We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Converting Measurements

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Converting Measurements

Harold has a (full) two liter bottle of soda in his refrigerator. He takes it out and pours eight-ounce glasses of soda for himself and each of his three friends that have come over. How many liters of soda are left in the bottle (rounded to two decimal places)?

1 liter = 33.814 fluid ounces

Possible Answers:

1.29L

0.95L

1.05L

0.71L

1.00L

Correct answer:

1.05L

Explanation:

Convert the two liters of soda into ounces.

2 * 33.814 = 67.628

Subtract the four eight-ounce glasses of soda that were poured.

67.628 - (4*8)=35.628

Convert the remaining ounces back into liters.

$35.628 * \frac{1}{33.814} = 1.05$

Alternatively, you could set it up as one equation and solve for , as shown below.

$x = 2 - [(8\times 4)\times\tfrac{1}{33.814}]$

x = 2 - 0.95

x=1.05

Report an Error

Example Question #1 : Converting Measurements

Convert 60 mph (miles per hour) into fps (feet per second).

Possible Answers:

$88\ fps$

$0.7\ fps$

$41\ fps$

$16\ fps$

$50\ fps$

Correct answer:

$88\ fps$

Explanation:

To replace hours with seconds, you must divide by 3600 (seconds in an hour), and to replace miles with feet you must multiply by 5280 (number of feet in a mile).

Report an Error

Example Question #1 : Converting Measurements

Edward is driving 225 miles to go home for Christmas vacation. The last time Edward took this trip, he drove miles per hour. How much shorter would Edward's trip be this time if he drives miles per hour?

Possible Answers:

$3\ \textup{hours}$

$1\ \textup{hour}$

$3\ \textup{hours and}\ 45\ \textup{minutes}$

$4\ \textup{hours}$

$45\ \textup{minutes}$

Correct answer:

$45\ \textup{minutes}$

Explanation:

This problem relies on the formula $\textup{distance = rate * time}$ , or d = rt .

Solving for in the case of both Edward's original trip and the trip Edward will take this time will give us the time each trip would take. The difference between these times is the answer.

The distance Edward travels is 225 miles. The rate at which he drives on the first trip is miles per hour. Remember that in writing out equations we can treat the word "per" as a division sign, so we express $60 \textup{ miles per hour}$ as $\frac{60 \ miles}{1 \ hour}$ . Solve for with these numbers in d = rt .

$225 \ miles = (\frac{60 \ miles}{1 \ hour}) * (t \ hours)$

$(225 \ miles) * (\frac{1 \ hour}{60 \ miles}) = (\frac{60 \ miles}{1 \ hour}) * (t \ hours) * (\frac{1 \ hour}{60 \ miles})$

$\frac{225}{60} \ hours = t \ hours$

$t = \frac{15}{4} \ hours = 3\tfrac{3}{4} \ hours$

To convert the remainder fraction of an hour into minutes, multiply it by $60 \ minutes \ per \ hour$ .

$\frac{3}{4} \ hours * \frac{60 \ minutes}{1 \ hour} = \frac{180}{4} \ minutes = 45 \ minutes$

So the total time for the original trip is hours and minutes.

Now use the same d = rt equation, but replace the miles per hour with miles per hour for the second trip.

$225 \ miles = (\frac{75 \ miles}{1 \ hour}) * (t \ hours)$

$(225 \ miles) * (\frac{1 \ hour}{75 \ miles}) = (\frac{75 \ miles}{1 \ hour}) * (t \ hours) * (\frac{1 \ hour}{75 \ miles})$

$\frac{225}{75} \ hours = t \ hours$

$t = 3 \ hours$

We now know the trip at miles per hour would be hours long. Subtracting this from the length of the original miles per hour trip gives us the amount of time by which this trip would be shorter than the original.

$(3 \ hours, 45 \ minutes) - (3 \ hours) = 45 \ minutes$

Report an Error

Example Question #2 : Converting Measurements

Albert is traveling at 70 kilometers per hour, Joseph is moving at 35 meters per second, and Katrina is moving at 1.9 kilometers per minute. Which person is traveling the fastest?

Possible Answers:

Katrina and Albert are tied for the fastest speed.

Joseph

All three individuals are traveling at the same speed.

Katrina

Albert

Correct answer:

Joseph

Explanation:

To compare these three different measurements, we need to convert them so they have the same units. Let's convert all three values into meters per second.

Multiplying 70 km/h by 1000 m/km gives us 70,000 meters per hour, and dividing that value by 3600 (since there are 3600 seconds in an hour) gives us 19.4. So, Albert is traveling at 19.4 meters per second.

We convert Katrina's speed in a similar way, multiplying 1.9 km/minute by 1000 m/km and then dividing by 60 (since there are 60 seconds in a minute). These calculations give us 31.67 m/s.

Since both of these values are slower than Joseph's speed of 35 m/s, Joseph is traveling the fastest.

Report an Error

Example Question #3 : Converting Measurements

The density of a substance is grams per cubic centimeter. In terms of , what is the mass, in kilograms, of one cubic meter of this substance?

Possible Answers:

$X \; \textrm{kg}$

$1,000,000X \; \textrm{kg}$

$\frac{1,000,000}{X} \; \textrm{kg}$

$\frac{1,000}{X} \; \textrm{kg}$

$1,000X \; \textrm{kg}$

Correct answer:

$1,000X \; \textrm{kg}$

Explanation:

1 meter is equal to 100 centimeters, so 1 cubic meter is equal to $100^{3} = 1,000,000$ cubic centimeters.

1,000,000 cubic centimeters has mass:

$1,000,000 \textrm{\;cm}^{3} \cdot X \frac{\textrm{g}}{\textrm{cm}^{3}} = 1,000,000X \textrm{\; g}$

1,000 grams are in a kilogram, so convert to kilograms by dividing this number by 1,000:

$1,000,000 X \div 1,000 = 1,000 X$

Report an Error

Example Question #4 : Converting Measurements

Three centimeters on a map represents 45 actual kilometers. In terms of , how many centimeters on the map represent actual kilometers?

Possible Answers:

$\frac{N}{135}$

15N

$\frac{135}{N}$

$\frac{N}{15}$

$\frac{15}{N}$

Correct answer:

$\frac{N}{15}$

Explanation:

Let be the number of map centimeters that represent kilometers.

Set up a proportion statement which equates two ratios, each of which compares map centimeters to actual kilometers represented. Then solve for

$\frac{x}{N} = \frac{3}{45}$

$\frac{x}{N} = \frac{1}{15}$

$\frac{x}{N} \cdot N = \frac{1}{15}\cdot N$

$x = \frac{N}{15}$

Report an Error

Example Question #5 : Converting Measurements

Three centimeters on a map represents 66 actual kilometers. In terms of , how many centimeters on the map represent actual kilometers?

Possible Answers:

22N

198N

$\frac{N}{22}$

$\frac{198}{N}$

$\frac{22}{N}$

Correct answer:

$\frac{N}{22}$

Explanation:

Let be the number of map centimeters that represent kilometers.

Set up a proportion statement which equates two ratios, each of which compares map centimeters to actual kilometers represented. Then solve for

$\frac{x}{N} = \frac{3}{66}$

$\frac{x}{N} = \frac{1}{22}$

$\frac{x}{N} \cdot N = \frac{1}{22}\cdot N$

$x = \frac{N}{22}$

Report an Error

Example Question #2 : Converting Measurements

Three centimeters on a map represents 66 actual kilometers. In terms of , how many actual kilometers are represented by centimeters on the map?

Possible Answers:

$\frac{22}{N}$

198N

$\frac{N}{22}$

$\frac{198}{N}$

22N

Correct answer:

22N

Explanation:

Let be the number of actual kilometers represented by map centimeters.

Set up a proportion statement which equates two ratios, each of which compares actual kilometers represented to map centimeters. Then solve for .

$\frac{x}{N} = \frac{66}{3}$

$\frac{x}{N} = 22$

$\frac{x}{N} \cdot N = 22 \cdot N$

x = 22N

Report an Error

Example Question #3 : Converting Measurements

Three centimeters on a map represents 45 actual kilometers. In terms of , how many actual kilometers are represented by centimeters on the map?

Possible Answers:

$\frac{N}{15}$

$\frac{15}{N}$

$\frac{N}{135}$

$\frac{135}{N}$

15N

Correct answer:

15N

Explanation:

Let be the number of actual kilometers represented by map centimeters.

Set up a proportion statement which equates two ratios, each of which compares actual kilometers represented to map centimeters. Then solve for .

$\frac{x}{N} = \frac{45}{3}$

$\frac{x}{N} = 15$

$\frac{x}{N} \cdot N = 15 \cdot N$

x = 15N

Report an Error

Example Question #5 : Converting Measurements

Daycare currently costs $240 per week. Starting next year, there will be a 15% increase in the cost of daycare. How much will one month of daycare cost?

Assume one month equals four weeks.

Possible Answers:

$\$976$

$\$244$

$\$276$

$\$1104$

Correct answer:

$\$1104$

Explanation:

15% is equal to $\small \frac{15}{100}$ , or 0.15. We can find the amount of the increase by multiplying the original cost by 0.15.

240*0.15=36

The new amount is the sum of the original amount and the increase.

$\small 240+36=276$

This gives us the new cost for one week. The cost for the new month will be four times this amount.

$\small 276*4=1104$

Report an Error

View Algebra Tutors

Ingrid
Certified Tutor

Northern Illinois University, Bachelor of Science, Elementary Education. Northern Illinois University, Master of Science, Cur...

View Algebra Tutors

Andrew
Certified Tutor

Cardiff Metropolitan University, Certificate, Mathematics Teacher Education.

View Algebra Tutors

Nathan
Certified Tutor

California Polytechnic State University, San Luis Obispo, Bachelor, Electrical Engineering.

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Miami, Calculus Tutors in New York City, French Tutors in Miami, ISEE Tutors in Philadelphia, Algebra Tutors in Philadelphia, Physics Tutors in Seattle, Spanish Tutors in Los Angeles, Algebra Tutors in Washington DC, GMAT Tutors in San Diego, GRE Tutors in Houston

Popular Courses & Classes

ACT Courses & Classes in New York City, SAT Courses & Classes in Houston, ISEE Courses & Classes in Chicago, ACT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Miami, SSAT Courses & Classes in San Diego, GMAT Courses & Classes in Boston, MCAT Courses & Classes in Los Angeles, GRE Courses & Classes in Phoenix

Popular Test Prep

GMAT Test Prep in Washington DC, ACT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Miami, ACT Test Prep in New York City, ISEE Test Prep in Chicago, MCAT Test Prep in Boston, GMAT Test Prep in Boston, SAT Test Prep in Los Angeles, SAT Test Prep in San Diego, MCAT Test Prep in San Diego

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 1 : Converting Measurements

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : Converting Measurements

Example Question #1 : Converting Measurements

Example Question #1 : Converting Measurements

Example Question #2 : Converting Measurements

Example Question #3 : Converting Measurements

Example Question #4 : Converting Measurements

Example Question #5 : Converting Measurements

Example Question #2 : Converting Measurements

Example Question #3 : Converting Measurements

Example Question #5 : Converting Measurements

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: