Prealgebra 2e

# Review Exercises

Prealgebra 2eReview 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
$−(y−18)−(y−18)$ and
$−y+18−y+18$ to show that $−(y−18)=−y+18−(y−18)=−y+18$

## 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.

$24 °C 24 °C$