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Algebra 1 : Converting Measurements

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Example Questions

Example Question #81 : Converting Measurements

Convert three inches to a foot.

Possible Answers:

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{36}$

$\frac{1}{8}$

Correct answer:

$\frac{1}{4}$

Explanation:

There are twelve inches in a foot.

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

Multiply the given dimension by the conversion.

$3\textup{ inches }(\frac{1\textup{ foot }}{12\textup{ inches}}) = \frac{3}{12}\textup{ foot}$

Reduce the fraction.

The answer is: $\frac{1}{4}\textup{ foot}$

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Example Question #81 : Converting Measurements

Convert four inches to yards.

Possible Answers:

$\frac{2}{7}$

$\frac{1}{12}$

$\frac{1}{18}$

$\frac{1}{9}$

$\frac{2}{9}$

Correct answer:

$\frac{1}{9}$

Explanation:

Before we can convert this, we will need the conversion factors from inches to feet and feet to yards.

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

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

Multiply four inches with the dimensional analyses to get the final dimension in yards.

$4\textup{ inches}( \frac{ 1\textup{ foot}}{12\textup{ inches }})(\frac{1\textup{ yard}}{3 \textup{ feet}})$

The feet and inches dimensions will cancel and yards will be the only dimension.

Simplify the expression.

$4( \frac{ 1}{12})(\frac{1\textup{ yard}}{3 }) = \frac{4 \textup{ yard}}{36 } = \frac{1}{9} \textup{ yard}$

The answer is: $\frac{1}{9}$

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Example Question #82 : Converting Measurements

Convert 64 inches to feet.

Possible Answers:

$\frac{1}{768}$

768

$\frac{3}{16}$

$\frac{16}{3}$

$\frac{75}{4}$

Correct answer:

$\frac{16}{3}$

Explanation:

There are 12 inches in a foot. Set up a proportion.

$\frac{12\textup{ inches}}{1\textup{ foot}} = \frac{64\textup{ inches}}{x\textup{ feet}}$

Cross multiply. The dimensions will cancel and we will be solving for the unknown variable.

12x=64

Divide by 12 on both sides.

$x=\frac{64}{12}$

Reduce the fraction by writing out the factors.

$x=\frac{64}{12} =\frac{4\times 4 \times 4 }{4\times 3 }$

Cancel the four and simplify.

The answer is: $x= \frac{16}{3}$

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Example Question #84 : Converting Measurements

Pecans can be purchased in bulk for $8.50 per pound at Charlie's grocery; the weight of the pecans purchased need not be a whole number of pounds. David has dollars on hand and wants to purchase as many pecans as he can afford. In terms of , how many ounces can he purchase?

Possible Answers:

$\frac{N}{272}$

272N

$\frac{N}{126}$

$\frac{17N} {32}$

$\frac{32N} {17}$

Correct answer:

$\frac{32N} {17}$

Explanation:

David has dollars and can purchase pecans at $8.50, or $8.5 = 8 \frac{1}{2} = \frac{17}{2}$ dollars, per pound. He can purchase

$N \div \frac{17}{2} = N \cdot \frac{2} {17} = \frac{2N} {17}$

pounds of pecans for dollars.

Since 16 ounces are equal to one pound, this converts to

$\frac{2N} {17} \cdot 16 = \frac{32N} {17}$

ounces of pecans.

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Example Question #83 : Converting Measurements

Danny drove miles in two hours. What was his average speed in feet per second?

Possible Answers:

$\frac{11}{60} N$

$\frac{15}{11} N$

None of the other responses gives a correct answer.

$\frac{11}{15} N$

$\frac{60}{11} N$

Correct answer:

$\frac{11}{15} N$

Explanation:

One mile is equal to 5,280 feet; one hour is equal to 3,600 seconds.

Danny drove miles, which is equal to 5,280N feet, in two hours, or $2 \cdot 3,600 = 7,200$ seconds. divide the distance by the time to get the rate:

$\frac{5,280N}{7,200} = \frac{5,280}{7,200} N = \frac{5,280 \div 480 }{7,200\div 480 } N =\frac{11}{15} N$ feet per second.

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Example Question #81 : Converting Measurements

A board comprises four segments, each of length 40 centimeters. What is the total length of the board in meters?

Possible Answers:

0.16 meters

1.6 meters

0.01 meters

0.1 meters

1 meter

Correct answer:

1.6 meters

Explanation:

$40 \times 4 = 160$ , so the board is 160 centimeters long. One meter is equal to 160 centimeters, so divide by 100 to convert to meters:

$160 \div 100 =1.6$ meters, the correct choice.

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Example Question #82 : Converting Measurements

One inch converts to 2.54 centimeters. Quinn is 5 feet, 6 inches tall. Which of the following is the closest to his height in meters?

Possible Answers:

1.6 meters

1.9 meters

1.7 meters

2 meters

1.8 meters

Correct answer:

1.7 meters

Explanation:

5 feet, 6 inches converts to $5 \times 12 + 6 = 60+6 = 66$ inches. Multiply this by conversion factor 2.54 to convert to centimeters:

$66 \times 2.54 = 167.64$ centimeters.

One meter converts to 100 centimeters, so divide by 100:

$167.64 \div 100 = 1.6764$ meters.

This rounds to 1.7 meters, making this the correct choice.

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Example Question #83 : Converting Measurements

Four of the following measurements are equal to one another. Which choice does not refer to the same length as the other four?

Possible Answers:

7 kilometers

7,000,000 millimeters

7,000 meters

700 decimeters

700,000 centimeters

Correct answer:

700 decimeters

Explanation:

One kilometer converts to 1,000 meters, so 7 kilometers converts to

$7 \times 1,000 = 7,000$ meters.

One meter converts to 10 decimeters, 100 centimeters, and 1,000 millimeters, so 7,000 meters converts to

$7,000 \times 10 = 70,000$ decimeters,

$7,000 \times 100 = 700,000$ centimeters,

and

$7,000 \times 1,000 = 7,000,000$ millimeters.

Therefore, 7 kilometers, 7,000 meters, 700,000 centimeters, and 7,000,000 millimeters refer to the same length. This length is equal to 70,000 decimeters, not 700 decimeters, 700 decimeters is the "odd man out" and is the correct choice.

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Example Question #1321 : Linear Equations

A gasoline tank holds quarts. If gasoline costs $2.10 per gallon, then how many dollars, in terms of , does it cost to fill the tank, assuming it started out empty?

Possible Answers:

8.4N

1.05N

4.2N

0.525N

Correct answer:

0.525N

Explanation:

One gallon is equal to four quarts, so divide the number of quarts by 4 to convert to gallons. This means the tank has capacity $\frac{N}{4}$ gallons. Multiply this by $2.10, the price per gallon:

$\frac{N}{4} \cdot 2.10 = \frac{2.10 N}{4} = 0.525N$

This is the cost in dollars to fill the tank, so this is the correct choice.

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Example Question #81 : Converting Measurements

Convert 2.5 miles to feet.

Possible Answers:

15485

12000

14560

12640

13200

Correct answer:

13200

Explanation:

There are 5280 feet in one mile.

Write the dimensional analysis and multiply by the given distance in miles. We will want to have feet as the designated unit.

$2.5 \textup{ miles }(\frac{5280 \textup{ feet}}{1 \textup{ mile}})= 13200 \textup{ feet}$

The answer is: $13200 \textup{ feet}$

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Algebra 1 : Converting Measurements

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #81 : Converting Measurements

Example Question #81 : Converting Measurements

Example Question #82 : Converting Measurements

Example Question #84 : Converting Measurements

Example Question #83 : Converting Measurements

Example Question #81 : Converting Measurements

Example Question #82 : Converting Measurements

Example Question #83 : Converting Measurements

Example Question #1321 : Linear Equations

Example Question #81 : Converting Measurements

All Algebra 1 Resources

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