Call Now to Set Up Tutoring:

(888) 888-0446

HSPT Math : How to multiply and divide fractions

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 #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 #11 : How To Multiply And Divide Fractions

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.

Yes.

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

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 #41 : Arithmetic

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

Possible Answers:

$\frac{4}{15}$

$\frac{7}{15}$

$\frac{2}{3}$

$\frac{1}{4}$

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 #45 : Problem Solving

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

Possible Answers:

$6\frac{3}{4}$

$6\frac{1}{3}$

$2\frac{1}{2}$

$2\frac{7}{12}$

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 #12 : How To Multiply And Divide 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:

$9cm^{2}$

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

$8cm^{2}$

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

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

Example Question #51 : Hspt Mathematics

The gas tank in Renee's mustang is filled to capacity at $13\frac{1}{2}$ gallons. She used $\frac{2}{3}$ of a tank of gas to take a drive to the shore. How much gas did it take to drive to the shore?

Possible Answers:

gallons

$8 \frac{1}{2}$ gallons

$9 \frac{1}{2}$ gallons

Correct answer:

gallons

Explanation:

To solve this word problem, multiply the fractions. First convert any mixed number to an improper fraction:

$13\frac{1}{2} = \frac{(2\times13 )+1}{2} = \frac{27}{2}$

Next, multiply the numerators and the denominators of both improper fractions.

$\frac{27}{2} \times\frac{2}{3} = \frac{54}{6} = 9$

gallons of gas was consumed on Renee's trip to the shore.

Report an Error

Example Question #51 : Problem Solving

The height or h of a triangle is $\frac{2}{3}$ inches. The base or b = $1\frac{1}{8}$ inches. What is the area of the triangle?

Possible Answers:

$A =\frac{2}{3}in^{2}$

$A =\frac{1}{2}in^{2}$

$A=\frac{5}{8}in^{2}$

$A =\frac{3}{8} in^{2}$

Correct answer:

$A =\frac{3}{8} in^{2}$

Explanation:

The formula for the Area of a triangle is:

$A= \frac{1}{2}(b\times h)$ where b represents the base and h represents height.

Convert any mixed numbers to improper fractions.

$1\frac{1}{8} = \frac{(8\times 1)+1}{8} = \frac{9}{8}$

Plug in the values for the base and the height into the formula; multiply.

$A = \frac{1}{2} (\frac{2}{3} \times \frac{9}{8})$

$A = \frac{(1\times 2\times 9)}{(2\times 3\times 8}) = \frac{18}{48}$

Reduce to simplest form by dividing the numerator and the denominator by the Greatest Common Factor (GCF) of 18 and 48, which is 6.

$18\div6 =3$

$48\div6 = 8$

Because a triangle is two-dimensional, the answer must be represented in square units.

$A = \frac{3}{8} in^{2}$

Report an Error

Example Question #52 : Problem Solving

A rectangular prism has a length of $2\frac{1}{2}$ cm, a width of $1\frac{1}{3}$ cm, and a height of $\frac{3}{4}$ cm. What is the volume of this rectangular prism?

Possible Answers:

$2\frac{3}{4}cm^{3}$

$3cm^{3}$

$2\frac{1}{2}cm^{3}$

$2\frac{1}{4}cm^{3}$

Correct answer:

$2\frac{1}{2}cm^{3}$

Explanation:

The formula for the Volume of a rectangular prism is: $V = l\times w \times h$ , where

l= length , w = width and h = height.

$V = 2\frac{1}{2} \times 1\frac{1}{3} \times \frac{3}{4}$

Convert mixed numbers (whole number and fraction) to improper fractions.

$2\frac{1}{2}= \frac{(2 \times 2)+1}{2} = \frac{5}{2}$

$1\frac{1}{3} = \frac{(3\times 1)+1}{3} = \frac{4}{3}$

$V = \frac{5}{2} \times \frac{4}{3}\times\frac{3}{4}$

$V = \frac{60}{24} cm^{3}$

$V = 2\frac{12}{24}cm^{3}$

Reduce to simplest form by dividing the numerator and the denominator of the fraction by the Greatest Common Factor of 12 and 24, which is 12.

A rectangular prism is a 3-dimensional shape, therefore the measurement must be expressed in cubic units.

$V = 2\frac{1}{2}cm^{3}$

Report an Error

Example Question #12 : How To Multiply And Divide Fractions

$-\frac{5}{6 }\times \frac{3}{5}$

Possible Answers:

$-\frac{5}{6}$

$-\frac{1}{2}$

$\frac{7}{11}$

$-\frac{1}{6}$

Correct answer:

$-\frac{1}{2}$

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.

$-\frac{5}{6\ }\times \frac{3}{5} =\frac{-5\times 3}{6\times 5}$

$\frac{-5\times 3}{6\times 5} = -\frac{15}{30}$ A negative times a positive is a negative.

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

View Tutors

Danielle
Certified Tutor

View Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Tutors

Colton
Certified Tutor

Texas State University-San Marcos, Bachelor of Science, Mathematics.

All HSPT Math Resources

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

Popular Subjects

SAT Tutors in Boston, LSAT Tutors in Los Angeles, Spanish Tutors in Los Angeles, Algebra Tutors in Boston, Physics Tutors in Houston, LSAT Tutors in Philadelphia, French Tutors in Philadelphia, Statistics Tutors in Boston, SAT Tutors in Washington DC, Biology Tutors in Dallas Fort Worth

Popular Courses & Classes

SAT Courses & Classes in Denver, Spanish Courses & Classes in Houston, MCAT Courses & Classes in Phoenix, SSAT Courses & Classes in New York City, SAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Phoenix, ISEE Courses & Classes in Washington DC, GRE Courses & Classes in Boston, SSAT Courses & Classes in Phoenix, ISEE Courses & Classes in Los Angeles

Popular Test Prep

GRE Test Prep in San Diego, SAT Test Prep in Denver, GRE Test Prep in Los Angeles, SSAT Test Prep in Washington DC, SSAT Test Prep in Chicago, SSAT Test Prep in New York City, SSAT Test Prep in Houston, GMAT Test Prep in Washington DC, LSAT Test Prep in Houston, ISEE Test Prep in Dallas Fort Worth

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 : How to multiply and divide fractions

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #43 : Arithmetic

Example Question #11 : How To Multiply And Divide Fractions

Example Question #45 : Problem Solving

Example Question #41 : Arithmetic

Example Question #45 : Problem Solving

Example Question #12 : How To Multiply And Divide Fractions

Example Question #51 : Hspt Mathematics

Example Question #51 : Problem Solving

Example Question #52 : Problem Solving

Example Question #12 : How To Multiply And Divide Fractions

All HSPT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: