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Prealgebra 2e

Review Exercises

Prealgebra 2eReview Exercises

Review Exercises

Rational and Irrational Numbers

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

302.

6 6

303.

−5 −5

304.

2.9 2.9

305.

1.8 1.8

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 , 1.95 0.75319… , 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.... , 8 9 , 16 , 9 −9 , 0 , 0.361.... , 8 9 , 16 , 9

311.

−5 , 2 1 4 , 4 , 0. 25 , 13 5 , 4 −5 , 2 1 4 , 4 , 0. 25 , 13 5 , 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.

3 n = ____ 3 n = ____

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

319.

1 2 ( 22 y ) = _____ 1 2 ( 22 y ) = _____

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.

6 y + 37 + ( −6 y ) 6 y + 37 + ( −6 y )

325.

1 4 + 11 15 + ( 1 4 ) 1 4 + 11 15 + ( 1 4 )

326.

14 11 · 35 9 · 11 14 14 11 · 35 9 · 11 14

327.

−18 · 15 · 2 9 −18 · 15 · 2 9

328.

( 7 12 + 4 5 ) + 1 5 ( 7 12 + 4 5 ) + 1 5

329.

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

330.

−12 ( 4 m ) −12 ( 4 m )

331.

30 ( 5 6 q ) 30 ( 5 6 q )

332.

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

333.

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

Distributive Property

In the following exercises, simplify using the distributive property.

334.

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

335.

9 ( u 4 ) 9 ( u 4 )

336.

−3 ( 6 m 1 ) −3 ( 6 m 1 )

337.

−8 ( −7 a 12 ) −8 ( −7 a 12 )

338.

1 3 ( 15 n 6 ) 1 3 ( 15 n 6 )

339.

( y + 10 ) · p ( y + 10 ) · p

340.

( a 4 ) ( 6 a + 9 ) ( a 4 ) ( 6 a + 9 )

341.

4 ( x + 3 ) 8 ( x 7 ) 4 ( x + 3 ) 8 ( x 7 )

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 = 29 29 + 0 = 29

348.

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

349.

9 · 1 + ( 3 ) = 9 + ( 3 ) 9 · 1 + ( 3 ) = 9 + ( 3 )

In the following exercises, find the additive inverse.

350.

−32 −32

351.

19.4 19.4

352.

3 5 3 5

353.

7 15 7 15

In the following exercises, find the multiplicative inverse.

354.

9 2 9 2

355.

−5 −5

356.

1 10 1 10

357.

4 9 4 9

In the following exercises, simplify.

358.

83 · 0 83 · 0

359.

0 9 0 9

360.

5 0 5 0

361.

0 ÷ 2 3 0 ÷ 2 3

362.

43 + 39 + ( −43 ) 43 + 39 + ( −43 )

363.

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

364.

5 13 · 57 · 13 5 5 13 · 57 · 13 5

365.

1 6 · 17 · 12 1 6 · 17 · 12

366.

2 3 · 28 · 3 7 2 3 · 28 · 3 7

367.

9 ( 6 x 11 ) + 15 9 ( 6 x 11 ) + 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 °F 95 °F

399.

23 °F 23 °F

400.

20 °F 20 °F

401.

64 °F 64 °F

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

402.

30 °C 30 °C

403.

−5 °C −5 °C

404.

−12 °C −12 °C

405.

24 °C 24 °C

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