We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Real Numbers

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #81 : Real Numbers

Evaluate: $\frac{7^{2} + (-7)^{3} + (-7)^{4}}{7}$

Possible Answers:

287

399

301

238

350

Correct answer:

301

Explanation:

$\frac{7^{2} + (-7)^{3} + (-7)^{4}}{7} =\frac{49 + (-343)+ 2401}{7} = \frac{2107}{7} = 301$

Report an Error

Example Question #82 : Integer Operations

Solve

$\left ( \frac{3}{4} \right)^{3}\times \left (\frac{2}{9}\right)^{2}$

Possible Answers:

$\frac{3}{144}$

$\frac{1}{48}$

$\frac{9}{432}$

$\frac{108}{5184}$

$\frac{18}{864}$

Correct answer:

$\frac{1}{48}$

Explanation:

First, distribute the exponents to the numerators and denominators:

$\frac{3^{3}}{4^{3}}\times\frac{2^{2}}{9^{2}}$ .

Then, rewrite the problem in expanded form:

$\frac{3\cdot3\cdot3}{4\cdot4\cdot4}\times\frac{2\cdot2}{9\cdot9}$

Next, rewrite the problem so that you only have prime factors in both numerators and denominators:

$\frac{3\cdot3\cdot3}{2\cdot2\cdot2\cdot2\cdot2\cdot2}\times\frac{2\cdot2}{3\cdot3\cdot3\cdot3}$ .

Last, simplify by "canceling out" like terms, leaving you with

$\frac{1}{2\cdot2\cdot2\cdot2}\times\frac{1}{3}$

and multiply across both numerators and denominators, which will give you $\frac{1}{48}$ .

Report an Error

Example Question #82 : Real Numbers

$\sqrt2 \times \sqrt18$

Possible Answers:

$2\sqrt18$

$\sqrt20$

Correct answer:

Explanation:

$\fn_cm When\; multiplying \; radicals, \; multiply \; the \; numbers \; under \; the \; radical\; and \; keep\; the\; radical.$

$\: \sqrt2 \times \sqrt18 = \sqrt36 = 6$

Report an Error

Example Question #15 : How To Multiply Integers

Multiply and express the product in scientific notation:

$\left (5 \times 10^{20} \right ) \left (8\times 10^{9} \right )$

Possible Answers:

$40 \times 10^{30}$

$40 \times 10^{180}$

$4 \times 10^{181}$

$4 \times 10^{30}$

$40 \times 10^{29}$

Correct answer:

$4 \times 10^{30}$

Explanation:

Use your power properties to multiply these numbers.

$\left (5 \times 10^{20} \right ) \left (8\times 10^{9} \right )$

$=\left (5 \cdot 8 \right )\times \left (10^{20} \cdot 10^{9} \right )$

$=40 \times 10^{20+9}$

$=40 \times 10^{29}$

This is not in scientific notation, so adjust as follows:

$40 \times 10^{29}$

$=4 \times 10^{1} \times 10^{29}$

$=4 \times 10^{1+29}$

$=4 \times 10^{30}$

Report an Error

Example Question #85 : Real Numbers

Multiply and express the product in scientific notation:

$\left (9.2 \times 10^{12} \right ) \left (1.5\times 10^{12} \right )$

Possible Answers:

$13.8 \times 10^{24}$

$1.38 \times 10^{25}$

$1.38 \times 10^{24}$

$0.138 \times 10^{26}$

$0.138 \times 10^{25}$

Correct answer:

$1.38 \times 10^{25}$

Explanation:

Use your power properties to multiply these numbers.

$\left (9.2 \times 10^{12} \right ) \left (1.5\times 10^{12} \right )$

$=\left (9.2 \cdot 1.5 \right )\times \left (10^{12} \cdot 10^{12} \right )$

$=13.8 \times 10^{12+12}$

$=13.8 \times 10^{24}$

This is not in scientific notation, so adjust as follows:

$13.8 \times 10^{24}$

$=1.38 \times 10^{1} \times 10^{24}$

$=1.38 \times 10^{1+24}$

$=1.38 \times 10^{25}$

Report an Error

Example Question #83 : Integer Operations

Rewrite as a number in base ten: $243_{\textrm{five}}$

Possible Answers:

Correct answer:

Explanation:

$243_{\textrm{five}}$

$= 2 \cdot 5^{2} + 4 \cdot 5^{1 } + 3$

$= 2 \cdot 25 + 4 \cdot 5 + 3$

= 50 +20+3 = 73

Report an Error

Example Question #87 : Real Numbers

Rewrite as a number in base ten: $231_{\textrm{six}}$

Possible Answers:

Correct answer:

Explanation:

$231_{\textrm{six}}$

$= 2 \cdot 6^{2} + 3 \cdot 6^{1} + 1$

$= 2 \cdot 36 + 3 \cdot 6 + 1$

= 72+ 18+ 1 =91

Report an Error

Example Question #88 : Real Numbers

Simplify the following:

4+5*10^2-5

Possible Answers:

499

8095

104

2499

Correct answer:

499

Explanation:

In this problem, you need to use the proper order of operations to find the correct answer: PEMDAS (Parentheses, Exponents, Multiplication-Division, Addition-Subtraction).

Exponents show up first in this problem, so the first step is to simplify:

10^2 = 100

This results in:

4+5*100-5

The next step is the multiplication:

5*100=500

This results in:

4+500-5

The next step is to do the remaining addition and subtraction from left to right.

4+500-5=499

499 is your final answer.

Report an Error

Example Question #1 : Mathematical Relationships

Evaluate the expression.

$\small (3+4)^2+(\frac{3+5}{2})+6\div 2$

Possible Answers:

Correct answer:

Explanation:

Follow the correct order of operations: parenthenses, exponents, multiplication, division, addition, subtraction.

$\small (3+4)^2+(\frac{3+5}{2})+6\div 2$

First, evaluate any terms in parenthesis.

$(7)^2+(\frac{8}{2})+6\div 2$

$7^2+4+6\div 2$

Next, evaluate the exponent.

$\small 49+4+6\div2$

Divide.

$\small 49+4+3$

Finally, add.

$\small 49+4+3=56$

Report an Error

Example Question #1851 : Algebra Ii

The quantity x varies directly with y. If x is 26 when y is 100, find x when y is 200.

Possible Answers:

6.5

104

Correct answer:

Explanation:

We must set up a proportion. Since x varies directly with y, when y is multiplied by 2, x is also multiplied by 2. 26 times 2 is 52.

Direct variation: $\frac{x_1}{x_2}=\frac{y_1}{y_2}$

$\frac{26}{x_2}=\frac{100}{200}$

$\frac{26}{x_2}=\frac{1}{2}$

x_2=2(26)=52

Report an Error

View Algebra Tutors

Alexander
Certified Tutor

Champlain College, Bachelor of Science, Game and Interactive Media Design.

View Algebra Tutors

John
Certified Tutor

Anderson University, Bachelor in Arts, Music Performance.

View Algebra Tutors

Shifrah
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Biology, General. Massachusetts College of Pharmacy and Health ...

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GRE Tutors in Phoenix, French Tutors in Miami, Physics Tutors in Philadelphia, Algebra Tutors in Miami, Algebra Tutors in Philadelphia, Math Tutors in Chicago, Reading Tutors in Washington DC, English Tutors in Denver, SAT Tutors in Phoenix, Math Tutors in Miami

Popular Courses & Classes

Spanish Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Boston, ACT Courses & Classes in Miami, GRE Courses & Classes in Miami, LSAT Courses & Classes in Philadelphia, ACT Courses & Classes in Philadelphia, ISEE Courses & Classes in Miami, SSAT Courses & Classes in Boston, LSAT Courses & Classes in San Diego, SAT Courses & Classes in Phoenix

Popular Test Prep

GRE Test Prep in San Diego, LSAT Test Prep in Los Angeles, GMAT Test Prep in Chicago, SSAT Test Prep in San Diego, GRE Test Prep in Boston, SSAT Test Prep in Boston, GRE Test Prep in Miami, GMAT Test Prep in Phoenix, SAT Test Prep in Los Angeles, ACT Test Prep in Miami

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra 1 : Real Numbers

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #81 : Real Numbers

Example Question #82 : Integer Operations

Example Question #82 : Real Numbers

Example Question #15 : How To Multiply Integers

Example Question #85 : Real Numbers

Example Question #83 : Integer Operations

Example Question #87 : Real Numbers

Example Question #88 : Real Numbers

Example Question #1 : Mathematical Relationships

Example Question #1851 : Algebra Ii

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: