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All Textbook Solutions for Elementary Algebra
In the following exercises, simplify each expression. 211. 48+(16)In the following exercises, simplify each expression. 212. 34+(19)In the following exercises, simplify each expression. 213. 14+(12)+4In the following exercises, simplify each expression. 214. 17+(18)+6In the following exercises, simplify each expression. 215. 135+(110)+83In the following exercises, simplify each expression. 216. 638+27+(8)+126In the following exercises, simplify each expression. 217. 19+2(3+8)In the following exercises, simplify each expression. 218. 24+3(5+9)In the following exercises, simplify. 219. 82In the following exercises, simplify. 220. 6(4)In the following exercises, simplify. 221. 54In the following exercises, simplify. 222. 72In the following exercises, simplify. 223. 8(4)In the following exercises, simplify. 224. 7(3)In the following exercises, simplify. 225. (a) 4428 (b) 44+(28)In the following exercises, simplify. 226. (a) 3516 (b) 35+(16)In the following exercises, simplify. 227. (a) 27(18) (b) 27+18In the following exercises, simplify. 228. (a) 46(37) (b) 46+37In the following exercises, simplify each expression. 229. 15(12)In the following exercises, simplify each expression. 230. 14(11)In the following exercises, simplify each expression. 231. 4887In the following exercises, simplify each expression. 232. 4569In the following exercises, simplify each expression. 232. 1742In the following exercises, simplify each expression. 232. 1946In the following exercises, simplify each expression. 235. 103(52)In the following exercises, simplify each expression. 236. 105(68)In the following exercises, simplify each expression. 237. 45(54)In the following exercises, simplify each expression. 238. 58(67)In the following exercises, simplify each expression. 239. 837In the following exercises, simplify each expression. 240. 965In the following exercises, simplify each expression. 241. 54+7In the following exercises, simplify each expression. 242. 38+4In the following exercises, simplify each expression. 243. 14(27)+9In the following exercises, simplify each expression. 244. 64+(17)9In the following exercises, simplify each expression. 245. (27)(38)(2)In the following exercises, simplify each expression. 246. (18)(29)In the following exercises, simplify each expression. 247. (68)(29)In the following exercises, simplify each expression. 248. (45)(78)In the following exercises, simplify each expression. 249. 25[10(312)]In the following exercises, simplify each expression. 250. 32[5(1520)]In the following exercises, simplify each expression. 251. 6.34.37.2In the following exercises, simplify each expression. 252. 5.78.24.9In the following exercises, simplify each expression. 253. 5262In the following exercises, simplify each expression. 254. 6272Elevation The highest elevation in the United States is Mount McKinley, Alaska, at 20,320 feet above sea level. The lowest elevation is Death Valley. California, at 282 feet below sea level. Use Integers to write the elevation of: Mount McKinley. Death Valley.Extreme temperatures The highest recorded temperature on Earth was 58° Celsius, recorded in the Sahara Desert in 1922. The lowest recorded temperature was 90º below 0º Celsius, recorded in Antarctica in 1983. Use integers to write the: highest recorded temperature. lowest recorded temperature.State budgets In June, 2011, the state of Pennsylvania estimated it would have a budget surplus of $540 million. That same month, Texas estimated it would have a budget deficit of $27 billion. Use integers to write the budget of: Pennsylvania. Texas.College enrollments Across the United States, community college enrollment grew by 1,400,000 students from Fall 2007 to Fall 2010. In California, community college enrollment declined by 110,171 students from Fall 2009 to Fall 2010. Use integers to write the change in enrollment: in the U.S. from Fall 2007 to Fall 2010. in California from Fall 2009 to Fall 2010.Stock Market The week of September 15, 2008 was one of the most volatile weeks ever for the US stock market. The closing numbers of the Dow Jones Industrial Average each day were: What was the overall change for the week? Was it positive or negative?Stock Market During the week of June 22, 2009, the closing numbers of the Dow Jones Industrial Average each day were: What was the overall change for the week? Was it positive or negative?Give an example of a negative number from your life experience.What are the three uses of the “” sign in Explain how they differ.Explain why the sum of 8 and 2 is negative, but the sum of 8 and 2 is positive.Give an example from your life experience of adding two negative numbers.Multiply: (a) 68 (b) 4(7) (c) 9(7) (d) 512 .Multiply: (a) -8·7 (b) 6(9) (c) 7(4) (d) 313Multiply: (a) 19 (b) 1(17) .Multiply: (a) 18 (b) 1(16) .Divide: (a) 426 (b) 117(3)Divide: (a) 637 (b) 115(5) .Simplify: 8(3)+5(7)4 .Simplify: 9(3)+7(8)1 .Simplify: (a) (3)4 (b) 34 .Simplify: (a) (7)2 (b) 72 .Simplify: 174(811) .Simplify: 166(713) .Simplify: 12(9)(3)3 .Simplify: 18(4)(2)3 .Simplify: 273+(5)(6) .Simplify: 324+(2)(7)When n=8 , evaluate (a) n+2 (b) n+2When y=9 , evaluate (a) y+8 (b) y+8 .Evaluate (x+y)2 when x=15 and y=29 .Evaluate (x+y)3 when x=8 and y=10 .Evaluate: 17K when (a) k=19 and (b) k=19 .Evaluate: 5b when (a) b=14 and b=14 .Evaluate: 3x22x+6 when x=3 .Evaluate: 4x2x5 when x=2 .Translate and simplify the sum of 9 and 16, increased by 4.Translate and simplify the sum of 8 and 12, increased by 7.Translate and simplify (a) the difference of 14 and 23 subtract 21 from 17.Translate and simplify (a) the difference of 11 and 19 (b) subtract 18 from 11.Translate to an algebraic expression and simplify if possible: the product of 5 and 12.Translate to an algebraic expression and simplify if possible: the product of 8 and 13.Translate to an algebraic expression and simplify if possible: the quotient of 63 and 9.Translate to an algebraic expression and simplify if possible: the quotient of 72 and 9.The temperature in Anchorage, Alaska one morning was 15 degrees. By mid-afternoon the temperature had dropped to 30 degrees below zero. What was the difference in the morning and afternoon temperatures?The temperature in Denver was 6 degrees at lunchtime. By sunset the temperature had dropped to 15 degrees. What was the difference in the lunchtime and sunset temperatures?The Bears played poorly and had seven penalties in the game. Each penalty resulted in a loss of 15 yards. What is the number of yards lost due to penalties?Bill uses the ATM on campus because it is convenient. However, each time he uses it he is charged a $2 fee. Last month he used the ATM eight times. How much was his total fee for using the ATM?In the following exercises, multiply. 265. 48In the following exercises, multiply. 266. 39In the following exercises, multiply. 267. 9(7)In the following exercises, multiply. 268. 13(5)In the following exercises, multiply. 268. 16In the following exercises, multiply. 270. 1.3In the following exercises, multiply. 271. 1(14)In the following exercises, multiply. 272. 1(19)In the following exercises, divide. 273. 246In the following exercises, divide. 274. 35(7)In the following exercises, divide. 275. 52(4)In the following exercises, divide. 276. 84(6)In the following exercises, divide. 277. 18015In the following exercises, divide. 278. 19212In the following exercises, simplify each expression. 279. 5(6)+7(2)3In the following exercises, simplify each expression. 280. 8(4)+5(4)6In the following exercises, simplify each expression. 281. (2)6In the following exercises, simplify each expression. 282. (3)5In the following exercises, simplify each expression. 283. 42In the following exercises, simplify each expression. 284. 62In the following exercises, simplify each expression. 285. 3(5)(6)In the following exercises, simplify each expression. 286. 4(6)(3)In the following exercises, simplify each expression. 287. (811)(912)In the following exercises, simplify each expression. 288. (611)(813)In the following exercises, simplify each expression. 289. 263(27)In the following exercises, simplify each expression. 290. 232(46)In the following exercises, simplify each expression. 291. 65(5)+(28)(7)In the following exercises, simplify each expression. 292. 52(4)+(32)(8)In the following exercises, simplify each expression. 293. 92[38(2)]In the following exercises, simplify each expression. 294. 113[74(2)]In the following exercises, simplify each expression. 295. (3)224(82)In the following exercises, simplify each expression. 296. (4)232(124)In the following exercises, evaluate each expression. 297. y+(14) when (a) y=33 (b) y=30In the following exercises, evaluate each expression. 298. x+(21) when (a) x=27 (b) x=44In the following exercises, evaluate each expression. 299. (a) a+3 when a=7 (b) a+3 when a=7In the following exercises, evaluate each expression. 300. (a) d+(9) when d=8 (b) d+(9) when d=8In the following exercises, evaluate each expression. 301. m+n when m=15,n=7In the following exercises, evaluate each expression. 302. p+q when p=9 , q=17In the following exercises, evaluate each expression. 303. r+s when r=9,s=7In the following exercises, evaluate each expression. 304. t+u when t=6,u=5In the following exercises, evaluate each expression. 305. (x+y)2 when x=3,y=14In the following exercises, evaluate each expression. 306. (y+z)2when y=3,z=15In the following exercises, evaluate each expression. 307 2x+17 when (a) x=8 (b) x=8In the following exercises, evaluate each expression. 308. 5y+14 when (a) y=9 (b) y=9In the following exercises, evaluate each expression. 309. 103m when (a) m=5 (b) m=5In the following exercises, evaluate each expression. 310. 184n when (a) n=3 (b) n=3In the following exercises, evaluate each expression. 311. 2w23w+7 when w=2In the following exercises, evaluate each expression. 312. 3u24u+5 when u=3In the following exercises, evaluate each expression. 313. 9a2b8 when a=6 and b=3In the following exercises, evaluate each expression. 314. 7m4n2 when m=4 and n=9In the following exercises, translate to an algebraic expression and simplify if possible. 315. the sum of 3 and 15, increased by 7In the following exercises, translate to an algebraic expression and simplify if possible. 316. the sum of 8 and 9, increased by 23In the following exercises, translate to an algebraic expression and simplify if possible. 317. the difference of 10 and 18In the following exercises, translate to an algebraic expression and simplify if possible. 318. subtract 11 from 25In the following exercises, translate to an algebraic expression and simplify If possible. 319. the difference of 5 and 30In the following exercises, translate to an algebraic expression and simplify If possible. 320. subtract 6 from 13In the following exercises, translate to an algebraic expression and simplify if possible. 321. the product of 3 and 15In the following exercises, translate to an algebraic expression and simplify if possible. 322. the product of 4 and 16In the following exercises, translate to an algebraic expression and simplify if possible. 323. the quotient of 60 and 20In the following exercises, translate to an algebraic expression and simplify if possible. 324. the quotient of 40 and 20In the following exercises, translate to an algebraic expression and simplify if possible. 325. the quotient of 6 and the sum of a and b.In the following exercises, translate to an algebraic expression and simplify if possible. 326. the quotient of 7 and the sum of m and nIn the following exercises, translate to an algebraic expression and simplify if possible. 327. the product of —10 and the difference of p and qIn the following exercises, translate to an algebraic expression and simplify if possible. 328. the product of 13 and the difference of c and dIn the following exercises, solve. 329. Temperature On January 15, the high temperature in Anaheim, California, was 84°. That same day, the high temperature in Embarrass, Minnesota was 12°. What was the difference between the temperature in Anaheim and the temperature in Embarrass?In the following exercises, solve. 330. Temperature On January 21, the high temperature in Palm Springs, California, was 89º, and the high temperature In Whitefleld, New Hampshire was 31º. What was the difference between the temperature in Palm Springs and the temperature In Whitefleld?In the following exercises, solve. 331. Football At the first down, the Chargers had the ball on their 25 yard line. On the next three downs, they lost 6 yards, gained 10 yards, and lost 8 yards. What was the yard line at the end of the fourth down?In the following exercises, solve. 332. Football At the first down, the Steelers had the ball on their 30 yard line. On the next three downs, they gained 9 yards. lost 14 yards, and lost 2 yards. What was the yard line at the end of the fourth down?In the following exercises, solve. 333. Checking Account Mayra has $124 in her checking account. She writes a check for $152. What is the new balance In her checking account?In the following exercises, solve. 334. Checking Account Selina has $165 in her checking account. She writes a check for $207. What is the new balance in her checking account?In the following exercises, solve. 335. Checking Account Diontre has a balance of $38 in his checking account. He deposits $225 to the account. What is the new balance?In the following exercises, solve. ¶ 336. Checking Account Reymonte has a balance of $49 in his checking account. He deposits $281 to the account. What is the new balance?Stock market Javier owns 300 shares of stock in one company. On Tuesday, the stock price dropped $12 per share. What was the total effect on Javier’s portfolio?Weight loss In the first week of a diet program, eight women lost an average of 3 pounds each. What was the total weight change for the eight women?In your own words, state the rules for multiplying integers.In your own words, state the rules for dividing integers.Why is 24(2)4 ?Why is 43=(4)3 ?Find three fractions equivalent to 35 .Find three fractions equivalent to 45 .Simplify: 4254 .Simplify: 4581 .Simplify: 69120 .Simplify: 120192 .Simplify: 7x7y .Simplify: 3a3b .Multiply: 1028815 .Multiply: 920512 .Multiply: 113(9a) .Multiply: 137(14b) .Divide: 35p7 .Divide: 58q3 .Find the quotient: 727(3536)Find the quotient: 514(1528)Simplify: 2356 .Simplify: 37611 .Simplify: a8ab6 .Simplify: p2pq8Simplify: 63(5)32+3Simplify: 44(6)32+3Simplify: 8(2)+4(3)5(2)+3 .Simplify: 7(1)+9(3)5(3)2 .Translate the English phrase into an algebraic expression: the quotient of the difference of a and b, and cd.Translate the English phrase into an algebraic expression: the quotient of the sum of p and q, and rIn the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra. 343. 38In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra. 344. 58In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra. 345. 59In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra. 346. 18In the following exercises, simplify. 347. 4088In the following exercises, simplify. 348. 6399In the following exercises, simplify. 349. 10863In the following exercises, simplify. 350. 10448In the following exercises, simplify. 351. 120252In the following exercises, simplify. 352. 182294In the following exercises, simplify. 353. 3x12yIn the following exercises, simplify. 354. 4x32yIn the following exercises, simplify. 355. 14x221yIn the following exercises, simplify. 356. 24a32b2In the following exercises, multiply. 357. 34910In the following exercises, multiply. 358. 4527In the following exercises, multiply. 359. 23(38)In the following exercises, multiply. 360. 34(49)In the following exercises, multiply. 361. 59310In the following exercises, multiply. 362. 38415In the following exercises, multiply. 363. (1415)(920)In the following exercises, multiply. 364. (910)(2533)In the following exercises, multiply. 365. (6384)(4490)In the following exercises, multiply. 366. (6360)(4088)In the following exercises, multiply. 367. 4511In the following exercises, multiply. 368. 583In the following exercises, multiply. 369. 3721nIn the following exercises, multiply. 370. 5630nIn the following exercises, multiply. 371. 8(174)In the following exercises, multiply. 372. (1)(67)In the following exercises, divide. 373. 3423In the following exercises, divide. 374. 4534In the following exercises, divide. 375. 79(74)In the following exercises, divide. 376. 56(56)In the following exercises, divide. 377. 34x11In the following exercises, divide. 378. 25y9In the following exercises, divide. 379. 518(1524)In the following exercises, divide. 380. 718(1427)In the following exercises, divide. 381. 8u1512v25In the following exercises, divide. 382. 12r2518s35In the following exercises, divide. 383. 512In the following exercises, divide. 384. 314In the following exercises, divide. 385. 34(12)In the following exercises, divide. 386. 15(53)In the following exercises, simplify. 387. 8211235In the following exercises, simplify. 388. 9163340In the following exercises, simplify. 389. 452In the following exercises, simplify. 390. 5310In the following exercises, simplify. 391. m3n2In the following exercises,, simplify. 392. 38y12In the following exercises,, simplify. 393. 22+310In the following exercises,, simplify. 394. 1946In the following exercises,, simplify. 395. 482415In the following exercises,, simplify. 396. 464+4In the following exercises, simplify. 397. 6+68+4In the following exercises, divide. 398- 6+3178In the following exercises, simplify. 399. 4366In the following exercises, simplify. 400. 6692In the following exercises, simplify. 401. 42125In the following exercises, simplify. 402. 72+160In the following exercises, simplify. 403. 83+2914+3In the following exercises, simplify. 404. 964722+3In the following exercises, simplify. 405. 563445+23In the following exercises, simplify 406. 897656+92In the following exercises, simplify. 407. 523235In the following exercises, simplify. 408. 624246In the following exercises, simplify. 409. 742(85)9335In the following exercises, simplify. 410. 973(128)8766In the following exercises, simplify. 411. 9(82)3(157)6(71)3(179)In the following exercises, simplify. 412. 8(92)4(149)7(83)3(169)In the following exercises, translate each English phrase into an algebraic expression. 413. the quotient of r and the sum of s and 10.In the following exercises, translate each English phrase into an algebraic expression. 414. the quotient of A and the difference of 3 and BIn the following exercises, translate each English phrase into an algebraic expression. 415. the quotient of the difference of x and y, and 3In the following exercises, translate each English phrase into an algebraic expression. 416. the quotient of the sum of m and n, and 4q.Baking. A recipe for chocolate chip cookies calls for 34 cup brown sugar. Imelda wants to double the recipe. (a) How much brown sugar will Imelda need? Show your calculation. (b) Measuring cups usually come in sets of 14,13,12 , and 1 cup. Draw a diagram to show two different ways that Imelda could measure 1the brown sugar needed to double the cookie recipe.Baking. Nina is making 4 pans of fudge to serve after a music recital. For each pan, she needs 23 cup of condensed milk. (a) How much condensed milk will Nina need? Show your calculation. (b) Measuring cups usually come in sets of 14,13,12 , and 1 cup. Draw a diagram to show two different ways that Nina could measure the condensed milk needed for 4 pans of fudge.Portions Don purchased a bulk package of candy that weighs 5 pounds. He wants to sell the candy in little bags that hold 14 pound. How many little bags of candy can he fill from the bulk package?Portions Kristen has 34 yards of ribbon that she wants to cut into 6 equal parts to make hair ribbons for her daughter’s 6 dolls. How long will each doll’s hair be?Rafael wanted to order half a medium pizza at a restaurant. The waiter told him that a medium pizza could be cut into 6 or 8 slices. Would he prefer 3 out of 6 slices or 4 out of 8 slices? Rafael replied that since he wasn’t very hungry, he would prefer 3 out of 6 slices. Explain what is wrong with Rafael’s reasoning.Give an example from everyday life that demonstrates how 12,23is13 .Explain how you find the reciprocal of a fraction.Explain how you find the reciprocal of a negative number.Find the sum: x4+34 .Find the sum: y8+58 .Find the difference: 1928728 .Find the difference: 2732132 .Find the difference: 9x7x .Find the difference: 17a5a .Simplify: 25+(49)79 .Simplify: 59+(49)79Add: 712+1115 .Add: 1315+1720 .Subtract: 13241732 .Subtract: 2132928 .Add: y6+79 .Add: x6+715 .Simplify: (a) 3a489 (b) 3a489 .Simplify: (a) 4k516 (b) 4k516 .Simplify: ( 1 3 )223+2 .Simplify: 1+42( 1 4 )2 .Simplify: 13+123413 .Simplify: 231214+13 .Evaluate x+34 when (a) x=74 (b) x=54 .Evaluate y+12 when (a) y=23 (b) y=34 .Evaluate 12y when y=14 .Evaluate 38y when x=52 .