7.8.1: Review Exercises

Review Exercises

Rational and Irrational Numbers

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

302.

$6$

303.

$\mathrm{-5}$

304.

$2.9$

305.

$1.8$

In the following exercises, determine which of the numbers is rational.

306.

$0.42,0.\stackrel{\text{–}}{3},\mathrm{2.56813\dots }$

307.

$\text{0.75319…},0.\stackrel{\text{—}}{16},1.95$

In the following exercises, identify whether each given number is rational or irrational.

308.

ⓐ$\sqrt{49}$ ⓑ$\sqrt{55}$

309.

ⓐ $\sqrt{72}$ ⓑ $\sqrt{64}$

In the following exercises, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.

310.

$\mathrm{-9},0,\text{0.361....},\frac{8}{9},\sqrt{16},9$

311.

$\mathrm{-5},-2\frac{1}{4},-\sqrt{4},0.\stackrel{\text{—}}{25},\frac{13}{5},4$

Commutative and Associative Properties

In the following exercises, use the commutative property to rewrite the given expression.

312.

$6+4=\_\_\_\_$

313.

$\mathrm{-14}·5=\_\_\_\_$

314.

$3n=\_\_\_\_$

315.

$a+8=\_\_\_\_$

In the following exercises, use the associative property to rewrite the given expression.

316.

$(13·5)·2=\_\_\_\_\_$

317.

$(22+7)+3=\_\_\_\_\_$

318.

$(4+9x)+x=\_\_\_\_\_$

319.

$\frac{1}{2}(22y)=\_\_\_\_\_$

In the following exercises, evaluate each expression for the given value.

320.

If $y=\frac{11}{12},$ evaluate:
ⓐ $y+0.7+(-y)$
ⓑ $y+(-y)+0.7$

321.

If $z=-\frac{5}{3},$ evaluate:
ⓐ $z+5.39+(-z)$
ⓑ $z+(-z)+5.39$

322.

If $k=65,$ evaluate:
ⓐ $\frac{4}{9}\left(\frac{9}{4}k\right)$
ⓑ $(\frac{4}{9}·\frac{9}{4})k$

323.

If $m=\mathrm{-13},$ evaluate:
ⓐ $-\frac{2}{5}\left(\frac{5}{2}m\right)$
ⓑ $(-\frac{2}{5}·\frac{5}{2})m$

In the following exercises, simplify using the commutative and associative properties.

324.

$6y+37+(\mathrm{-6}y)$

325.

$\frac{1}{4}+\frac{11}{15}+\left(-\frac{1}{4}\right)$

326.

$\frac{14}{11}·\frac{35}{9}·\frac{11}{14}$

327.

$\mathrm{-18}·15·\frac{2}{9}$

328.

$\left(\frac{7}{12}+\frac{4}{5}\right)+\frac{1}{5}$

329.

$\left(3.98d+0.75d\right)+1.25d$

330.

$\mathrm{-12}\left(4m\right)$

331.

$30\left(\frac{5}{6}q\right)$

332.

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

333.

$52m+(\mathrm{-20}n)+(\mathrm{-18}m)+(\mathrm{-5}n)$

Distributive Property

In the following exercises, simplify using the distributive property.

334.

$7(x+9)$

335.

$9(u-4)$

336.

$\mathrm{-3}(6m-1)$

337.

$\mathrm{-8}(\mathrm{-7}a-12)$

338.

$\frac{1}{3}(15n-6)$

339.

$(y+10)·p$

340.

$(a-4)-(6a+9)$

341.

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

In the following exercises, evaluate using the distributive property.

342.

If $u=2,$ evaluate
ⓐ $3(8u+9)\text{and}$
ⓑ $3·8u+3·9$ to show that $3(8u+9)=3·8u+3·9$

343.

If $n=\frac{7}{8},$ evaluate
ⓐ$8(n+\frac{1}{4})$ and
ⓑ$8·n+8·\frac{1}{4}$ to show that $8(n+\frac{1}{4})=8·n+8·\frac{1}{4}$

344.

If $d=14,$ evaluate
ⓐ $\mathrm{-100}\left(0.1d+0.35\right)$ and
ⓑ$\mathrm{-100}·(0.1d)+\left(\mathrm{-100}\right)\left(0.35\right)$ to show that $\mathrm{-100}\left(0.1d+0.35\right)=\mathrm{-100}·(0.1d)+\left(\mathrm{-100}\right)\left(0.35\right)$

345.

If $y=\mathrm{-18},$ evaluate
ⓐ$-\left(y-18\right)$ and
ⓑ$-y+18$ to show that $-\left(y-18\right)=-y+18$

Properties of Identities, Inverses, and Zero

In the following exercises, identify whether each example is using the identity property of addition or multiplication.

346.

$\mathrm{-35}(1)=\mathrm{-35}$

347.

$29+0=29$

348.

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

349.

$9·1+\left(-3\right)=9+\left(-3\right)$

In the following exercises, find the additive inverse.

350.

$\mathrm{-32}$

351.

$19.4$

352.

$\frac{3}{5}$

353.

$-\frac{7}{15}$

In the following exercises, find the multiplicative inverse.

354.

$\frac{9}{2}$

355.

$\mathrm{-5}$

356.

$\frac{1}{10}$

357.

$-\frac{4}{9}$

In the following exercises, simplify.

358.

$83·0$

359.

$\frac{0}{9}$

360.

$\frac{5}{0}$

361.

$0÷\frac{2}{3}$

362.

$43+39+(\mathrm{-43})$

363.

$(n+6.75)+0.25$

364.

$\frac{5}{13}·57·\frac{13}{5}$

365.

$\frac{1}{6}·17·12$

366.

$\frac{2}{3}·28·\frac{3}{7}$

367.

$9(6x-11)+15$

Systems of Measurement

In the following exercises, convert between U.S. units. Round to the nearest tenth.

368.

A floral arbor is $7$ feet tall. Convert the height to inches.

369.

A picture frame is $42$ inches wide. Convert the width to feet.

370.

Kelly is $5$ feet $4$ inches tall. Convert her height to inches.

371.

A playground is $45$ feet wide. Convert the width to yards.

372.

The height of Mount Shasta is $\mathrm{14,179}$ feet. Convert the height to miles.

373.

Shamu weighs $4.5$ tons. Convert the weight to pounds.

374.

The play lasted $1\frac{3}{4}$ hours. Convert the time to minutes.

375.

How many tablespoons are in a quart?

376.

Naomi’s baby weighed $5$ pounds $14$ ounces at birth. Convert the weight to ounces.

377.

Trinh needs $30$ 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 $4$ lobsters. The weights of the lobsters were $1$ pound $9$ ounces, $1$ pound $12$ ounces, $4$ pounds $2$ ounces, and $2$ pounds $15$ 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 $50,25,83,45,32,60,\text{and}135$ minutes. How much time, in hours and minutes, did Pedro spend reading?

380.

Fouad is $6$ feet $2$ inches tall. If he stands on a rung of a ladder $8$ feet $10$ inches high, how high off the ground is the top of Fouad’s head?

381.

Dalila wants to make pillow covers. Each cover takes $30$ inches of fabric. How many yards and inches of fabric does she need for $4$ pillow covers?

In the following exercises, convert between metric units.

382.

Donna is $1.7$ meters tall. Convert her height to centimeters.

383.

Mount Everest is $\mathrm{8,850}$ meters tall. Convert the height to kilometers.

384.

One cup of yogurt contains $488$ milligrams of calcium. Convert this to grams.

385.

One cup of yogurt contains $13$ grams of protein. Convert this to milligrams.

386.

Sergio weighed $2.9$ kilograms at birth. Convert this to grams.

387.

A bottle of water contained $650$ milliliters. Convert this to liters.

In the following exercises, solve.

388.

Minh is $2$ meters tall. His daughter is $88$ centimeters tall. How much taller, in meters, is Minh than his daughter?

389.

Selma had a $\text{1-liter}$ bottle of water. If she drank $145$ milliliters, how much water, in milliliters, was left in the bottle?

390.

One serving of cranberry juice contains $30$ grams of sugar. How many kilograms of sugar are in $30$ servings of cranberry juice?

391.

One ounce of tofu provides $2$ grams of protein. How many milligrams of protein are provided by $5$ ounces of tofu?

In the following exercises, convert between U.S. and metric units. Round to the nearest tenth.

392.

Majid is $69$ inches tall. Convert his height to centimeters.

393.

A college basketball court is $84$ feet long. Convert this length to meters.

394.

Caroline walked $2.5$ kilometers. Convert this length to miles.

395.

Lucas weighs $78$ kilograms. Convert his weight to pounds.

396.

Steve’s car holds $55$ liters of gas. Convert this to gallons.

397.

A box of books weighs $25$ pounds. Convert this weight to kilograms.

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

398.

$95\text{°F}$

399.

$23\text{°F}$

400.

$20\text{°F}$

401.

$64\text{°F}$

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

402.

$30\text{°C}$

403.

$\mathrm{-5}\text{°C}$

404.

$\mathrm{-12}\text{°C}$

405.

$24\text{°C}$