3.8.1: Review Exercises

Review Exercises

Introduction to Integers

Locate Positive and Negative Numbers on the Number Line

In the following exercises, locate and label the integer on the number line.

353.

$5$

354.

$\mathrm{-5}$

355.

$\mathrm{-3}$

356.

$3$

357.

$\mathrm{-8}$

358.

$\mathrm{-7}$

Order Positive and Negative Numbers

In the following exercises, order each of the following pairs of numbers, using $<$ or $\text{>.}$

359.

$4\text{\_\_}8$

360.

$\mathrm{-6}\text{\_\_}3$

361.

$\mathrm{-5}\text{\_\_}\mathrm{-10}$

362.

$\mathrm{-9}\text{\_\_}\mathrm{-4}$

363.

$2\text{\_\_}\mathrm{-7}$

364.

$\mathrm{-3}\text{\_\_}1$

Find Opposites

In the following exercises, find the opposite of each number.

365.

$6$

366.

$\mathrm{-2}$

367.

$\mathrm{-4}$

368.

$3$

In the following exercises, simplify.

369.

1. ⓐ$-(8)$
2. ⓑ$-(\mathrm{-8})$

370.

1. ⓐ$-(9)$
2. ⓑ$-(\mathrm{-9})$

In the following exercises, evaluate.

371.

$-x,\text{when}$

1. ⓐ$x=$
2. ⓑ$x=\mathrm{-32}$

372.

$-n,\text{when}$

1. ⓐ$n=20$
2. ⓐ$n=\mathrm{-20}$

Simplify Absolute Values

In the following exercises, simplify.

373.

$\left|\mathrm{-21}\right|$

374.

$\left|\mathrm{-42}\right|$

375.

$\left|36\right|$

376.

$-\left|15\right|$

377.

$\left|0\right|$

378.

$-\left|\mathrm{-75}\right|$

In the following exercises, evaluate.

379.

$\left|x\right|\text{when}x=\mathrm{-14}$

380.

$-\left|r\right|\text{when}r=27$

381.

$-\left|-y\right|\text{when}y=33$

382.

$\left|\mathit{\text{−n}}\right|\text{when}n=\mathrm{-4}$

In the following exercises, fill in $\text{<},\text{>},\text{or}=$ for each of the following pairs of numbers.

383.

$-\left|\mathrm{-4}\right|\text{\_\_}4$

384.

$\mathrm{-2}\text{\_\_}\left|\mathrm{-2}\right|$

385.

$-\left|\mathrm{-6}\right|\text{\_\_}\mathrm{-6}$

386.

$-\left|\mathrm{-9}\right|\text{\_\_}\left|\mathrm{-9}\right|$

In the following exercises, simplify.

387.

$-(\mathrm{-55})\text{and}-\left|\mathrm{-55}\right|$

388.

$-(\mathrm{-48})\text{and}-\left|\mathrm{-48}\right|$

389.

$\left|12-5\right|$

390.

$\left|9+7\right|$

391.

$6\left|\mathrm{-9}\right|$

392.

$\left|14\mathrm{-8}\right|-\left|\mathrm{-2}\right|$

393.

$\left|9-3\right|-\left|5-12\right|$

394.

$5+4\left|15-3\right|$

Translate Phrases to Expressions with Integers

In the following exercises, translate each of the following phrases into expressions with positive or negative numbers.

395.

the opposite of $16$

396.

the opposite of $\mathrm{-8}$

397.

negative $3$

398.

$19$ minus negative $12$

399.

a temperature of $10$ below zero

400.

an elevation of $\text{85 feet}$ below sea level

Add Integers

Model Addition of Integers

In the following exercises, model the following to find the sum.

401.

$3+7$

402.

$\mathrm{-2}+6$

403.

$5+(\mathrm{-4})$

404.

$\mathrm{-3}+(\mathrm{-6})$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

405.

$14+82$

406.

$\mathrm{-33}+(\mathrm{-67})$

407.

$\mathrm{-75}+25$

408.

$54+(\mathrm{-28})$

409.

$11+(\mathrm{-15})+3$

410.

$\mathrm{-19}+(\mathrm{-42})+12$

411.

$\mathrm{-3}+6(\mathrm{-1}+5)$

412.

$10+4(\mathrm{-3}+7)$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

413.

$n+4\text{when}$

1. ⓐ$n=\mathrm{-1}$
2. ⓑ$n=\mathrm{-20}$

414.

$x+(\mathrm{-9})\text{when}$

1. ⓐ$x=3$
2. ⓑ$x=\mathrm{-3}$

415.

${(x+y)}^3\text{when}x=\mathrm{-4},y=1$

416.

${(u+v)}^2\text{when}u=\mathrm{-4},v=11$

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

417.

$\text{the sum of −8 and 2}$

418.

$\text{4 more than −12}$

419.

$\text{10 more than the sum of −5 and −6}$

420.

$\text{the sum of}3\text{and}\mathrm{-5},\text{increased by 18}$

Add Integers in Applications

In the following exercises, solve.

421.

Temperature On Monday, the high temperature in Denver was $\text{−4 degrees.}$ Tuesday’s high temperature was $\text{20 degrees}$ more. What was the high temperature on Tuesday?

422.

Credit Frida owed $\text{\$75}$ on her credit card. Then she charged $\text{\$21}$ more. What was her new balance?

Subtract Integers

Model Subtraction of Integers

In the following exercises, model the following.

423.

$6-1$

424.

$\mathrm{-4}-(\mathrm{-3})$

425.

$2-(\mathrm{-5})$

426.

$\mathrm{-1}-4$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

427.

$24-16$

428.

$19-(\mathrm{-9})$

429.

$\mathrm{-31}-7$

430.

$\mathrm{-40}-(\mathrm{-11})$

431.

$\mathrm{-52}-(\mathrm{-17})-23$

432.

$25-(\mathrm{-3}-9)$

433.

$(1-7)-(3-8)$

434.

$3^2-7^2$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

435.

$x-7\text{when}$

1. ⓐ$x=5$
2. ⓑ$x=\mathrm{-4}$

436.

$10-y\text{when}$

1. ⓐ$y=15$
2. ⓑ$y=\mathrm{-16}$

437.

$2n^2-n+5\text{when}n=\mathrm{-4}$

438.

$\mathrm{-15}-3u^2\text{when}u=\mathrm{-5}$

Translate Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

439.

the difference of $\mathrm{-12}\text{and}5$

440.

subtract $23$ from $\mathrm{-50}$

Subtract Integers in Applications

In the following exercises, solve the given applications.

441.

Temperature One morning the temperature in Bangor, Maine was $\text{18 degrees.}$ By afternoon, it had dropped $\text{20 degrees.}$ What was the afternoon temperature?

442.

Temperature On January 4, the high temperature in Laredo, Texas was $\text{78 degrees,}$ and the high in Houlton, Maine was $\mathrm{-28}\text{degrees}.$ What was the difference in temperature of Laredo and Houlton?

Multiply and Divide Integers

Multiply Integers

In the following exercises, multiply.

443.

$\mathrm{-9}\cdot 4$

444.

$5(\mathrm{-7})$

445.

$(\mathrm{-11})(\mathrm{-11})$

446.

$\mathrm{-1}\cdot 6$

Divide Integers

In the following exercises, divide.

447.

$56÷(\mathrm{-8})$

448.

$\mathrm{-120}÷(\mathrm{-6})$

449.

$\mathrm{-96}÷12$

450.

$96÷(\mathrm{-16})$

451.

$45÷(\mathrm{-1})$

452.

$\mathrm{-162}÷(\mathrm{-1})$

Simplify Expressions with Integers

In the following exercises, simplify each expression.

453.

$5(\mathrm{-9})-3(\mathrm{-12})$

454.

${(\mathrm{-2})}^5$

455.

$-3^4$

456.

$(\mathrm{-3})(4)(\mathrm{-5})(\mathrm{-6})$

457.

$42-4(6-9)$

458.

$(8-15)(9-3)$

459.

$\mathrm{-2}(\mathrm{-18})÷9$

460.

$45÷(\mathrm{-3})-12$

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

461.

$7x-3\text{when}x=\mathrm{-9}$

462.

$16-2n\text{when}n=\mathrm{-8}$

463.

$5a+8b\text{when}a=\mathrm{-2},b=\mathrm{-6}$

464.

$x^2+5x+4\text{when}x=\mathrm{-3}$

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

465.

the product of $\mathrm{-12}$ and $6$

466.

the quotient of $3$ and the sum of $\mathrm{-7}$ and $s$

Solve Equations using Integers; The Division Property of Equality

Determine Whether a Number is a Solution of an Equation

In the following exercises, determine whether each number is a solution of the given equation.

467.

$5x-10=\mathrm{-35}$

1. ⓐ$x=\mathrm{-9}$
2. ⓑ$x=\mathrm{-5}$
3. ⓒ$x=5$

468.

$8u+24=\mathrm{-32}$

1. ⓐ$u=\mathrm{-7}$
2. ⓑ$u=\mathrm{-1}$
3. ⓒ$u=7$

Using the Addition and Subtraction Properties of Equality

In the following exercises, solve.

469.

$a+14=2$

470.

$b-9=\mathrm{-15}$

471.

$c+(\mathrm{-10})=\mathrm{-17}$

472.

$d-(\mathrm{-6})=\mathrm{-26}$

Model the Division Property of Equality

In the following exercises, write the equation modeled by the envelopes and counters. Then solve it.

473.

474.

Solve Equations Using the Division Property of Equality

In the following exercises, solve each equation using the division property of equality and check the solution.

475.

$8p=72$

476.

$\mathrm{-12}q=48$

477.

$\mathrm{-16}r=\mathrm{-64}$

478.

$\mathrm{-5}s=\mathrm{-100}$

Translate to an Equation and Solve.

In the following exercises, translate and solve.

479.

$\text{The product of −6 and}y\text{is}\mathrm{-42}$

480.

$\text{The difference of}z\text{and −13 is −18.}$

481.

Four more than $m$ is $\mathrm{-48}.$

482.

$\text{The product of −21 and}n\text{is 63.}$

Everyday Math

483.

Describe how you have used two topics from this chapter in your life outside of your math class during the past month.