We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #7 : Subtraction With Fractions

Subtract these fractions:

$\frac{1}{8}-\frac{1}{9}$

Possible Answers:

$\frac{1}{36}$

$\frac{1}{17}$

$\frac{1}{24}$

$\frac{1}{72}$

Correct answer:

$\frac{1}{72}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 9 over 9 and the second fraction by 8 over 8.

$\frac{1}{8}*\frac{9}{9}=\frac{9}{72}$

$\frac{1}{9}*\frac{8}{8}=\frac{8}{72}$

Subtract the numerators of these fractions to get the final answer.

$\frac{9}{72}-\frac{8}{72}=\frac{1}{72}$

Report an Error

Example Question #41 : Operations With Fractions

Subtract these fractions:

$\frac{6}{7}-\frac{1}{3}$

Possible Answers:

$\frac{3}{7}$

$\frac{12}{21}$

$\frac{10}{21}$

$\frac{11}{21}$

Correct answer:

$\frac{11}{21}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 3 over 3 and the second fraction by 7 over 7.

$\frac{6}{7}*\frac{3}{3}=\frac{18}{21}$

$\frac{1}{3}*\frac{7}{7}=\frac{7}{21}$

Subtract the numerators of these fractions to get the final answer.

$\frac{18}{21}-\frac{7}{21}=\frac{11}{21}$

Report an Error

Example Question #21 : Adding And Subtracting Fractions

$\frac{9x}{x-1}-\frac{4+x}{3x-3}$

Possible Answers:

$\frac{2(13x-2)}{3(x)}$

$\frac{2(13x-2)}{(x-1)}$

$\frac{2(13x-2)}{3(x-1)}$

$\frac{2(x-2)}{3(x-1)}$

$\frac{13x-2)}{3(x-1)}$

Correct answer:

$\frac{2(13x-2)}{3(x-1)}$

Explanation:

To solve this problem, first identify the common denominator, which happens to be: 3x-3. Therefore, you just need to offset the first fraction so that it becomes $\frac{9x(3)}{(x-1)(3)}$ . Then, combine the numerators, remembering that there is a subtraction sign: 9x(3)-(4+x)=27x-4-x=26x-4 . Put that over the denominator so that you have: $\frac{26x-4}{3x-3}$ . I'd factor to make sure you can't simplify anymore: $\frac{2(13x-2)}{3(x-1)}$ . It turns out you can't so this is your final answer.

Report an Error

Example Question #22 : Adding And Subtracting Fractions

$\frac{2}{x+1}-\frac{3}{x-5}$

Possible Answers:

$\frac{-x-13}{(x-5)}$

$\frac{-x-13}{(x+1)(x-5)}$

$\frac{x-13}{(x+1)(x-5)}$

$\frac{-x-13}{(x-5)}$

$\frac{x+13}{(x+1)(x-5)}$

Correct answer:

$\frac{-x-13}{(x+1)(x-5)}$

Explanation:

To combine these two fractions, you must first identify the common denominator. In this case, it's the product of the two denominators (x+1)(x-5) . Then, multiply each of the numerators by their missing piece of the denominator: $\frac{2(x-5)}{(x+1)(x-5)}-\frac{3(x+1)}{(x-5)(x+1)}$ . Now, you can combine the numerators to get: $\frac{2x-10-3x-3}{(x+1)(x-5)}$ . Simplify and combine like terms to get: $\frac{-x-13}{(x+1)(x-5)}$ .

Report an Error

Example Question #23 : Adding And Subtracting Fractions

Simplify: $\frac{1+3}{\frac{2}{3+2}} + \frac{1}{2}$

Possible Answers:

$2\frac{1}{5}$

$\frac{3}{7}$

$1\frac{1}{8}$

$\frac{9}{10}$

$10\frac{1}{2}$

Correct answer:

$10\frac{1}{2}$

Explanation:

Simplify the complex fraction $\frac{1+3}{\frac{2}{3+2}}$ first.

$\frac{1+3}{\frac{2}{3+2}} = \frac{4}{\frac{2}{5}}$

Rewrite the complex fraction using a division sign.

$\frac{4}{\frac{2}{5}} = 4 \div \frac{2}{5}$

Turn the division sign to a multiplication sign and take the reciprocal of the second term. Simplify.

$4 \div \frac{2}{5} = 4\times \frac{5}{2} = \frac{20}{2} = 10$

Add this number with the second term.

$\frac{1+3}{\frac{2}{3+2}} + \frac{1}{2} = 10+\frac{1}{2} = 10\frac{1}{2}$

Report an Error

Example Question #4391 : Algebra Ii

Add: $\frac{3}{ab} + \frac{a+3}{a}$

Possible Answers:

$\frac{6+a+b}{ab}$

$\frac{ab+6b}{ab}$

$\frac{6+a}{a^2b}$

$\frac{a+6b}{ab}$

$\frac{3+ab+3b}{ab}$

Correct answer:

$\frac{3+ab+3b}{ab}$

Explanation:

In order to add the numerators of the fractions, we need to find the least common denominator.

The least common denominator is:

We will need to multiply the numerator and denominator by to match the denominators of both fractions.

$\frac{3}{ab} + \frac{b\left (a+3 \right )}{ab}$

Simplify the fraction.

$\frac{3}{ab} + \frac{b\left (a+3 \right )}{ab} = \frac{3}{ab}+\frac{ab+3b}{ab}$

Combine the two fractions.

The answer is: $\frac{3+ab+3b}{ab}$

Report an Error

Example Question #24 : Adding And Subtracting Fractions

Solve: $\frac{1}{3} -\frac{2}{5}+\frac{1}{4}$

Possible Answers:

$\frac{11}{60}$

$\frac{7}{60}$

$\frac{21}{50}$

$\frac{11}{30}$

Correct answer:

$\frac{11}{60}$

Explanation:

Find the least common denominator. One method is to multiply all three uncommon denominators together.

$3 \times 5 \times 4 = 60$

Rewrite the fractions. For each fraction, multiply the numerator with what was multiplied on the denominator to get the least common denominator.

$\frac{1}{3} -\frac{2}{5}+\frac{1}{4} = \frac{20}{60}- \frac{24}{60}+ \frac{15}{60}$

Add the numerators. The denominators do not change.

$\frac{20}{60}- \frac{24}{60}+ \frac{15}{60} = \frac{11}{60}$

Report an Error

Example Question #52 : Fractions

Add the following fractions: $\frac{3}{2}+ \frac{4}9{}$

Possible Answers:

$\frac{35}{18}$

$\frac{16}{9}$

$\frac{7}{18}$

$\frac{7}{11}$

$\frac{2}{3}$

Correct answer:

$\frac{35}{18}$

Explanation:

In order to add the fractions, we must find a least common denominator.

Multiply the denominators together.

$2 \times 9 =18$

Reconvert the fractions.

$\frac{3}{2}+ \frac{4}{9} = \frac{27}{18}+ \frac{8}{18} = \frac{35}{18}$

The answer is: $\frac{35}{18}$

Report an Error

Example Question #53 : Fractions

Perform the following operation:

$\frac{5}{16}+\frac{3}{8}$

Possible Answers:

$\frac{11}{16}$

$\frac{8}{16}$

$\frac{15}{16}$

$\frac{11}{8}$

Correct answer:

$\frac{11}{16}$

Explanation:

Perform the following operation:

$\frac{5}{16}+\frac{3}{8}$

To start, we will need a common denominator. In this case, let's use 16, because it is the smallest possible common denominator.

$\frac{3}{8}*\frac{2}{2}=\frac{6}{16}$

Next, simply add across the top and we have our answer!

$\frac{5}{16}+\frac{6}{16}=\frac{11}{16}$

Report an Error

Example Question #31 : Adding And Subtracting Fractions

Add the fractions: $\frac{2}{x-3}+\frac{1}{x+2}$

Possible Answers:

$\frac{3x+1}{x-6}$

$\frac{3}{(x-3)(x+2)}$

$\frac{x+1}{(x+2)(x-3)}$

$\frac{x+1}{(x-3)(x+2)}$

$\frac{3x+1}{(x-3)(x+2)}$

Correct answer:

$\frac{3x+1}{(x-3)(x+2)}$

Explanation:

$\frac{2}{x-3}+\frac{1}{x+2}$

To add fractions we must find a common denominator. In this example we do so by multiplying each side by the denominator of the other fraction:

$\frac{x+2}{x+2}*\frac{2}{x-3}+\frac{1}{x+2}*\frac{x-3}{x-3}$

Add the numerators:

$\frac{2(x+2)+x-3}{(x-3)(x+2)}\rightarrow \mathbf{\frac{3x+1}{(x-3)(x+2)}}$

Report an Error

View Algebra 2 Tutors

Abigail
Certified Tutor

Morehead State University, Bachelor of Science, Mathematics. The University of Tennessee, Doctor of Science, Nuclear Engineer...

View Algebra 2 Tutors

Lamar
Certified Tutor

Cleveland State University, Bachelors, Mathematics.

View Algebra 2 Tutors

Sonu
Certified Tutor

Rajasthan Technical University Kota, Bachelor, Electrical.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

English Tutors in Denver, Physics Tutors in Dallas Fort Worth, Biology Tutors in Dallas Fort Worth, Reading Tutors in Seattle, Computer Science Tutors in Los Angeles, GRE Tutors in Los Angeles, Spanish Tutors in Houston, ACT Tutors in Dallas Fort Worth, ACT Tutors in San Diego, Computer Science Tutors in San Diego

Popular Courses & Classes

GMAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Atlanta, Spanish Courses & Classes in Philadelphia, SSAT Courses & Classes in Atlanta, SAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Houston, LSAT Courses & Classes in New York City, SAT Courses & Classes in Chicago, SSAT Courses & Classes in Washington DC

Popular Test Prep

GRE Test Prep in Philadelphia, GRE Test Prep in Miami, MCAT Test Prep in Houston, ACT Test Prep in Boston, SAT Test Prep in Chicago, GMAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Boston, ISEE Test Prep in San Diego, SAT Test Prep in Boston, GMAT Test Prep in Washington DC

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 II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #7 : Subtraction With Fractions

Example Question #41 : Operations With Fractions

Example Question #21 : Adding And Subtracting Fractions

Example Question #22 : Adding And Subtracting Fractions

Example Question #23 : Adding And Subtracting Fractions

Example Question #4391 : Algebra Ii

Example Question #24 : Adding And Subtracting Fractions

Example Question #52 : Fractions

Example Question #53 : Fractions

Example Question #31 : Adding And Subtracting Fractions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: