Prealgebra

# Review Exercises

PrealgebraReview Exercises

### Review Exercises

##### Rational and Irrational Numbers

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

302.

$66$

303.

$−5−5$

304.

$2.92.9$

305.

$1.81.8$

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.

$0.75319…,0.16—,1.950.75319…,0.16—,1.95$

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.

$−9,0,0.361....,89,16,9−9,0,0.361....,89,16,9$

311.

$−5,−214,−4,0.25—,135,4−5,−214,−4,0.25—,135,4$

##### 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.

$3n=____3n=____$

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.

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

319.

$12(22y)=_____12(22y)=_____$

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.

$6y+37+(−6y)6y+37+(−6y)$

325.

$14+1115+(−14)14+1115+(−14)$

326.

$1411·359·14111411·359·1411$

327.

$−18·15·29−18·15·29$

328.

$(712+45)+15(712+45)+15$

329.

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

330.

$−12(4m)−12(4m)$

331.

$30(56q)30(56q)$

332.

$11x+8y+16x+15y11x+8y+16x+15y$

333.

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

##### 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.

$−3(6m−1)−3(6m−1)$

337.

$−8(−7a−12)−8(−7a−12)$

338.

$13(15n−6)13(15n−6)$

339.

$(y+10)·p(y+10)·p$

340.

$(a−4)−(6a+9)(a−4)−(6a+9)$

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
$3(8u+9)and 3(8u+9)and$
$3·8u+3·93·8u+3·9$ 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.

$29+0=2929+0=29$

348.

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

349.

$9·1+(−3)=9+(−3)9·1+(−3)=9+(−3)$

In the following exercises, find the additive inverse.

350.

$−32−32$

351.

$19.419.4$

352.

$3535$

353.

$−715−715$

In the following exercises, find the multiplicative inverse.

354.

$9292$

355.

$−5−5$

356.

$110110$

357.

$−49−49$

In the following exercises, simplify.

358.

$83·083·0$

359.

$0909$

360.

$5050$

361.

$0÷230÷23$

362.

$43+39+(−43)43+39+(−43)$

363.

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

364.

$513·57·135513·57·135$

365.

$16·17·1216·17·12$

366.

$23·28·3723·28·37$

367.

$9(6x−11)+159(6x−11)+15$

##### 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.

$95°F95°F$

399.

$23°F23°F$

400.

$20°F20°F$

401.

$64°F64°F$

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

402.

$30°C30°C$

403.

$−5°C−5°C$

404.

$−12°C−12°C$

405.

$24°C24°C$

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