There are twelve inches in a foot. Write the dimensional analysis.

\(\displaystyle 12 \textup{ inches } = 1\textup{ foot}\)

To get an answer in feet, we will need to eliminate the inches dimension.

\(\displaystyle 54\textup{ inches}\left (\frac{1 \textup{ foot}}{12 \textup{ inches}} \right )\)

The answer is:  \(\displaystyle 4.5\textup{ feet}\)

There are twelve inches in a foot.   Write the dimensional analysis.

\(\displaystyle 12 \textup{ inches } = 1\textup{ foot}\)

To get an answer in feet, we will need to eliminate the inches dimension.

\(\displaystyle 60 \textup{ inches}(\frac{1 \textup{ foot}}{12 \textup{ inches}})\)

The answer is:  \(\displaystyle 5\textup{ feet}\)

There are twelve inches in a foot.

\(\displaystyle 12\textup{ inches} = 1\textup{ foot}\)

Multiply the given dimension by the conversion.

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

Reduce the fraction.

The answer is:  \(\displaystyle \frac{1}{4}\textup{ foot}\)

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

\(\displaystyle 12\textup{ inches }= 1\textup{ foot}\)

\(\displaystyle 3 \textup{ feet}= 1\textup{ yard}\)

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

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

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

Simplify the expression.

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

The answer is:  \(\displaystyle \frac{1}{9}\)

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

\(\displaystyle \frac{12\textup{ inches}}{1\textup{ foot}} = \frac{64\textup{ inches}}{x\textup{ feet}}\)

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

\(\displaystyle 12x=64\)

Divide by 12 on both sides.

\(\displaystyle x=\frac{64}{12}\)

Reduce the fraction by writing out the factors.

\(\displaystyle x=\frac{64}{12} =\frac{4\times 4 \times 4 }{4\times 3 }\)

Cancel the four and simplify.

The answer is:  \(\displaystyle x= \frac{16}{3}\)

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

\(\displaystyle N \div \frac{17}{2} = N \cdot \frac{2} {17} = \frac{2N} {17}\) 

pounds of pecans for \(\displaystyle N\)dollars.

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

\(\displaystyle \frac{2N} {17} \cdot 16 = \frac{32N} {17}\) 

ounces of pecans.

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

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

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

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

\(\displaystyle 160 \div 100 =1.6\) meters, the correct choice.

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

\(\displaystyle 66 \times 2.54 = 167.64\) centimeters.

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

\(\displaystyle 167.64 \div 100 = 1.6764\) meters.

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

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

\(\displaystyle 7 \times 1,000 = 7,000\) meters.

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

\(\displaystyle 7,000 \times 10 = 70,000\) decimeters,

\(\displaystyle 7,000 \times 100 = 700,000\) centimeters,

and 

\(\displaystyle 7,000 \times 1,000 = 7,000,000\) 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.