Call Now to Set Up Tutoring:

(888) 888-0446

HSPT Math : Arithmetic

Study concepts, example questions & explanations for HSPT Math

Create An Account

All HSPT Math Resources

6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Multiply And Divide Fractions

Divide: $\frac{(\frac{2}{3})}{6}$

Possible Answers:

$\frac{1}{9}$

$\frac{2}{9}$

$\frac{1}{4}$

Correct answer:

$\frac{1}{9}$

Explanation:

Rewrite the expression using a division sign.

$\frac{2}{3}\div 6$

Convert the sign to a multiplication sign, and take the inverse of the second term.

$\frac{2}{3}\times \frac{1}{6} = \frac{1}{9}$

Report an Error

Example Question #41 : Problem Solving

A tree feet high casts a shadow 20 feet long at the same time a tree 30 feet high casts a shadow how many feet long? Give your answer in terms of .

Possible Answers:

$\frac{600}{M}$

$\frac{20M}{30}$

$\frac{M}{600}$

$\frac{30M}{20}$

Correct answer:

$\frac{600}{M}$

Explanation:

The ratio of the height of an object to the length of the shadow it casts at a point in time is the same for all objects, so, if we let the length of the shadow cast by the second tree be :

$\frac{30}{N} = \frac{M}{20}$

Set the cross-products equal to each other and solve for

$M \cdot N = 20 \cdot 30$

$M \cdot N = 600$

$M \cdot N\div M = 600 \div M$

$N = \frac{600}{M}$ , the correct choice.

Report an Error

Example Question #43 : Arithmetic

The length and width of a given make of car are 4.5 and 1.8 meters, respectively.

A scale model of this make of car will be feet long. In terms of , how wide will this scale model be?

Possible Answers:

$\frac{10}{81}L$

$\frac{81}{10}L$

$\frac{2}{5} L$

$\frac{5}{2} L$

Correct answer:

$\frac{2}{5} L$

Explanation:

The ratio of the width of the scale model to its length is the same as the comparable ratio for the actual car, so we can set up this equation:

$\frac{W}{L} = \frac{1.8}{4.5} = \frac{1.8 \cdot 10 }{4.5\cdot 10 }= \frac{18 }{45}= \frac{18 \div 9}{45 \div 9}=\frac{2}{5}$

$\frac{W}{L} \cdot L =\frac{2}{5}\cdot L$

$W=\frac{2}{5} L$

Report an Error

Example Question #42 : Problem Solving

Edna needs $1\frac{1}{2}$ cups of sugar to make 24 of her world-famous Oatmeal Chocolate Dynamite Cookies.

She has cups of sugar on hand. If the other ingredients are sufficiently plentiful, then in terms of , how many cookies can she make? (Note: the number of cookies need not be a multiple of 24.)

Possible Answers:

36N

$\frac{16}{N}$

16N

$\frac{36}{N}$

Correct answer:

16N

Explanation:

An easier way to look at the number of cookies Edna can make with her sugar is as follows:

$1\frac{1}{2}$ cups of sugar go into making 24 cookies, so

$1\frac{1}{2} \times 2 = 3$ cups of sugar go into making $24 \times 2 = 48$ cookies.

1 cup of sugar, therefore, goes into making $48 \div 3 = 16$ cookies.

cups go into making $16 \cdot N$ , or 16 N , cookies. This is the correct response.

Report an Error

Example Question #43 : Arithmetic

On a map, one half of an inch represents miles of real distance.

On the map, Lincoln County, which is perfectly rectangular, is four and one-fourth inches wide by three and three-fourths inches high. In terms of , give the area of Lincoln County in square miles.

Possible Answers:

$\frac{255}{4}N^{2}$

$255N^{2}$

$\frac{255}{16}N^{2}$

$\frac{255}{2}N^{2}$

Correct answer:

$\frac{255}{4}N^{2}$

Explanation:

The dimensions of Lincoln County on the map are $4 \frac{1}{4} = \frac{17}{4}$ inches by $3 \frac{3}{4} = \frac{15}{4}$ inches.

One half of an inch represents miles, so one whole inch represents twice this, or miles. Consequently,

$\frac{17}{4}$ inches represents $\frac{17}{4} \cdot 2N = \frac{17}{2} N$ miles, and

$\frac{15}{4}$ inches represents $\frac{15}{4} \cdot 2N = \frac{15}{2} N$ miles.

Therefore, in real distance, Lincoln County has dimensions $\frac{17}{2} N$ miles and $\frac{15}{2} N$ miles, and the area is the product of these two, or

$\frac{17}{2} N \cdot \frac{15}{2} N = \frac{255}{4}N^{2}$ .

Report an Error

Example Question #41 : Arithmetic

One of Floyd's World Famous Ooey Gooey Butter Cakes requires two and one-half cups of flour and four eggs, among other ingredients.

Floyd wants to make seven of these cakes for a wedding. He has sixteen cups of flour on hand as well as three dozen eggs. Assuming he has enough of all other ingredients, can Floyd make the seven cakes he wants to make?

Possible Answers:

No, because he does not have enough eggs.

No, because he does not have enough flour or enough eggs.

Yes.

No, because he does not have enough flour.

Correct answer:

No, because he does not have enough flour.

Explanation:

In order to make seven butter cakes, Floyd must use

$4 \times 7 = 28$ eggs.

Floyd has three dozen, or 36, eggs on hand, so he has enough eggs.

Floyd must use

$2 \frac{1}{2} \times 7 = \frac{5}{2} \times \frac{7}{1} = \frac{35}{2} = 17 \frac{1}{2}$ cups of flour.

Floyd has 16 cups on hand, so he does not have enough flour.

Report an Error

Example Question #45 : Problem Solving

$3\frac{1}{2 }\times 2\frac{2}{3}$

Possible Answers:

$9\frac{2}{3}$

$9\frac{1}{3}$

$6\frac{1}{3}$

$6\frac{2}{3}$

Correct answer:

$9\frac{1}{3}$

Explanation:

The formula for multiplication of fractions is:

$\frac{a}{b\ }\times \frac{c}{d} =\frac{ac}{bd}$

Where $b\neq 0$ and $d\neq 0.$

Convert each mixed number to an improper fraction; then multiply.

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

$2\frac{2}{3} = \frac{(3\times 2) +2}{3} = \frac{8}{3}$

It doesn't matter if the denominators are not the same. Just multiply the numerators, then multiply the denominators and simplify.

$\frac{7}{2} \times \frac{8}{3} = \frac{7\times 8}{2\times 3} = \frac{56}{6}$

Convert the improper fraction back to a mixed number by dividing the numerator by the denominator.

$56\div6 = 9\frac{2}{6}$

Simplify by dividing the numerator and denominator of the fraction part of the mixed number by the GCF or Greatest Common Factor which is 2.

$\frac{2\div 2}{6\div2 } = \frac{1}{3}$

$9 \frac{2}{6}$ reduced to simplest form is $9\frac{1}{3}.$

To simplify, divide the numerator and the denominator by the GCF or the greatest common factor, which is 15.

$-\frac{15\div 15}{30\div 15} =-\frac{1}{2}$

Report an Error

Example Question #12 : How To Multiply And Divide Fractions

$\frac{4}{9} \times\frac{3}{5}$

Possible Answers:

$\frac{2}{3}$

$\frac{1}{4}$

$\frac{7}{15}$

$\frac{4}{15}$

Correct answer:

$\frac{4}{15}$

Explanation:

The formula for multiplication of fractions is:

$\frac{a}{b\ }\times \frac{c}{d} =\frac{ac}{bd}$

Where $b\neq 0$ and $d\neq 0.$ It doesn't matter if the denominators are not the same. Just multiply the numerators, then multiply the denominators and simplify.

$\frac{4}{9\ }\times \frac{3}{5} =\frac{4\times 3}{9\times 5}$

$\frac{4\times 3}{9\times 5} = \frac{12}{45}$

To simplify, divide the numerator and the denominator by the GCF or the greatest common factor, which is 3.

$\frac{12\div 3}{45\div 3} =\frac{4}{15}$

Report an Error

Example Question #12 : How To Multiply And Divide Fractions

$6 \frac{8}{9}\times\frac{3}{8}$

Possible Answers:

$6\frac{1}{3}$

$2\frac{1}{2}$

$6\frac{3}{4}$

$2\frac{7}{12}$

Correct answer:

$2\frac{7}{12}$

Explanation:

The formula for multiplication of fractions is:

$\frac{a}{b\ }\times \frac{c}{d} =\frac{ac}{bd}$

Where $b\neq 0$ and $d\neq 0.$ It doesn't matter if the denominators are not the same. Just multiply the numerators, then multiply the denominators and simplify.

Convert any mixed number (whole number and fraction) to an improper fraction:

$6\frac{8}{9} = \frac{(9\times6)+8}{9} = \frac{62}{9}$

$\frac{62}{9 }\times \frac{3}{8} = \frac{62\times 3}{9\times 8}$

$\frac{186}{72} = 2\frac{42}{72}$

To simplify, divide the numerator and the denominator by the GCF, or the greatest common factor, which is 6.

$2\frac{42}{72} = 2\frac{42\div 6}{72\div 6} =$

$2\frac{7}{12}$

Report an Error

Example Question #22 : Fractions

What is the area of a rectangle with $l =3\frac{5}{9}$ cm and a $w = 2 \frac{1}{4}$ cm?

Possible Answers:

$8cm^{2}$

$8\frac{1}{2}cm^{2}$

$9cm^{2}$

$5 \frac{6}{13}cm^{2}$

Correct answer:

$8cm^{2}$

Explanation:

The formula for Area of a rectangle is $A = l\times w$ , where l = length and w = width.

To solve $3\frac{5}{9} \times 2\frac{1}{4}$ , first convert both mixed numbers to improper fractions.

$3\frac{5}{9} = \frac{(9 \times 3)+5}{9} = \frac{32}{9}$

$2\frac{1}{4} = \frac{(4\times 2) +1}{2} = \frac{9}{2}$

Then multiply the numerators and the denominators. Simplify.

$\frac{32}{9} \times \frac{9}{4} =\frac{32\times 9}{9\times 4}$

Because there is a 9 in the numerator and a 9 in the denominator the nines cancel each other out, and you are left with:

$\frac{32}{4} = 8$

Area is 2-dimensional: it has a length and a width. Area is measured in square units.

The area of the rectangle is $8cm^{2}$ .

Report an Error

View Tutors

Mikhail
Certified Tutor

Stony Brook University, Bachelor of Science, Biology, General. American University of the Caribbean School of Medicine, Curre...

View Tutors

Kaitlyn
Certified Tutor

Fairfield University, Bachelor of Science, Biology, General. NUI Galway Ireland, Master of Science, Neuroscience.

View Tutors

Usman
Certified Tutor

New York University, Bachelor in Arts, Political Science and Government.

All HSPT Math Resources

6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

LSAT Tutors in Los Angeles, MCAT Tutors in Los Angeles, Math Tutors in Chicago, Chemistry Tutors in Dallas Fort Worth, Math Tutors in Seattle, Physics Tutors in San Francisco-Bay Area, Statistics Tutors in Los Angeles, English Tutors in San Diego, Biology Tutors in Boston, GMAT Tutors in Los Angeles

Popular Courses & Classes

LSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Denver, MCAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Philadelphia, GMAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Chicago, GRE Courses & Classes in Phoenix, SSAT Courses & Classes in Houston, ACT Courses & Classes in Denver, ACT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

SSAT Test Prep in Miami, ISEE Test Prep in San Diego, GMAT Test Prep in Los Angeles, MCAT Test Prep in Dallas Fort Worth, ACT Test Prep in Miami, LSAT Test Prep in Miami, GMAT Test Prep in Philadelphia, GMAT Test Prep in Seattle, MCAT Test Prep in Boston, LSAT Test Prep in San Francisco-Bay Area

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

HSPT Math : Arithmetic

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1 : How To Multiply And Divide Fractions

Example Question #41 : Problem Solving

Example Question #43 : Arithmetic

Example Question #42 : Problem Solving

Example Question #43 : Arithmetic

Example Question #41 : Arithmetic

Example Question #45 : Problem Solving

Example Question #12 : How To Multiply And Divide Fractions

Example Question #12 : How To Multiply And Divide Fractions

Example Question #22 : Fractions

All HSPT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: