Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Multiplying and Dividing 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 #1 : Multiplying And Dividing Fractions

Solve the following equation to find .

$\frac{2}{3}x=\frac{4}{15}+\frac{3}{15}$

Possible Answers:

$x=\frac{14}{45}$

$x=-\frac{7}{10}$

$x=\frac{30}{21}$

$x=\frac{7}{10}$

Correct answer:

$x=\frac{7}{10}$

Explanation:

The first step in solving this equation is to add the fractions, giving us:

$\frac{2}{3}x=\frac{7}{15}$

To solve for , we need to divide both sides by $\frac{2}{3}$ .

Remember: When we divide a number by a fraction, we "switch" (find the reciprocal) of the fraction and mulitply it to the number.

$\bigg(\frac{3}{2}\bigg)\bigg(\frac{2}{3}\bigg)x=\bigg(\frac{7}{15}\bigg) \bigg(\frac{3}{2}\bigg)$

The right side of the equation cancels out leaving alone:

$x=\frac{7\times 3}{15\times 2}=\frac{21}{30}$

Notice: Both the numerator and denominator are divisble by so we can simplify this further.

$x=\frac{7}{10}$

Report an Error

Example Question #1 : Multiplying And Dividing Fractions

Simplify $\frac{3}{6}\cdot\frac{12}{4}$ .

Possible Answers:

$\text{None of the answers listed.}$

$\frac{3}{2}$

$\frac{36}{24}$

$\frac{6}{4}$

$\frac{2}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

The problem can be made easier by first simplifying each fraction: $\frac{3}{6}=\frac{1}{2}$ and $\frac{12}{4}=\frac{3}{1}$ .

This brings our new problem to $\frac{1}{2}\cdot\frac{3}{1}$ .

Now, the numerators are multiplied by each other then the denomenators are multiplied by each other: $\frac{1\cdot3}{2\cdot1}=\frac{3}{2}$ .

Report an Error

Example Question #1 : Multiplying And Dividing Fractions

Simplify $\frac{5}{3}\div\frac{7}{6}$ .

Possible Answers:

$\frac{21}{3}$

$\frac{35}{18}$

$\frac{3}{10}$

$\frac{10}{7}$

$\frac{30}{21}$

Correct answer:

$\frac{10}{7}$

Explanation:

To solve, we must turn the division problem into a multiplication problem by "flipping" the second fraction (dividing by a fraction is the same as multiplying by its reciprocal):

$\frac{5}{3}\div\frac{7}{6}=\frac{5}{3}\cdot\frac{6}{7}$ .

Then, we multiply the numerators followed by the denomenators:

$\frac{5\cdot6}{3\cdot7}=\frac{30}{21}$ .

Lastly, the fraction must be simplified by a factor of 3:

$\frac{30}{21}=\frac{10}{7}$ , which gives us our final answer.

Report an Error

Example Question #1 : Multiplying And Dividing Fractions

Multiply:

$\left(\frac{x^2}{z}\right)\cdot \left(\frac{x^2z^2}{y}\right)$

Possible Answers:

x^4z^2y

$\frac{x^4}{zy}$

$\frac{x^4z}{y}$

x^4yz

Correct answer:

$\frac{x^4z}{y}$

Explanation:

To multiply fractions, just multiply the numerators, then the denominators, and then simplify.

$(\frac{x^2}{z})(\frac{x^2z^2}{y})=\frac{x^4z^2}{zy}=\frac{x^4z}{y}$

Report an Error

Example Question #171 : Fractions

Multiply:

$\left(\frac{ab^2c}{a^{\frac{1}{2}}b^4c^3}\right)\cdot \left(\frac{abc^2}{c}\right)$

Possible Answers:

$\frac{a^\frac{3}{2}}{bc}$

$a^{\frac{3}{2}}bc$

$\frac{bc}{a^{\frac{3}{2}}}$

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

Correct answer:

$\frac{a^\frac{3}{2}}{bc}$

Explanation:

To multiply fractions, multiply the numerators and denominators together, then simplify.

$(\frac{ab^2c}{a^{\frac{1}{2}}b^4c^3})(\frac{abc^2}{c})=\frac{a^2b^3c^3}{a^{\frac{1}{2}}b^4c^4}=\frac{a^{\frac{3}{2}}}{bc}$

Report an Error

Example Question #1 : Multiplying And Dividing Fractions

Multiply:

$\left(\frac{4}{5}x\right)\cdot \left(\frac{6}{13}y\right)$

Possible Answers:

$\frac{15}{8}xy$

$\frac{8}{15xy}$

$\frac{8x}{15y}$

$\frac{24}{65}xy$

Correct answer:

$\frac{24}{65}xy$

Explanation:

Multiply the numerators and denominators. Then, simplify.

$(\frac{4}{5}x)(\frac{6}{13}y)=(\frac{4x}{5})(\frac{6y}{13})=\frac{24xy}{65}$

Report an Error

Example Question #3 : Multiplying And Dividing Fractions

Multiply:

$\left(\frac{15}{7x}\right)\cdot \left(\frac{12x^2}{5}\right)$

Possible Answers:

$\frac{36x^2}{7}$

$\frac{7}{36}x$

$\frac{36}{7}x$

$\frac{36}{7x}$

Correct answer:

$\frac{36}{7}x$

Explanation:

Multiply the numerators and denominators, then simplify.

$(\frac{15}{7x})(\frac{12x^2}{5})=\frac{180x^2}{35x}=\frac{36}{7}x$

Report an Error

Example Question #2 : Multiplying And Dividing Fractions

Simplify:

$\frac{36x^2y}{5x^5 y^{-2}}\div\frac{9x^{-3}}{25}$

Possible Answers:

20xy^3

20y^3

$\frac{y^3}{20x^4}$

$\frac{20}{y^3}$

Correct answer:

20y^3

Explanation:

In order to divide fractions, you need to multiply the first fraction by the reciprocal of the second one.

$\frac{36x^2y}{5x^5y^{-2}}\div\frac{9x^{-3}}{25}=\frac{36x^2y}{5x^5y^{-2}}\times\frac{25}{9x^{-3}}$

Now, multiply the numerators and denominators together, then simplify.

$\frac{36x^2y}{5x^5y^{-2}}\times\frac{25}{9x^{-3}}=\frac{900x^2y}{45x^2y^{-2}}=20y^3$

Report an Error

Example Question #8 : Solving Rational And Fractional Functions

Simplify:

$\frac{25st^2}{6s^3t^5}\div\frac{30s^{-9}}{45s^2t^7}$

Possible Answers:

$\frac{25}{4s^9t^4}$

$\frac{4}{25s^2t}$

$\frac{25s^9t^4}{4}$

$\frac{4s^9t^4}{25}$

Correct answer:

$\frac{25s^9t^4}{4}$

Explanation:

To divid fractions, you need to multiply the first fraction by the reciprocal of the second.

$(\frac{25st^2}{6s^3t^5})\div(\frac{30s^{-9}}{45s^2t^7})=(\frac{25st^2}{6s^3t^5})\times(\frac{45s^2t^7}{30s^{-9}})$

Now, multiply the numerators and denominators together, then simplify.

$(\frac{25st^2}{6s^3t^5})\times(\frac{45s^2t^7}{30s^{-9}})=\frac{1125s^3t^9}{180s^{-6}t^5}=\frac{25s^9t^4}{4}$

Report an Error

Example Question #2 : Multiplying And Dividing Fractions

Simplify:

$\frac{12m^2n}{16m^3n^4}\div\frac{8m^{-4}n}{18m^4n^2}$

Possible Answers:

$\frac{27m^7}{16n^2}$

$\frac{16n^2}{27m^7}$

27m^7n^2

$\frac{27n^2}{16m^7}$

Correct answer:

$\frac{27m^7}{16n^2}$

Explanation:

To divide fractions, you need to multiply the first fraction by the reciprocal of the second.

$(\frac{12m^2n}{16m^3n^4})\div(\frac{8m^{-4}n}{18m^4n^2})=(\frac{12m^2n}{16m^3n^4})\times(\frac{18m^4n^2}{8m^{-4}n})$

Now, multiply the numerators and denominators, then simplify.

$(\frac{12m^2n}{16m^3n^4})\times(\frac{18m^4n^2}{8m^{-4}n})=\frac{216m^6n^3}{128m^{-1}n^5}=\frac{27m^7}{16n^2}$

Report an Error

View Algebra 2 Tutors

John
Certified Tutor

The University of Texas at Arlington, Bachelor of Science, Mathematics. Stanford University, Master of Science, Aerospace Eng...

View Algebra 2 Tutors

Nicholas
Certified Tutor

Salem State University, Bachelor of Science, GIS Technology.

View Algebra 2 Tutors

Sharon
Certified Tutor

Tabor College, Bachelor of Science, Mathematics Teacher Education. Tabor College, Masters in Education, Education.

All Algebra II Resources

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

Popular Subjects

GRE Tutors in Seattle, GRE Tutors in San Francisco-Bay Area, Statistics Tutors in Miami, Spanish Tutors in Phoenix, Reading Tutors in San Francisco-Bay Area, MCAT Tutors in Seattle, Calculus Tutors in New York City, SAT Tutors in San Francisco-Bay Area, SAT Tutors in Phoenix, GMAT Tutors in Seattle

Popular Courses & Classes

MCAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Boston, SAT Courses & Classes in San Diego, LSAT Courses & Classes in San Diego, Spanish Courses & Classes in Los Angeles, GRE Courses & Classes in Phoenix, MCAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Chicago, MCAT Courses & Classes in Miami, ACT Courses & Classes in Denver

Popular Test Prep

GMAT Test Prep in Chicago, SAT Test Prep in New York City, ISEE Test Prep in Houston, SSAT Test Prep in Denver, ACT Test Prep in Washington DC, ACT Test Prep in Boston, ACT Test Prep in Phoenix, SSAT Test Prep in Miami, ISEE Test Prep in Seattle, GRE Test Prep in Phoenix

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 : Multiplying and Dividing Fractions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Multiplying And Dividing Fractions

Example Question #1 : Multiplying And Dividing Fractions

Example Question #1 : Multiplying And Dividing Fractions

Example Question #1 : Multiplying And Dividing Fractions

Example Question #171 : Fractions

Example Question #1 : Multiplying And Dividing Fractions

Example Question #3 : Multiplying And Dividing Fractions

Example Question #2 : Multiplying And Dividing Fractions

Example Question #8 : Solving Rational And Fractional Functions

Example Question #2 : Multiplying And Dividing Fractions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: