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Algebra 1 : Converting Measurements

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Example Question #11 : Converting Measurements

On a faraway planet, the measurement of distance has been warped, so that one foot contains only eight inches, instead of the twelve inches it takes to equal one foot here on Earth. On this faraway planet, how many inches are in 3.5 feet?

Possible Answers:

42in

30in

24in

32in

28in

Correct answer:

28in

Explanation:

Use a proportion to answer this question, keeping in mind that one foot is eight inches on this faraway planet.

$\frac{1 ft}{8 inches} = \frac{3.5ft}{x}$

Cross-multiply and simplify.

(x)(1ft)=(8in)(3.5ft)

x=28in

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Example Question #11 : Converting Measurements

What is the value of 4.5 meters per second in kilometers per hour?

Possible Answers:

$16.2\, \frac{km}{h}$

$9.0\, \frac{km}{hr}$

$13.5\, \frac{km}{hr}$

$1.3\, \frac{km}{hr}$

$45\, \, \frac{km}{hr}$

Correct answer:

$16.2\, \frac{km}{h}$

Explanation:

This conversion has two components: converting meters into kilometers and converting seconds into hours. Let's focus on seconds first. Because there are 3600 seconds in one hour, we need to multiply $\frac{4.5\ m}{1\ s}\cdot \frac{3600\ s}{1\ hr}$

giving us

$\frac{16,200\ m}{hr}$

Next, since there are 1000 meters in one kilometer, we multiply $\frac{16,200\ m}{1\ hr}\cdot \frac{1\ km}{1000\ m}$

giving us a final answer of 16.2.

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Example Question #11 : Converting Measurements

A rectangle has dimensions 56 inches by 28 inches. Write its area in square feet.

Possible Answers:

$9 \frac{4}{9} \textrm{ ft}^{2}$

$9 \frac{8}{9} \textrm{ ft}^{2}$

$10 \frac{8}{9} \textrm{ ft}^{2}$

$8 \frac{1}{9} \textrm{ ft}^{2}$

$9 \frac{1}{9} \textrm{ ft}^{2}$

Correct answer:

$10 \frac{8}{9} \textrm{ ft}^{2}$

Explanation:

12 inches make a foot, so we can convert the dimensions as follows:

$56 \textrm{ in }\div \frac{12 \textrm{ in }}{1 \textrm{ ft }} = \frac{56}{12} \textrm{ ft }$ ;

$\frac{56}{12} = \frac{56 \div 4}{12 \div 4}= \frac{14}{3} \textrm{ ft }$

$28 \textrm{ in }\div \frac{12 \textrm{ in }}{1 \textrm{ ft }} = \frac{28}{12} \textrm{ ft }$ ;

$\frac{28}{12} = \frac{28 \div 4}{12 \div 4}= \frac{7}{3} \textrm{ ft }$

Now multiply these dimensions to get the area in square feet:

$\frac{14}{3} \cdot \frac{7}{3} = \frac{98}{9} = 10 \frac{8}{9} \textrm{ ft}^{2}$

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Example Question #11 : Converting Measurements

Convert 42.6 inches to meters:

1 in = 2.54 cm

1 m = 100 cm

Possible Answers:

$0.17\ m$

$1678\ m$

$1.08\ m$

$108\ m$

Correct answer:

$1.08\ m$

Explanation:

$\frac{42.6in}{1}\times \frac{2.54cm}{1in}\times\frac{1m}{100cm}=1.08m$

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Example Question #15 : Converting Measurements

1 mile = 5,280 feet

Kevin ran 10,000 feet on his 30-minute morning run. If he kept up that pace, how many miles would Kevin run in 1 hour? (to two decimal places)

Possible Answers:

20,000

3.79

2.00

0.01

1.89

Correct answer:

3.79

Explanation:

Set up an equation that says 10,000 feet per 30 minutes equals (unknown) miles in one hour, like below.

$\frac{10,000}{30}=\frac{x}{1}$

Multiply the left side of the equation by the conversion rates to change feet/minute to miles/hour.

$\frac{10,000}{30}\times\frac{1}{5280}\times\frac{60}{1}=\frac{600,000}{158,400}=3.79$

Check if this answer makes sense. There are 5,280 feet in a mile so 10,000 feet is a bit less than two miles. 30 minutes is half an hour so 20,000 should be a bit less than four miles.

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Example Question #16 : Converting Measurements

Convert three yards to inches.

Possible Answers:

108

180

Correct answer:

108

Explanation:

To solve this problem, we need to know the conversions between yards to feet, and feet to inches. Write their correct conversions.

$1 \textup{ yard}= 3\textup{ feet}$

$1\textup{ foot}= 12 \textup{ inches}$

Convert three yards to feet.

$3 \textup{ yards}\left(\frac{3 \textup{ feet}}{1 \textup{ yard}}\right)= 9 \textup{ feet}$

Convert nine feet to inches.

$9 \textup{ feet}\left(\frac{12 \textup{ inches}}{1 \textup{ foot}}\right)= 108\textup{ inches}$

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Example Question #11 : Converting Measurements

Convert feet to inches.

Possible Answers:

0.5

Correct answer:

Explanation:

We know inches make up foot. Since we are looking for inches in feet, we can write a proportion.

$\frac{1\ foot}{12\ inches}=\frac{2\ feet}{x\ inches}$

Cross-multiply.

$(x\ inches)(1\ foot)=(2\ feet)(12\ inches)$

Divide each side by foot.

$x\ inches= 2(12\ inches)$

$x=24\ inches$

Therefore, $2\ feet = 24\ inches$ .

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Example Question #18 : Converting Measurements

Convert inches to feet.

Possible Answers:

288

576

Correct answer:

Explanation:

We know inches make up foot. Since we are looking for feet in inches, we can write a proportion.

$\frac{1\ foot}{12\ inches}=\frac{x\ feet}{48\ inches}$

Cross-multiply.

$(x\ feet)(12\ inches)=(1\ foot)(48\ inches)$

Divide both sides by inches.

$x\ feet=4(1\ foot)$

Multiply.

$x=4\ feet$

Therefore, $48\ inches=4\ feet$ .

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Example Question #19 : Converting Measurements

Convert pounds to ounces.

Possible Answers:

0.375

Correct answer:

Explanation:

We know ounces make up pound. Since we are looking for pounds in ounces, we can write a proportion.

$\frac{1\ pound}{16\ ounces}=\frac{6\ pounds}{x\ ounces}$

Cross-multiply.

$(x\ ounces)(1\ pound)=(16\ ounces)(6\ pounds)$

Divide each side by pound.

$x\ ounces=6(16\ ounces)$

$x=96\ ounces$

Therefore, $6\ pounds=96\ ounces$ .

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Example Question #20 : Converting Measurements

Convert liters to milliliters.

Possible Answers:

3000

30000

300

Correct answer:

3000

Explanation:

We know 1000 milliliters make up liter. Since we are looking for liters in milliliters, we can write a proportion.

$\frac{1\ liter}{1000\ milliliters}=\frac{3\ liters}{x\ milliliters}$

Cross-multiply.

$(x\ milliliters)(1\ liter)=(3\ liters)(1000\ milliliters)$

Divide by liter.

$x\ milliliters=3(1000\ milliliters)$

$x=3000\ milliliters$

Therefore, $3\ liters=3000\ milliliters$ .

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Algebra 1 : Converting Measurements

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #11 : Converting Measurements

Example Question #11 : Converting Measurements

Example Question #11 : Converting Measurements

Example Question #11 : Converting Measurements

Example Question #15 : Converting Measurements

Example Question #16 : Converting Measurements

Example Question #11 : Converting Measurements

Example Question #18 : Converting Measurements

Example Question #19 : Converting Measurements

Example Question #20 : Converting Measurements

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