Question 174807
<font size = 7 color = "red"><b>Edwin's solution:</b></font>
<pre><font size = 4 color = "indigo"><b>
We must know that:

{{{1km = 1000m}}}, with possible unit fractions {{{(1km)/(1000m)}}},{{{(1000m)/(1km)}}}

{{{1m = 100cm}}}, with possible unit fractions {{{(1m)/(100cm)}}},{{{(100cm)/(1m)}}}

{{{1cm = 2.54in}}}, with possible unit fractions {{{(2.54cm)/(1in)}}},{{{(2.54in)/(1cm)}}}

{{{12in = 1ft}}}, with possible unit fractions {{{(12in)/(1ft)}}},{{{(1ft)/(12in)}}}

5280ft = 1mi, with possible unit fractions {{{(5280ft)/(1mi)}}},{{{(1mi)/(5280ft)}}}

We start by putting {{{5km}}} over {{{1}}}:

{{{(5km)/1}}}

Then we multiply by the unit fraction with {{{km}}}
in the denominator, so it will cancel with the {{{km}}}
in the numerator, so we now we have:

{{{matrix(1,3,(5km)/1, "×", (1000m)/(1km))}}}

so that the {{{km}}}'s will cancel:

{{{matrix(1,3,(5cross(km))/1, "×", (1000m)/(1cross(km)))}}}

Then we multiply by the unit fraction with {{{m}}}
in the denominator, so it will cancel with the {{{m}}}
in the numerator, so now we have:

{{{matrix(1,5,(5cross(km))/1, "×", (1000m)/(1cross(km)), "×",(100cm)/(1m) )}}}

and after canceling:


{{{matrix(1,5,(5cross(km))/1, "×", (1000cross(m))/(1cross(km)), "×",(100cm)/(1cross(m)) )}}}


Then we multiply by the unit fraction with {{{cm}}}
in the denominator, so it will cancel with the {{{cm}}}
in the numerator, so now we have:

{{{matrix(1,7,(5cross(km))/1, "×", (1000cross(m))/(1cross(km)), "×",(100cm)/(1cross(m)),"×",(1in)/(2.54cm) )}}}

and after cancelling:

{{{matrix(1,7,(5cross(km))/1, "×", (1000cross(m))/(1cross(km)), "×",(100cross(cm))/(1cross(m)),"×",(1in)/(2.54cross(cm)) )}}}


Then we multiply by the unit fraction with {{{in}}}
in the denominator, so it will cancel with the {{{in}}}
in the numerator, so now we have:

{{{matrix(1,9,(5cross(km))/1, "×", (1000cross(m))/(1cross(km)), "×",(100cross(cm))/(1cross(m)),"×",(1in)/(2.54cross(cm)), "×", (1ft)/(12in) )}}}

and after canceling:

{{{matrix(1,9,(5cross(km))/1, "×", (1000cross(m))/(1cross(km)), "×",(100cross(cm))/(1cross(m)),"×",(1cross(in))/(2.54cross(cm)), "×", (1ft)/(12cross(in)) )}}}

Then we multiply by the unit fraction with {{{ft}}}
in the denominator, so it will cancel with the {{{ft}}}
in the numerator, so now we have:

{{{matrix(1,11,(5cross(km))/1, "×", (1000cross(m))/(1cross(km)), "×",(100cross(cm))/(1cross(m)),"×",(1cross(in))/(2.54cross(cm)), "×", (1ft)/(12cross(in)), "×", (1mi)/(5280ft) )}}}

and after canceling:

{{{matrix(1,11,(5cross(km))/1, "×", (1000cross(m))/(1cross(km)), "×",(100cross(cm))/(1cross(m)),"×",(1cross(in))/(2.54cross(cm)), "×", (1cross(ft))/(12cross(in)), "×", (1mi)/(5280cross(ft)) )}}}

Putting together everything that hasn't been canceled:

{{{((5)(1000)(100)(mi))/((2.54)(12)(5280))}}}

{{{(500000mi)/160934.4}}}

{{{3.106855961mi}}}

Or just a tiny bit over 3.1 miles.

Edwin</pre>