 16 (b) 196 (c) 100 .Given the numbers 3,2,0.3,95,4,49 , list the (a) whole numbers (b) integers (c) rational numbers (d) irrational numbers (e) real numbers.Given numbers 25,38,1,6,121, 2.041975..., list the (a) whole numbers (b) integers (c) rational numbers (d) irrational numbers (e) real numbers.Locate and label the following on a number line: 1,13,65,74,92,5,83 .Locate and label the following on a number line: 2,23,75,74,72,3,73 .Locate on the number line: (a) 0.6 (b) 0.25 .Locate on the number line: (a) 0.9 (b) 0.75 .In the following exercises, round each number to the nearest (a) hundredth (b) tenth (c) whole number. 239. 5.781In the following exercises, round each number to the nearest (a) hundredth (b) tenth (c) whole number. 240. 1.638In the following exercises, round each number to the nearest (a) hundredth (b) tenth (c) whole number. 241. 0.299In the following exercises, round each number to the nearest (a) hundredth (b) tenth (c) whole number. 242. 0.697In the following exercises, round each number to the nearest (a) hundredth (b) tenth (c) whole number. 243. 63.479In the following exercises, round each number to the nearest (a) hundredth (b) tenth (c) whole number. 244. 84.281In the following exercises, add or subtract. 245. 16.5324.38In the following exercises, add or subtract. 246. 19.4732.58In the following exercises, add or subtract. 247. 38.69+31.47In the following exercises, add or subtract. 248. 29.83+19.76In the following exercises, add or subtract. 249. 72.5100In the following exercises, add or subtract. 250. 86.2100In the following exercises, add or subtract. 251. 91.75(10.462)In the following exercises, add or subtract. 252. 94.69(12.678)In the following exercises, add or subtract. 253. 55.013.7In the following exercises, add or subtract. 254. 59.084.6In the following exercises, add or subtract. 255. 2.517.4In the following exercises, add or subtract. 256. 3.846.1In the following exercises, multiply. 257. 94.69(12.678)In the following exercises, multiply. 258. (8.5)(1.69)In the following exercises, multiply. 259. (5.18)(65.23)In the following exercises, multiply. 260. (9.16)(68.34)In the following exercises, multiply. 261. (0.06)(21.75)In the following exercises, multiply. 262. (0.08)(52.45)In the following exercises, multiply. 263. (9.24)(10)In the following exercises, multiply. 264. (6.531)(10)In the following exercises, multiply. 265. (0.025)(100)In the following exercises, multiply. 266. (0.037)(100)In the following exercises, multiply. 267. (55.2)(1000)In the following exercises, multiply. 268. (99.4)(1000)In the following exercises, divide. Round money monetary answers to the nearest cent. 269. 117.2548In the following exercises, divide. Round money monetary answers to the nearest cent. 270. 109.2436In the following exercises, divide. Round money monetary answers to the nearest cent. 271. 1.44(0.3)In the following exercises, divide. Round money monetary answers to the nearest cent. 272. 1.15(0.05)In the following exercises, divide. Round money monetary answers to the nearest cent. 273. 5.22.5In the following exercises, divide. Round money monetary answers to the nearest cent. 274. 140.35zIn the following exercises, write each decimal as a fraction. 275. 0.04In the following exercises, write each decimal as a fraction. 276. 1.464In the following exercises, write each decimal as a fraction. 277. 0.095In the following exercises, write each decimal as a fraction. 278. 0.375In the following exercises, convert each fraction to a decimal. 279. 1720In the following exercises, convert each fraction to a decimal. 280. 174In the following exercises, convert each fraction to a decimal. 281. 31025In the following exercises, convert each fraction to a decimal. 282. 1811In the following exercises, convert each percent to a decimal. 283. 71%In the following exercises, convert each percent to a decimal. 284. 150%In the following exercises, convert each percent to a decimal. 285. 39.3%In the following exercises, convert each percent to a decimal. 286. 7.8%In the following exercises, convert each decimal to a percent. 287. 1.56In the following exercises, convert each decimal to a percent. 288. 3In the following exercises, convert each decimal to a percent. 289. 0.0625In the following exercises, convert each decimal to a percent. 290. 2.254In the following exercises, simplify. 291. 64In the following exercises, simplify. 292. 169In the following exercises, simplify. 293. 144In the following exercises, simplify. 294. 4In the following exercises, simplify. 295. 100In the following exercises, simplify. 296. 121In the following exercises, list the (a) whole numbers, (b) integers, (c) rational numbers, (d) irrational numbers, (e) real numbers for each set of numbers. 297. 8,0,1.95286...,125,36,9In the following exercises, list the (a) whole numbers, (b) integers, (c) rational numbers, (d) irrational numbers, (e) real numbers for each set of numbers. 298. 9,349,9,0.409,116,7In the following exercises, list the (a) whole numbers, (b) integers, (c) rational numbers, (d) irrational numbers, (e) real numbers for each set of numbers. 299. 100,7,83,1,0.77,314In the following exercises, list the (a) whole numbers, (b) integers, (c) rational numbers, (d) irrational numbers, (e) real numbers for each set of numbers. 300. 6,52,0,0.714285,215,14In the following exercises, locate the numbers on a number line. 301. 310,72,116,4In the following exercises, locate the numbers on a number line. 302. 710,52,138,3In the following exercises, locate the numbers on a number line. 303. 34,34,123,123,52,52In the following exercises, locate the numbers on a number line. 304. 25,25,134,134,83,83In the following exercises, locate the numbers on a number line. 305. (a) 0.8 (b) 1.25In the following exercises, locate the numbers on a number line. 306. (a) -0.9 (b) 2.75In the following exercises, locate the numbers on a number line. 307. (a) 1.6 (b) 3.25In the following exercises, locate the numbers on a number line. 308. (a) 3.1 (b) 3.65How does knowing about U.S. money help you learn about decimals?When the Szetos sold their home, the selling price was 500% of what they had paid for the house 30 years ago. Explain what 500% means in this context.In your own words, explain the difference between a rational number and an irrational number.Explain how the sets of numbers (counting, whole, integer, rational, irrationals, reals) are related to each other.Simplify: 23r+14s+9r+15s .Simplify: 37m+21n+4m15n .Simplify: (715+58)+38 .Simplify: (29+712)+512 .Simplify: 27a+(48a)+27a .Simplify: 39x+(92x)+(39x) .Simplify: 916549169 .Simplify: 6171125176 .Simplify: (a) 0m+7 , where m7, (b) 186c0 ,where 186c0 .Simplify: (a) 0d4 where d4 (b) 154q0 , where 154q0 .Simplify: 4(x+2) .Simplify: 6(x+7) .Simplify: 6(56y+12) .Simplify: 12(13n+34) .Simplify: 100(0.7+0.15p) .Simplify: 100(0.04+0.35d) .Simplify: 5(23a) .Simplify: 7(815y) .Simplify: (z11) .Simplify: (x4) .Simplify: 93(x+2) .Simplify: 7x5(x+4) .Simplify: 6(x9)(x+12) .Simplify: 8(x1)(x+5) .In the following exercises, simplify. 313. 43m+(12n)+(16m)+(9n)In the following exercises, simplify. 314. 22p+17q+(35p)+(27q)In the following exercises, simplify. 315. 38g+112h+78g+512hIn the following exercises, simplify. 316. 56a+310b+16a+910bIn the following exercises, simplify. 317. 6.8p+9.14q+(4.37p)+(0.88q)In the following exercises, simplify. 318. 9.6m+7.22n+(2.19m)+(0.65n)In the following exercises, simplify. 319. 24738In the following exercises, simplify. 320. 361149In the following exercises, simplify. 321. (56+815)+715In the following exercises, simplify. 322. (1112+49)+59In the following exercises, simplify. 323. 17(0.25)(4)In the following exercises, simplify. 324. 36(0.2)(5)In the following exercises, simplify. 325. [2.48(12)](0.5)In the following exercises, simplify. 326. [9.731(4)](0.75)In the following exercises, simplify. 327. 12(56p)In the following exercises, simplify. 328. 20(35q)In the following exercises, simplify. 329. 19a+4419aIn the following exercises, simplify. 330. 27c+1627cIn the following exercises, simplify. 331. 12+78+(12)In the following exercises, simplify. 332. 25+512+(25)In the following exercises, simplify. 333. 10(0.1d)In the following exercises, simplify. 334. 100(0.01p)In the following exercises, simplify. 335. 3204911203In the following exercises, simplify. 336. 13182571813In the following exercises, simplify. 337. 0u4.99, where u4.99In the following exercises, simplify. 338. 0(y16) where x16In the following exercises, simplify. 339. 325a0, where 325a0In the following exercises, simplify. 340. 289b0, where 289b0In the following exercises, simplify. 341. (34+910m)0 where 34+910m0In the following exercises, simplify. 342. (516n37)0, where 516n370In the following exercises, simplify using the Distributive Property. 343. 8(4y+9)In the following exercises, simplify using the Distributive Property. 344. 9(3w+7)In the following exercises, simplify using the Distributive Property. 345. 6(c13)In the following exercises, simplify using the Distributive Property. 346. 7(y13)In the following exercises, simplify using the Distributive Property. 347. 14(3q+12)In the following exercises, simplify using the Distributive Property. 348. 15(4m+20)In the following exercises, simplify using the Distributive Property. 349. 9(59y13)In the following exercises, simplify using the Distributive Property. 350. 10(310x25)In the following exercises, simplify using the Distributive Property. 351. 12(14+23r)In the following exercises, simplify using the Distributive Property. 352. 12(16+34s)In the following exercises, simplify using the Distributive Property. 353. 1535(4d+10)In the following exercises, simplify using the Distributive Property. 354. 1856(15h+24)In the following exercises, simplify using the Distributive Property. 355. r(s18)In the following exercises, simplify using the Distributive Property. 356. u(v10)In the following exercises, simplify using the Distributive Property. 357. (y+4)pIn the following exercises, simplify using the Distributive Property. 358. (a+7)xIn the following exercises, simplify using the Distributive Property. 359. 7(4p+1)In the following exercises, simplify using the Distributive Property. 360. 9(9a+4)In the following exercises, simplify using the Distributive Property. 361. 3(x6)In the following exercises, simplify using the Distributive Property. 362. 4(q7)In the following exercises, simplify using the Distributive Property. 363. (3x7)In the following exercises, simplify using the Distributive Property. 364. (5p4)In the following exercises, simplify using the Distributive Property. 365. 163(y+8)In the following exercises, simplify using the Distributive Property. 366. 184(x+2)In the following exercises, simplify using the Distributive Property. 367. 411(3c2)In the following exercises, simplify using the Distributive Property. 368. 96(7n5)In the following exercises, simplify using the Distributive Property. 369. 22(a+3)In the following exercises, simplify using the Distributive Property. 370. 8(r7)In the following exercises, simplify using the Distributive Property. 371. (5m3)(m+7)In the following exercises, simplify using the Distributive Property. 372. (4y1)(y2)In the following exercises, simplify using the Distributive Property. 373. 9(8x3)(2)In the following exercises, simplify using the Distributive Property. 374. 4(6x1)(8)In the following exercises, simplify using the Distributive Property. 375. 5(2n+9)+12(n3)In the following exercises, simplify using the Distributive Property. 376. 9(5u+8)+2(u6)In the following exercises, simplify using the Distributive Property. 377. 14(c1)8(c6)In the following exercises, simplify using the Distributive Property. 378. 11(n7)5(n1)In the following exercises, simplify using the Distributive Property. 379. 6(7y+8)(30y15)In the following exercises, simplify using the Distributive Property. 380. 7(3n+9)(4n13)In your own words, state the Associative Property of addition.What is the difference between the additive inverse and the multiplicative inverse of a number?Simplify 8(x14) using the Distributive Property and explain each step.Explain how you can multiply 4($5. 97) without paper or calculator by thinking of $5. 97 as 60.03 and then using the Distributive Property.Use the divisibility tests to determine whether 180 is divisible by 2, by 3, by 5, by 6, and by 10.Find the prime factorization of 252.Find the least common multiple of 24 and 40.In the following exercises, simplify each expression. 388. 243+4(52)In the following exercises, simplify each expression. 389. 7+3[64(54)]32In the following exercises, evaluate the following expressions. 390. When x=4, (a) x3 (b) 5x (c) 2x25x+3In the following exercises, evaluate the following expressions. 391. 2x24xy3y2 when x=3,y=1In the following exercises, simplify the following expressions by combining like terms. 392. 12y+7+2y5In the following exercises, simplify the following expressions by combining like terms. 393. 14x29x+118x2+8x6In the following exercises, translate the phrases into algebraic expressions. 394. (a) the sum of 4ab2and 7a3b2 (b) the product of 6y2and 3y (c) twelve more than 5x (d) 5y less than 8y2In the following exercises, translate the phrases into algebraic expressions. 395. (a) eleven times the difference of y and two (b) the difference of eleven times y and twoIn the following exercises, translate the phrases into algebraic expressions. 396. Dushko has nickels and pennies in his pocket. The number of pennies is four less than five the number of nickels. Let n represent the number of nickels. Write an expression for the number of pennies.In the following exercise, fill in < ,> , or = for each of the following pairs of numbers. 397. (a) |7| ___ |7| (b) 8|8| (c) |13| ___ 13 (d) |12| ___ (12)In the following exercises, simplify. 398. 9|3(48)|In the following exercises, simplify. 399. 123|14(42)|In the following exercises, simplify each expression. 400. 12+(8)+7In the following exercises, simplify each expression. 401. (a) 157 (b) 15(7) (c) 157 (d) 15(7)In the following exercises, simplify each expression. 402. 11(12)+5In the following exercises, simplify each expression. 403. (a) 23(17) (b) 23+17In the following exercises, simplify each expression. 404. (711)(35)In the following exercise, multiply or divide. 405. (a) 279 (b) 120(8) (c) 4(14) (d) 1(17)In the following exercises, simplify each expression. 406. (a) (7)3 (b) 73In the following exercises, simplify each expression. 407. (711)(613)In the following exercises, simplify each expression. 408. 63(9)+(36)(4)In the following exercises, simplify each expression. 409. 63|4(12)(75)|In the following exercises, simplify each expression. 410. (2)424(135)For the following exercises, evaluate each expression. 411. (y+z)2 when y=4,z=7For the following exercises, evaluate each expression. 412. 3x22xy+4y2 when x=2,y=3In the following exercises, translate to an algebraic expression and simplify if possible. 413. the sum of 4 and 9 , increased by 23In the following exercises, translate to an algebraic expression and simplify if possible. 414. (a) the difference of 17 and 8 (b) subtract 17 from 25In the following exercise, solve. 415. Temperature On July 10, the high temperature in Phoenix, Arizona, was 109°, and the high temperature in Juneau, Alaska, was 63°. What was the difference between the temperature in Phoenix and the temperature in Juneau?In the following exercises, simplify. 416. 204228In the following exercises, simplify. 417. 270x3198y2In the following exercises, perform the indicated operation. 418. (1415)(1021)In the following exercises, perform the indicated operation. 419. 6x259y20In the following exercises, perform the indicated operation. 420. 49821In the following exercises, perform the indicated operation. 421. 518+712In the following exercises, perform the indicated operation. 422. 11361548In the following exercises, perform the indicated operation. 423. (a) 58+34 (b) 5834In the following exercises, perform the indicated operation. 424. (a) 3y1056 (b) 3y1056In the following exercises, simplify. 425. 432563+23In the following exercises, simplify. 426. 4(73)2(49)3(4+2)+7(36)In the following exercises, simplify. 427. 4342( 4 5 )2In the following exercises, evaluate. 428. 4x2y2 when x=23 and y=34In the following exercises, evaluate. 429. a+bab when a=4,b=6Round 6.738 to the nearest (a) hundredth (b) tenth (c) whole number.In the following exercises, perform the indicated operation. 431. 23.67+29.84In the following exercises, perform the indicated operation. 432.54.3100In the following exercises, perform the indicated operation. 433. 79.38(17.598)In the following exercises, perform the indicated operation. 434. (2.8)(3.97)In the following exercises, perform the indicated operation. 435. (8.43)(57.91)In the following exercises, perform the indicated operation. 436. (53.48)(10)In the following exercises, perform the indicated operation. 437. (0.563)(100)In the following exercises, perform the indicated operation. 438. 118.352.6In the following exercises, perform the indicated operation. 439.1.84(0.8)In the following exercises, write each decimal as a fraction. 440.1320In the following exercises, write each decimal as a fraction. 441. 24025In the following exercises, convert each fraction to a decimal. 442. 58In the following exercises, convert each fraction to a decimal. 443. 1411In the following exercises, convert each decimal to a percent. 444. 2.43In the following exercises, convert each decimal to a percent. 445. 0.0475In the following exercises, simplify. 446. 289In the following exercises, simplify. 447. 121In the following exercise, list the (a) whole numbers (b) integers (c) rational numbers (d) irrational numbers (e) real numbers for each set of numbers 448. 8,0,1.95286...,125,36,9In the following exercises, locate the numbers on a number line. 449. 34,34,113,123,72,52In the following exercises, locate the numbers on a number line. 450. (a) 3.2 (b) 1.35In the following exercises, simplify. 451. 58x+512y+18x+712yIn the following exercises, simplify. 452. 32958In the following exercises, simplify. 453. (1115+38)+58In the following exercises, simplify. 454. 47+815+(47)In the following exercises, simplify. 455. 13159171513In the following exercises, simplify. 456. 0x3,x3In the following exercises, simplify. 457. 5x70,5x70In the following exercises, simplify using the Distributive Property. 458. 8(a4)In the following exercises, simplify using the Distributive Property. 459. 12(23b+56)In the following exercises, simplify using the Distributive Property. 460. 1856(2x5)In the following exercises, simplify using the Distributive Property. 461.(x5)pIn the following exercises, simplify using the Distributive Property. 462. 4(y3)In the following exercises, simplify using the Distributive Property. 463. 126(x+3)In the following exercises, simplify using the Distributive Property. 464. 6(3x4)(5)In the following exercises, simplify using the Distributive Property. 465. 5(2y+3)(4y1)Find the prime factorization of 756.Combine like terms: 5n+8+2n1Evaluate when x=2 and y=3:|3x4y|6Translate to an algebraic expression and simplify: (a) eleven less than negative eight (b) the difference of 8 and 3 , increased by 5Dushko has nickels and pennies in his pocket. The number of pennies is seven less than four times the number of nickels. Let n represent the number of nickels. Write an expression for the number of pennies.Round 28.1458 to the nearest (a) hundredth (b) thousandthConvert (a) 511 to a decimal (b) 1.15 to a percentLocate 35,2.8 , and 52 on a number line.In the following exercises, simplify each expression. 474. 8+3[63(52)]42In the following exercises, simplify each expression. 475. (49)(95)In the following exercises, simplify each expression. 476. 56(8)+(27)(3)In the following exercises, simplify each expression. 477. 162|3(14)(85)|In the following exercises, simplify each expression. 478. 5+2(3)29In the following exercises, simplify each expression. 479. 180204In the following exercises, simplify each expression. 480. 718+512In the following exercises, simplify each expression. 481. 45(1225)In the following exercises, simplify each expression. 482. 939159In the following exercises, simplify each expression. 483. 4(3+2( 36))3(113( 2+3))In the following exercises, simplify each expression. 484. 51347135In the following exercises, simplify each expression. 485. 591021In the following exercises, simplify each expression. 486. 4.8+(6.7)In the following exercises, simplify each expression. 487. 34.6100In the following exercises, simplify each expression. 488. 12.04(4.2)