We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Adding and Subtracting Fractions

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 #61 : Adding And Subtracting Fractions

Add the fractions: $\frac{3}{4}+\frac{8}{3}$

Possible Answers:

$\frac{31}{12}$

$\frac{38}{12}$

$\frac{21}{12}$

$\frac{41}{12}$

Correct answer:

$\frac{41}{12}$

Explanation:

Find the least common denominator to these fractions.

Multiply both denominators together.

$4\times3=12$

Convert the fractions using this denominator.

$\frac{3}{4}+\frac{8}{3} = \frac{9}{12}+\frac{32}{12} = \frac{41}{12}$

The answer is: $\frac{41}{12}$

Report an Error

Example Question #91 : Fractions

Subtract the fractions: $\frac{2}{5}-\frac{1}{3}-\frac{3}{4}$

Possible Answers:

$-\frac{30}{7}$

$-\frac{11}{60}$

$-\frac{41}{60}$

$-\frac{15}{4}$

Correct answer:

$-\frac{41}{60}$

Explanation:

In order to subtract the fractions, we must find the least common denominator of the three fractions.

Multiply all three numbers together to find the common denominator.

$5 \times 3 \times 4=60$

Convert all the fractions to this denominator, and multiply the numerators with what was multiplied to the denominator to get the new numerator.

$\frac{2}{5}-\frac{1}{3}-\frac{3}{4}=\frac{2(3)(4)}{60}-\frac{1(5)(4)}{60}-\frac{3(3)(5)}{60}$

Simplify the numerators.

$=\frac{24}{60}-\frac{20}{60}-\frac{45}{60} = -\frac{41}{60}$

The answer is: $-\frac{41}{60}$

Report an Error

Example Question #62 : Adding And Subtracting Fractions

Add the following fractions: $\frac{2}{a}+\frac{2}{a^3b}$

Possible Answers:

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

$\frac{2}{a+a^3b}$

$\frac{4a^2b+2}{a^3b}$

$\frac{2a^2b+2}{a^3b}$

$\frac{4}{a+a^3b}$

Correct answer:

$\frac{2a^2b+2}{a^3b}$

Explanation:

To be able to add the fractions, we will need to determine the least common denominator.

The least common denominator is a^3b since this is the minimal term that is both divisible by and itself.

Convert only the first fraction with the denominator of a^3b .

$\frac{2}{a}+\frac{2}{a^3b}= \frac{2(a^2b)}{a(a^2b)}+\frac{2}{a^3b} = \frac{2a^2b+2}{a^3b}$

The answer is: $\frac{2a^2b+2}{a^3b}$

Report an Error

Example Question #62 : Adding And Subtracting Fractions

Add the following fractions: $\frac{1}{7}+\frac{4}{42}$

Possible Answers:

$\frac{5}{49}$

$\frac{10}{49}$

$\frac{20}{49}$

$\frac{11}{42}$

$\frac{5}{21}$

Correct answer:

$\frac{5}{21}$

Explanation:

In order to add the fractions, we will need a common denominator.

Notice that the largest denominator is divisible by seven. We can change just the first fraction to the least common denominator.

Rewrite the fraction.

$\frac{1}{7}+\frac{4}{42} = \frac{6}{42}+\frac{4}{42} = \frac{10}{42}$

Reduce this fraction by writing out the common factors of the numerator and denominator.

$\frac{10}{42} =\frac{2\times 5}{2\times 21} =\frac{5}{21}$

The answer is: $\frac{5}{21}$

Report an Error

Example Question #63 : Adding And Subtracting Fractions

Determine the sum as a mixed fraction: $\frac{2}{3}+\frac{1}{4}+\frac{8}{3}$

Possible Answers:

$2\frac{5}{12}$

$3\frac{3}{4}$

$4\frac{3}{4}$

$3\frac{7}{12}$

$1\frac{1}{10}$

Correct answer:

$3\frac{7}{12}$

Explanation:

The denominators are not common. Convert the denominators to a least common denominator.

To obtain the LCD, we can multiply four times three.

$4\times 3=12$

This value is the least possible value divisible by four and three.

Convert the fractions. Multiply the numerators by what was multiplied on the denominator to get the LCD.

$\frac{2}{3}+\frac{1}{4}+\frac{8}{3}=\frac{2(4)}{12}+\frac{1(3)}{12}+\frac{8(4)}{12}$

Simplify the fractions and add the numerators. The denominator stays the same.

$\frac{8}{12}+\frac{3}{12}+\frac{32}{12} = \frac{43}{12}$

Forty three goes into twelve three times. The remainder is seven, which can be written as seven-twelves.

The answer is: $3\frac{7}{12}$

Report an Error

Example Question #64 : Adding And Subtracting Fractions

Add the fractions: $\frac{7}{9}+\frac{16}{3}$

Possible Answers:

$\frac{55}{9}$

$\frac{55}{12}$

$\frac{23}{9}$

$\frac{23}{12}$

$\frac{55}{6}$

Correct answer:

$\frac{55}{9}$

Explanation:

In order to add these fractions, we will need a common denominator. Notice that the least common denominator is nine since it's the least number divisible by both denominators.

Convert the second fraction to the correct denominator.

$\frac{7}{9}+\frac{16}{3} = \frac{7}{9}+\frac{16(3)}{3(3)}$

Simplify the fractions.

$\frac{7}{9}+\frac{48}{9} = \frac{55}{9}$

The answer is: $\frac{55}{9}$

Report an Error

Example Question #65 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{7}{3}-\frac{11}{12}$

Possible Answers:

$\frac{17}{12}$

$-\frac{2}{9}$

$-\frac{1}{3}$

$\frac{1}{3}$

$-\frac{17}{12}$

Correct answer:

$\frac{17}{12}$

Explanation:

The least common denominator is 12. Convert the first fraction to this denominator in order to subtract the numerators. The denominators will remain the same.

$\frac{7}{3}-\frac{11}{12}=\frac{7(4)}{3(4)}-\frac{11}{12}$

Simplify the fractions.

$\frac{28}{12}-\frac{11}{12} = \frac{17}{12}$

The answer is: $\frac{17}{12}$

Report an Error

Example Question #66 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{1}{30}- \frac{3}{4}$

Possible Answers:

$-\frac{43}{120}$

$-\frac{43}{60}$

$\frac{43}{60}$

$-\frac{13}{120}$

$\frac{7}{10}$

Correct answer:

$-\frac{43}{60}$

Explanation:

To subtract the fractions, we will need to find the least common denominator.

Write out the factors for both denominators.

30-[30,60]

4-[4,8,12,16,20,24,...,48,52,56,60]

Multiply four by 15 to get the least common denominator.

The least common denominator is .

Convert both fractions.

$\frac{1}{30}- \frac{3}{4}= \frac{2}{60}-\frac{45}{60} = -\frac{43}{60}$

The answer is: $-\frac{43}{60}$

Report an Error

Example Question #67 : Adding And Subtracting Fractions

Add the fractions: $\frac{2}{3}+\frac{1}{6}+\frac{2}{9}$

Possible Answers:

$\frac{5}{18}$

$\frac{17}{18}$

$\frac{13}{18}$

$\frac{19}{18}$

$\frac{19}{13}$

Correct answer:

$\frac{19}{18}$

Explanation:

Determine the least common denominator. Expand the factors for each denominator.

3-[3,6,9,12,15,18,21,24,27,30,33,36]

6-[6,12,18,24,30,36]

9-[9,18,27,36]

The least common denominator is .

$\frac{2}{3}+\frac{1}{6}+\frac{2}{9}=\frac{24}{36}+\frac{6}{36}+\frac{8}{36}$

Add the numerators.

$\frac{38}{36} = \frac{19\times 2}{18\times 2} = \frac{19}{18}$

The answer is: $\frac{19}{18}$

Report an Error

Example Question #68 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{\sqrt2}{6}-\frac{\sqrt2}{24}$

Possible Answers:

$\frac{\sqrt{2}}{4}$

$\frac{\sqrt{2}}{8}$

$\frac{1}{4}$

$\frac{\sqrt{2}}{6}$

$\frac{\sqrt{2}}{3}$

Correct answer:

$\frac{\sqrt{2}}{8}$

Explanation:

In order to subtract these fractions, we will need to convert the first fraction with a common denominator of 24. Multiply the top and bottom by four.

$\frac{\sqrt2}{6}-\frac{\sqrt2}{24}=\frac{4\sqrt2}{6(4)}-\frac{\sqrt2}{24}$

Simplify the numerator by combining like-terms.

$\frac{3\sqrt2}{24}$

Simplify the fraction.

$\frac{3\sqrt2}{3 \times 8} = \frac{\sqrt{2}}{8}$

The answer is: $\frac{\sqrt{2}}{8}$

Report an Error

View Algebra 2 Tutors

Kinza
Certified Tutor

University of Georgia, Bachelor of Science, Biology, General.

View Algebra 2 Tutors

Aaron
Certified Tutor

Austin Peay State University, Bachelor, Education.

View Algebra 2 Tutors

Cassandra
Certified Tutor

Marygrove College, Master of Arts, High School Teaching.

All Algebra II Resources

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

Popular Subjects

English Tutors in Los Angeles, Reading Tutors in Phoenix, ACT Tutors in Houston, Algebra Tutors in Houston, Algebra Tutors in Atlanta, Calculus Tutors in Washington DC, GMAT Tutors in San Diego, ACT Tutors in Miami, ACT Tutors in Boston, Calculus Tutors in Chicago

Popular Courses & Classes

MCAT Courses & Classes in Phoenix, MCAT Courses & Classes in Miami, SAT Courses & Classes in San Diego, Spanish Courses & Classes in Houston, ACT Courses & Classes in San Diego, LSAT Courses & Classes in San Diego, MCAT Courses & Classes in Boston, MCAT Courses & Classes in San Diego, Spanish Courses & Classes in Denver, SSAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

LSAT Test Prep in Los Angeles, MCAT Test Prep in San Diego, SAT Test Prep in Boston, ACT Test Prep in San Diego, SAT Test Prep in Los Angeles, SSAT Test Prep in Miami, GRE Test Prep in Washington DC, ACT Test Prep in Dallas Fort Worth, SAT Test Prep in Atlanta, ISEE Test Prep in Boston

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 : Adding and Subtracting Fractions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #61 : Adding And Subtracting Fractions

Example Question #91 : Fractions

Example Question #62 : Adding And Subtracting Fractions

Example Question #62 : Adding And Subtracting Fractions

Example Question #63 : Adding And Subtracting Fractions

Example Question #64 : Adding And Subtracting Fractions

Example Question #65 : Adding And Subtracting Fractions

Example Question #66 : Adding And Subtracting Fractions

Example Question #67 : Adding And Subtracting Fractions

Example Question #68 : 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: