We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Fractions and Percentage

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

← Previous 1 2 Next →

Example Question #1 : Fractions

$\frac{5.5}{10}$ is equivalent to what percentage?

Possible Answers:

4.5%

5.5%

55%

15%

45%

Correct answer:

55%

Explanation:

Divide the fraction out to get the decimal

5.5 / 10 = 0.55

To find the percentage, shift the decimal point two to the right = 55%

Report an Error

Example Question #1 : Fractions And Percentage

Write $\frac{27}{25}$ as a percent

Possible Answers:

$93\%$

$127\%$

$108\%$

$27\%$

$8\%$

Correct answer:

$108\%$

Explanation:

To find a percent from a fraction you can either divide the number on your calculator and multiply by 100:

$100\cdot\frac{27}{25}=108$

or you can just multiply the numerator and denominator by the same number that makes the denominator equal to 100 (because a % is just #/100):

$\frac{27}{25}\cdot\frac{4}{4}=\frac{108}{100}$

Report an Error

Example Question #7 : Fractions

One half of a group of professors is made up of mathematicians, and one fourth of the remaining portion is made up of philosophers. The remaining portion is made up of sociologists. If there are 464 professors in the room, how many are sociologists?

Possible Answers:

110

146

174

Correct answer:

174

Explanation:

To begin, remember with percentages that "of" means multiplication and "is" means "equals." Now, we know that one fourth of the remaining half are philosophers. This means that he philosophers really are:

$\frac{1}{4}*\frac{1}{2}=\frac{1}{8}$

So, there are $1-\frac{1}{2}-\frac{1}{8}$ sociologists as a percentage. This is:

$1-\frac{1}{2}-\frac{1}{8}=\frac{8}{8}-\frac{4}{8}-\frac{1}{8}=\frac{3}{8}$

Therefore, $\frac{3}{8}$ of the 464 are sociologists, or:

$\frac{3}{8}*464=174$ are sociologists.

Report an Error

Example Question #1 : Fractions

Convert the following fraction into a percent.

$\frac{2}{5}$

Possible Answers:

$40\%$

$25\%$

$36\%$

$20\%$

Correct answer:

$40\%$

Explanation:

To convert a fraction into a percent, make the denominator 100 and then the numerator will be the percent. Thus,

$\frac{2}{5}*\frac{20}{20}=\frac{40}{100}=40\%$

Report an Error

Example Question #1 : Fractions

On a 15,000 acre plot of land, there are acres in which deer live. What percentage of the land does this represent? Round to the nearest hundredth.

Possible Answers:

$0.04\%$

$0.01\%$

$0\%$

$0.25\%$

$0.05\%$

Correct answer:

$0.05\%$

Explanation:

For percentages, it is always easiest to translate into language that uses "is" and "of." "Is" means "equals" and "of" means "multiply." So, we have:

What percentage of 15,000 is ? This is the same as:

x * 15,000=7

Solving for , you get:

$x=\frac{7}{15000}=0.00046666666667$

Now, as a percent, this is equal to:

$0.00046666666667 * 100= 0.046666666667\%$

Rounding to the nearest hundredth, you have $0.05\%$ .

Report an Error

Example Question #1 : Fractions And Percentage

is $8\frac{1}{3} \%$ of , which is 35% of . All three are positive integers. In which range does the smallest possible value of X+Y+Z fall?

Possible Answers:

Between 700 and 800

Between 600 and 700

Between 300 and 400

Between 500 and 600

Between 400 and 500

Correct answer:

Between 300 and 400

Explanation:

is 35% of , so $Y = \frac{35}{100}Z = \frac{7}{20}Z$ .

is $8\frac{1}{3} \%$ of , so $X = \frac{8\frac{1}{3}}{100}Y = \frac{8\frac{1}{3}\times 3}{100 \times 3}Y = \frac{25}{300 }Y = \frac{1}{12}Y$ .

Consequently,

$X = \frac{1}{12}Y = \frac{1}{12} \cdot \frac{7}{20}Z = \frac{7}{240}Z$

The smallest integer can be is 240. If this happens,

$Y = \frac{7}{20}Z = \frac{7}{20} \cdot 240 = 84$

$X = \frac{7}{240} \cdot 240 = 7$

Their sum is

X + Y + Z = 7 + 84 + 240 = 331

The correct choice is that the sum is between 300 and 400.

Report an Error

Example Question #1391 : Act Math

is $16\frac{2}{3} \%$ of and $62\frac{1}{2} \%$ of ; all are positive integers. Give the smallest possible value of .

Possible Answers:

Correct answer:

Explanation:

is $16\frac{2}{3} \%$ of and $62\frac{1}{2} \%$ of , so

$A = \frac{16\frac{2}{3} }{100}B = \frac{16\frac{2}{3}\cdot 3 }{100 \cdot 3}B = \frac{50}{300}B = \frac{1}{6} B$ ,

so B = 6A .

$A = \frac{62\frac{1}{2} }{100}C = \frac{62\frac{1}{2} \cdot 2 }{100 \cdot 2}C= \frac{125}{200}C = \frac{5}{8} C$

so $C = \frac{8} {5}A$

must be divisible by 5, so the least possible value is 5 itself.

Report an Error

Example Question #1392 : Act Math

is $7\frac{1}{2} \%$ of . Which of the following expressions is equal to ?

Possible Answers:

$\frac{2M}{15}$

$\frac{3M}{40}$

$\frac{15M}{2}$

None of the other responses gives a correct answer.

$\frac{40M}{3}$

Correct answer:

$\frac{40M}{3}$

Explanation:

is $7\frac{1}{2} \%$ of , so

$M = \frac{7\frac{1}{2}}{100} \cdot N = \frac{7\frac{1}{2} \cdot 2}{100\cdot 2} \cdot N = \frac{15}{200} N = \frac{3}{40} N$

$N = \frac{40}{3}M = \frac{40M}{3}$

Report an Error

Example Question #1393 : Act Math

is $15 \frac{5}{8} \%$ of , which is 80% of . What percent of is ?

Possible Answers:

The correct answer is not given among the other responses.

$19\frac{17}{32} \%$

$12\frac{1}{2} \%$

$8 \%$

$5\frac{3}{25} \%$

Correct answer:

The correct answer is not given among the other responses.

Explanation:

is 80% of , so $N = \frac{80 }{100}P = \frac{4}{5}P$ .

Consequently, $P = \frac{5}{4}N$

is $15 \frac{5}{8} \%$ of , so $M = \frac{15 \frac{5}{8} }{100} N = \frac{15 \frac{5}{8} \cdot 8 }{100\cdot 8} N = \frac{5 }{32} N$

Consequently, $N = \frac{32} {5 }M$ .

$P = \frac{5}{4} \cdot\frac{32} {5 }M = \frac{32}{4}M = 8M$ , so

is 800% of . This is not one of the choices.

Report an Error

Example Question #1 : Fractions And Percentage

is $22\frac{1}{2} \%$ of .

$\frac{2}{M}$ is what percent of $\frac{5}{N}$ ?

Possible Answers:

The correct answer is not given among the other responses.

$177 \frac{7}{9} \%$

$56\frac{1}{4} \%$

$3,600\%$

$277\frac{7}{9} \%$

Correct answer:

$177 \frac{7}{9} \%$

Explanation:

is $22\frac{1}{2} \%$ of , so

$M = \frac{22\frac{1}{2}}{100} N= \frac{22\frac{1}{2}\cdot 2}{100\cdot 2} N= \frac{45}{200 } N= \frac{9}{40} N=\frac{9N}{40}$ ,

$\frac{1}{M} = \frac{40}{9N}$

and

$\frac{2}{M} = \frac{80}{9N}$

The question can be rewritten as

$\frac{80}{9N}$ is what percent of $\frac{5}{N}$ ?

The answer is

$\frac{\frac{80}{9N}}{\frac{5}{N}} \times 100 \%$

$=\left ( \frac{80}{9N} \div \frac{5}{N}} \right ) \times 100 \%$

$=\left ( \frac{80}{9N} \cdot \frac{N}{5} \right ) \times 100 \%$

$= \frac{16}{9 } \times 100 \%$

$= 177 \frac{7}{9} \%$

Report an Error

← Previous 1 2 Next →

View ACT Math Tutors

Yucheng
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Mechanical Engineering.

View ACT Math Tutors

Eklavya
Certified Tutor

Indira Gandhi National Open University, Bachelor, Physics.

View ACT Math Tutors

Emily
Certified Tutor

University of Maryland-College Park, Bachelor of Science, Education.

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

GMAT Courses & Classes in Chicago, MCAT Courses & Classes in Atlanta, Spanish Courses & Classes in Los Angeles, ISEE Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Miami, Spanish Courses & Classes in Washington DC, ACT Courses & Classes in Miami, Spanish Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Boston

Popular Test Prep

ISEE Test Prep in Dallas Fort Worth, GMAT Test Prep in Chicago, SSAT Test Prep in Atlanta, LSAT Test Prep in Phoenix, SSAT Test Prep in Philadelphia, GRE Test Prep in Los Angeles, MCAT Test Prep in Washington DC, SAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Washington DC, GMAT Test Prep in Los Angeles

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 and Percentage

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Fractions

Example Question #1 : Fractions And Percentage

Example Question #7 : Fractions

Example Question #1 : Fractions

Example Question #1 : Fractions

Example Question #1 : Fractions And Percentage

Example Question #1391 : Act Math

Example Question #1392 : Act Math

Example Question #1393 : Act Math

Example Question #1 : Fractions And Percentage

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: