Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis

Review Exercises

Rational and Irrational Numbers

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

302.

$6$

303.

$−5$

304.

$2.9$

305.

$1.8$

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

306.

$0.42, 0. \overset{–}{3}, 2.56813…$

307.

$0.75319…, 0. \overset{—}{16}, 1.95$

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.

$−9, 0, 0.361...., \frac{8}{9}, \sqrt{16}, 9$

311.

$−5, - 2 \frac{1}{4}, - \sqrt{4}, 0. \overset{—}{25}, \frac{13}{5}, 4$

Commutative and Associative Properties

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

312.

$6 + 4 =____$

313.

$−14 \cdot 5 =____$

314.

$3 n =____$

315.

$a + 8 =____$

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

316.

$(13 \cdot 5) \cdot 2 =_____$

317.

$(22 + 7) + 3 =_____$

318.

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

319.

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

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:
ⓐ $\frac{4}{9} (\frac{9}{4} k)$
ⓑ $(\frac{4}{9} \cdot \frac{9}{4}) k$

323.

If $m = −13,$ evaluate:
ⓐ $- \frac{2}{5} (\frac{5}{2} m)$
ⓑ $(- \frac{2}{5} \cdot \frac{5}{2}) m$

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

324.

$6 y + 37 + (−6 y)$

325.

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

326.

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

327.

$−18 \cdot 15 \cdot \frac{2}{9}$

328.

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

329.

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

330.

$−12 (4 m)$

331.

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

332.

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

333.

$52 m + (−20 n) + (−18 m) + (−5 n)$

Distributive Property

In the following exercises, simplify using the distributive property.

334.

$7 (x + 9)$

335.

$9 (u - 4)$

336.

$−3 (6 m - 1)$

337.

$−8 (−7 a - 12)$

338.

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

339.

$(y + 10) \cdot p$

340.

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

341.

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

In the following exercises, evaluate using the distributive property.

342.

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

343.

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

344.

If $d = 14,$ evaluate
ⓐ $−100 (0.1 d + 0.35)$ and
ⓑ $−100 \cdot (0.1 d) + (−100) (0.35)$ to show that $−100 (0.1 d + 0.35) = −100 \cdot (0.1 d) + (−100) (0.35)$

345.

If $y = −18,$ evaluate
ⓐ $- (y - 18)$ and
ⓑ $- y + 18$ to show that $- (y - 18) = - y + 18$

Properties of Identities, Inverses, and Zero

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

346.

$−35 (1) = −35$

347.

$29 + 0 = 29$

348.

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

349.

$9 \cdot 1 + (- 3) = 9 + (- 3)$

In the following exercises, find the additive inverse.

350.

$−32$

351.

$19.4$

352.

$\frac{3}{5}$

353.

$- \frac{7}{15}$

In the following exercises, find the multiplicative inverse.

354.

$\frac{9}{2}$

355.

$−5$

356.

$\frac{1}{10}$

357.

$- \frac{4}{9}$

In the following exercises, simplify.

358.

$83 \cdot 0$

359.

$\frac{0}{9}$

360.

$\frac{5}{0}$

361.

$0 \div \frac{2}{3}$

362.

$43 + 39 + (−43)$

363.

$(n + 6.75) + 0.25$

364.

$\frac{5}{13} \cdot 57 \cdot \frac{13}{5}$

365.

$\frac{1}{6} \cdot 17 \cdot 12$

366.

$\frac{2}{3} \cdot 28 \cdot \frac{3}{7}$

367.

$9 (6 x - 11) + 15$

Systems of Measurement

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

368.

A floral arbor is $7$ 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 $14,179$ 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 $50, 25, 83, 45, 32, 60, and 135$ 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 $8,850$ 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 $1-liter$ 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.

$95 °F$

399.

$23 °F$

400.

$20 °F$

401.

$64 °F$

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

402.

$30 °C$

403.

$−5 °C$

404.

$−12 °C$

405.

$24 °C$