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 #1759 : Mathematical Relationships And Basic Graphs

Add/Subtract $\frac {2}{3}-\frac {4}{7}+\frac {3}{2}$

Possible Answers:

$\frac{42}{67}$

$\frac{-67}{42}$

$\frac{67}{42}$

Correct answer:

$\frac{67}{42}$

Explanation:

Step 1: Find the Lowest Common Denominator (LCD) of all fractions. We can get the lowest denominator by writing out multiples of each denominator until we get a match on all three:

$3: 3,6,9,12,15,18,21,24,27,30,33,36,39,{\color{Blue} 42}$
$7: 7,14,21,28,35,{\color{Blue} 42}$
$2: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,{\color{Blue} 42}$

We see that the LCD is .

Step 2: Change all fractions into denominator .

$\frac {2}{3}=\frac {x}{42}$

Cross-Multiply:

$\frac {{\color{Red} 2}}{{\color{Blue} 3}}=\frac {\color{Blue} x}{{\color{Red} 42}}=3x=84->x=28$

The first fraction is $\frac {28}{42}$

Second Fraction: $\frac {-4}{7}=\frac {-24}{42}$

Third Fraction: $\frac {3}{2}=\frac {63}{42}$

Step 3: Re-Write the equations:

$\frac {28}{42}-\frac {24}{42}+\frac {63}{42}=\frac {28-24+63}{42}=\frac {67}{42}$

The final answer is $\frac {67}{42}$

Report an Error

Example Question #52 : Adding And Subtracting Fractions

Simplify: $x=\frac{5}{7} +\frac{1}{4}$ .

Possible Answers:

$\frac{15}{28}$

$\frac{27}{11}$

$\frac{6}{7}$

$\frac{1}{6}$

$\frac{27}{28}$

Correct answer:

$\frac{27}{28}$

Explanation:

To simplify, we multiply each fraction by the denominator of the other:

$x=\frac{20}{28} +\frac{7}{28}$

Then we add the numerators:

$x=\frac{27}{28}$

We can't simplify our answer, so we're done.

Report an Error

Example Question #53 : Adding And Subtracting Fractions

Simplify: $x= \frac{5}{7} + 2\frac{1}{3}$

Possible Answers:

$\frac{17}{19}$

$\frac{64}{21}$

$2\frac{22}{21}$

$3\frac{27}{29}$

Correct answer:

$\frac{64}{21}$

Explanation:

First, let's start by putting everything into proper fractions:

$x=\frac{5}{7}+\frac{7}{3}$

Next, we find a common denominator by multiplying each fraction by the denominator of the other fraction:

$x=\frac{15}{21}+\frac{49}{21}$

Finally, we add numerators together:

$x=\frac{64}{21}$

Report an Error

Example Question #54 : Adding And Subtracting Fractions

Add the fractions: $\frac{7}{10} + \frac{1}{5}+\frac{2}{3}$

Possible Answers:

$\frac{1}{15}$

$\frac{47}{30}$

$\frac{5}{9}$

$\frac{29}{30}$

$\frac{5}{6}$

Correct answer:

$\frac{47}{30}$

Explanation:

In order to add the fractions, the denominators must be common.

Find the least common denominator. The least common denominator is since this is the smallest number possible that is divisible by all three denominators.

Convert the fractions. Multiply the top with what was multiplied to the denominators to achieve the least common denominator.

$\frac{7}{10} + \frac{1}{5}+\frac{2}{3} = \frac{21}{30}+\frac{6}{30}+\frac{20}{30} = \frac{47}{30}$

The answer is: $\frac{47}{30}$

Report an Error

Example Question #55 : Adding And Subtracting Fractions

Solve the fractions: $\frac{3}{8}+\frac{1}{4}-\frac{3}{10}$

Possible Answers:

$\textup{The answer is not given.}$

$\frac{13}{80}$

$\frac{13}{40}$

$\frac{17}{120}$

$\frac{1}{22}$

Correct answer:

$\frac{13}{40}$

Explanation:

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

The least common denominator is since this is the least number that all three denominators are divisible by.

Convert all the fractions.

$\frac{3(5)}{8(5)}+\frac{1(10)}{4(10)}-\frac{3(4)}{10(4)}=\frac{15}{40}+\frac{10}{40}-\frac{12}{40}$

The answer is: $\frac{13}{40}$

Report an Error

Example Question #56 : Adding And Subtracting Fractions

Add the fractions: $\frac{6}{7}+\frac{1}{11}$

Possible Answers:

$\frac{3}{7}$

$\frac{7}{17}$

$\frac{73}{77}$

$\frac{7}{18}$

$\frac{1}{11}$

Correct answer:

$\frac{73}{77}$

Explanation:

Find the least common denominator by multiplying the denominators together and convert the fractions.

$\frac{6}{7}+\frac{1}{11} = \frac{6(11)}{7(11)}+ \frac{1(7)}{7(11)} =\frac{6(11)+1(7)}{77}$

Now that the denominators are common, we can simplify the numerator.

$\frac{6(11)+1(7)}{77} =\frac{66+7}{77}= \frac{73}{77}$

The answer is: $\frac{73}{77}$

Report an Error

Example Question #57 : Adding And Subtracting Fractions

Subtract the fractions: $\frac{1}{16}-\frac{2}{3}$

Possible Answers:

$\frac{9}{16}$

$-\frac{35}{48}$

$\frac{35}{48}$

$-\frac{9}{16}$

$-\frac{29}{48}$

Correct answer:

$-\frac{29}{48}$

Explanation:

Notice that the first term is smaller than the second term.

Convert the fractions to a common denominator by multiplying both denominators together. The least common denominator is not 16!

$16\times 3=48$

Convert both fractions with this LCD.

$\frac{1(3)}{16(3)}-\frac{2(16)}{3(16)} = \frac{3}{48}-\frac{32}{48}$

Subtract the numerators.

The answer is: $-\frac{29}{48}$

Report an Error

Example Question #58 : Adding And Subtracting Fractions

Add the following fractions: $\frac{2}{3}+\frac{7}{9}+\frac{1}{2}$

Possible Answers:

$\frac{5}{6}$

$\frac{3}{2}$

$\frac{31}{18}$

$\frac{4}{3}$

$\frac{35}{18}$

Correct answer:

$\frac{35}{18}$

Explanation:

In order to add and combine the numerators, we will need a similar denominator.

The least common denominator is , since this is the smallest number that is divisible by all the denominators in the expression.

Concert all fractions with this denominator.

$\frac{2}{3}+\frac{7}{9}+\frac{1}{2}=\frac{2(6)}{3(6)}+\frac{7(2)}{9(2)}+\frac{1(9)}{2(9)}$

Simplify the terms.

$\frac{12}{18}+\frac{14}{18}+\frac{9}{18}=\frac{35}{18}$

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

Report an Error

Example Question #59 : Adding And Subtracting Fractions

Subtract the following fractions: $6\frac{2}{9}- 14\frac{1}{3}$

Possible Answers:

$\frac{19}{9}$

$-\frac{70}{9}$

$\textup{The answer is not given.}$

$-\frac{73}{9}$

$\frac{13}{6}$

Correct answer:

$-\frac{73}{9}$

Explanation:

Convert both fractions to improper fractions.

The numerator can be obtained by multiplying the denominator with the whole number, and then add the numerator. Denominators remain the same.

$6\frac{2}{9}- 14\frac{1}{3}=\frac{(9\times 6)+2}{9}-\frac{(3\times 14)+1}{3}$

Simplify both fractions.

$\frac{56}{9}-\frac{43}{3}$

Convert the second fraction so that it has the same denominator as the first fraction.

$\frac{56}{9}-\frac{43(3)}{3(3)}=\frac{56}{9}-\frac{129}{9} =-\frac{73}{9}$

The answer is: $-\frac{73}{9}$

Report an Error

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

View Algebra 2 Tutors

Blossom
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Computer Science.

View Algebra 2 Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View Algebra 2 Tutors

Sahibzada
Certified Tutor

Northwestern University, Bachelor of Science, Materials Engineering.

All Algebra II Resources

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

Popular Subjects

GMAT Tutors in Denver, SSAT Tutors in Miami, Chemistry Tutors in Denver, SAT Tutors in Washington DC, Biology Tutors in Boston, ISEE Tutors in Miami, SSAT Tutors in Boston, Algebra Tutors in Chicago, Spanish Tutors in Miami, ACT Tutors in New York City

Popular Courses & Classes

LSAT Courses & Classes in Chicago, ISEE Courses & Classes in Philadelphia, GRE Courses & Classes in Miami, Spanish Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Washington DC, SSAT Courses & Classes in Philadelphia, ACT Courses & Classes in Washington DC, GMAT Courses & Classes in Chicago, LSAT Courses & Classes in Atlanta, ISEE Courses & Classes in Boston

Popular Test Prep

SSAT Test Prep in Los Angeles, GMAT Test Prep in Miami, GMAT Test Prep in Chicago, SAT Test Prep in Miami, ACT Test Prep in Washington DC, ACT Test Prep in Chicago, LSAT Test Prep in Phoenix, SSAT Test Prep in Boston, MCAT Test Prep in Phoenix, LSAT Test Prep in Chicago

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 #1759 : Mathematical Relationships And Basic Graphs

Example Question #52 : Adding And Subtracting Fractions

Example Question #53 : Adding And Subtracting Fractions

Example Question #54 : Adding And Subtracting Fractions

Example Question #55 : Adding And Subtracting Fractions

Example Question #56 : Adding And Subtracting Fractions

Example Question #57 : Adding And Subtracting Fractions

Example Question #58 : Adding And Subtracting Fractions

Example Question #59 : Adding And Subtracting Fractions

Example Question #61 : 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: