Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Fractions

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Fractions And Percentage

A stadium holds a total of 13,758 seats. Of that total, 6,732 seats are full with spectators. How many seats, to the nearest percent, are currently full?

Possible Answers:

$43\%$

$44\%$

$49\%$

$39\%$

$51\%$

Correct answer:

$49\%$

Explanation:

To answer this question, we must find the percentage of the amount of seats filled up within the stadium. To find a percentage, there are two steps.

First, you divide the part of the total number by the total number itself (in this case the amount of seats filled divided by the total number of seats). So, for this data:

$\frac{part}{whole} = \frac{6,732}{13,758} = 0.489$

The second step is to multiply your answer by 100 so that it will now be represented as a percentage. So for this data:

$\frac{6,732}{13,758} = 0.489 \cdot 100 = 48.9 %$

The question asked us to round our answer to the nearest whole percent. To do this, we round a number up one place if the last digit is a 5, 6, 7, 8, or 9, and we round it down if the last digit is a 1, 2, 3, or 4. Therefore:

$48.9% \rightarrow 49%$ $48.9 \rightarrow 49$

So our answer for the amount of seats filled within the stadium is $49\%$ .

Report an Error

Example Question #1 : Complex Fractions

Which of the following is equal to $\frac{\left(7+\frac{1}{x}\right)}{\left(14+\frac{2}{x}\right)}$ ?

Possible Answers:

x^2+14x+2

$\frac{x}{2}$

$\frac{1}{2}$

$\frac{1}{2x}$

$\frac{7x}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

First we must take the numerator of our whole problem. There is a fraction in the numerator with as the denominator. Therefore, we multiply the numerator of our whole problem by $\frac{x}{x}$ , giving us $7+\frac{1}{x}=7x+1$ .

Now we look at the denominator of the whole problem, and we see that there is another fraction present with as a denominator. So now, we multiply the denominator by $\frac{x}{x}$ , giving us $14+\frac{2}{x}=14x+2$ .

Our fraction should now read $\frac{(7x+1)}{(14x+2)}$ . Now, we can factor our denominator, making the fraction $\frac{(7x+1)}{(2(7x+1))}$ .

Finally, we cancel out 7x+1 from the top and the bottom, giving us $\frac{1}{2}$ .

Report an Error

Example Question #2 : Complex Fractions

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

Possible Answers:

$\frac{3}{2}$

$\frac{9}{2}$

$\frac{3}{2}$

Correct answer:

Explanation:

Rewrite $\frac{3}{\frac{3}{2}}$ into the following form:

$3\div \frac{3}{2}$

Change the division sign to a multiplication sign by flipping the 2nd term and simplify.

$3\cdot \frac{2}{3}=2$

Report an Error

Example Question #1 : Complex Fractions

Evaluate: $\frac{\frac{1}{x}}{x^2}$

Possible Answers:

$\frac{1}{2x^2}$

$\frac{1}{x+x^2}$

$\frac{1}{x}$

$\frac{1}{x^3}$

Correct answer:

$\frac{1}{x^3}$

Explanation:

The expression $\frac{\frac{1}{x}}{x^2}$ can be rewritten as:

$\frac{1}{x}\div{x^2}$

Change the division sign to a multiplication sign and take the reciprocal of the second term. Evaluate.

$\frac{1}{x}\cdot\frac{1}{x^2}=\frac{1}{x^3}$

Report an Error

Example Question #2 : Complex Fractions

Simplify: $\frac{\frac{1}{6}}{3} + \frac{\frac{1}{3}}{6}$

Possible Answers:

$\frac{1}{9}$

$\frac{1}{4}$

$\frac{2}{9}$

$\frac{5}{2}$

Correct answer:

$\frac{1}{9}$

Explanation:

The expression $\frac{\frac{1}{6}}{3} + \frac{\frac{1}{3}}{6}$ can be simplified as follows:

We can simplify each fraction by multiplying the numerator by the reciprocal of the denominator.

$\frac{1}{6}\div3 \rightarrow \frac{1}{6}\cdot \frac{1}{3}=\frac{1}{9}$

$\frac{1}{3}\div 6 \rightarrow \frac{1}{3}\cdot \frac{1}{6}=\frac{1}{9}$

From here we add our two new fractions together and simplify.

$=\frac{1}{18}+\frac{1}{18}=\frac{2}{18}=\frac{1}{9}$

Report an Error

Example Question #1 : Complex Fractions

Simplify the following:

$\frac{7+\frac{1}{3}}{\frac{3}{5}}$

Possible Answers:

$\frac{110}{9}$

$\frac{25}{4}$

$\frac{28}{5}$

$\frac{13}{7}$

$\frac{7}{10}$

Correct answer:

$\frac{110}{9}$

Explanation:

Begin by simplifying your numerator. Thus, find the common denominator:

$\frac{\frac{21}{3}+\frac{1}{3}}{\frac{3}{5}}$

Next, combine the fractions in the numerator:

$\frac{\frac{22}{3}}{\frac{3}{5}}$

Next, remember that to divide fractions, you multiply the numerator by the reciprocal of the denominator:

$\frac{22}{3}\times \frac{5}{3}$

Since nothing needs to be simplified, this is just:

$\frac{22}{3}\times \frac{5}{3}=\frac{110}{9}$

Report an Error

Example Question #1 : Complex Fractions

Simplify,

$\frac{\frac{ab}{c} + \frac{c}{a}}{\frac{b}{c}} - a$

Possible Answers:

$\frac{ab + c - a}{c^2}$

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

$\frac{c^2}{ab}$

$\frac{ba^2 + c}{ab}$

$\frac{b}{ac}$

Correct answer:

$\frac{c^2}{ab}$

Explanation:

Convert the numerators and denominators into single fractions, then simplify.

Start by finding the lowest common denominator in both the numerator and denominator of the complex fraction.

$\frac{\frac{ab}{c} + \frac{c}{a}}{\frac{b}{c}} - a$

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

$\frac{\frac{a^2b}{ac} + \frac{c^2}{ac}}{\frac{b}{c}} - a$

Add fractions with like denominators.

$\frac{\frac{a^2b + c^2}{ac}}{\frac{b}{c}} - a$

Simplify. Divide complex fractions by multiplying the numerator by the reciprocal of the denominator.

$\frac{\frac{a^2b + c^2}{ac}}{\frac{b}{c}} - a = \frac{a^2b + c^2}{ac}\cdot \frac{c}{b} - a = \frac{a^2b + c^2}{ab} - a$

Solve.

$\frac{a^2b + c^2}{ab} - a\left ( \frac{ab}{ab} \right ) = \frac{a^2b + c^2}{ab} - \frac{a^2b}{ab} = \frac{c^2}{ab}$

Report an Error

Example Question #2 : Complex Fractions

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

Possible Answers:

$-\frac{4}{5}$

$-\frac{1}{2}$

$\frac{1}{30}$

$\frac{1}{6}$

Correct answer:

$\frac{1}{30}$

Explanation:

The least common multiple can be found by multiplying the denominators: 2, 3, and 5. The common denominator of these numbers is 30. Multiply the numerator with what was multiplied to the denominator of each term, and then solve.

$\frac{3}{2}-\frac{2}{3}-\frac{4}{5}$

$\frac{3(3*5)}{2(3*5)}-\frac{2(2*5)}{3(2*5)}-\frac{4(2*3)}{5(2*3)}$

$\frac{45}{30}-\frac{20}{30}-\frac{24}{30}=\frac{1}{30}$

Report an Error

Example Question #3 : Complex Fractions

What is $\frac{\frac{4}{9}}{2} - \frac{\frac{5}{12}}3{}$ ?

Possible Answers:

$\frac{3}{18}$

$\frac{1}{36}$

$\frac{1}{12}$

$\frac{5}{36}$

$\frac{1}{4}$

Correct answer:

$\frac{1}{12}$

Explanation:

First, simplify both sides. $\frac{\frac{4}{9}}{2}$ becomes $\frac{4}{18}$ and $\frac{\frac{5}{12}}{3}$ becomes $\frac{5}{36}$ . The LCF between $\frac{4}{18}$ and $\frac{5}{36}$ is 36. Thus, $\frac{8}{36} - \frac{5}{36} = \frac{3}{36}.$ This simplifies to $\frac{1}{12}$ .

Report an Error

Example Question #2 : How To Subtract Complex Fractions

Simplify:

$\frac{4}{\frac{4-12}{6}}-\frac{\frac{3}{4}}{5}$

Possible Answers:

$\frac{-63}{20}$

$\frac{-15}{4}$

$\frac{-3}{7}$

$\frac{40}{3}$

$\frac{3}{7}$

Correct answer:

$\frac{-63}{20}$

Explanation:

Begin by simplifying the denominator of the first fraction:

$\frac{4}{\frac{4-12}{6}}-\frac{\frac{3}{4}}{5}=\frac{4}{\frac{-8}{6}}-\frac{\frac{3}{4}}{5}$

Now, remember that division of fractions is done by multiplying the numerator by the reciprocal of the denominator. Thus:

$\frac{4}{\frac{-8}{6}}-\frac{\frac{3}{4}}{5}=4*\frac{-6}{8}-\frac{3}{4}*\frac{1}{5}$

Simplify a bit:

$\frac{-3}{1}-\frac{3}{20}=\frac{-60}{20}-\frac{3}{20}=\frac{-63}{20}$

Report an Error

View ACT Math Tutors

Daniel
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Psychology.

View ACT Math Tutors

Sanchita
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Psychology.

View ACT Math Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

SAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Atlanta, GRE Courses & Classes in Houston, GMAT Courses & Classes in Denver, ISEE Courses & Classes in Chicago, SAT Courses & Classes in New York City, GMAT Courses & Classes in Boston, GMAT Courses & Classes in New York City, GRE Courses & Classes in San Diego, GRE Courses & Classes in Seattle

Popular Test Prep

LSAT Test Prep in Seattle, MCAT Test Prep in Boston, MCAT Test Prep in New York City, SAT Test Prep in Seattle, GMAT Test Prep in Boston, SAT Test Prep in San Francisco-Bay Area, GRE Test Prep in New York City, SSAT Test Prep in New York City, GRE Test Prep in Houston, SAT 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

ACT Math : Fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #11 : Fractions And Percentage

Example Question #1 : Complex Fractions

Example Question #2 : Complex Fractions

Example Question #1 : Complex Fractions

Example Question #2 : Complex Fractions

Example Question #1 : Complex Fractions

Example Question #1 : Complex Fractions

Example Question #2 : Complex Fractions

Example Question #3 : Complex Fractions

Example Question #2 : How To Subtract Complex Fractions

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: