Question 320558
A rectangular piece of land is 1300 yd x 1500 yd. 

a) What is the area in square miles?
<pre><b>
There are 3ft in 1yd
There are 5280ft in 1mi 

Start with the product of the dimensions, each placed over 1:

{{{1300yd/1}}}{{{"×"}}}{{{1300yd/1}}}

Multiply by unit multiplier {{{3ft/(1yd)}}} twice to cancel away the
yd's and bring in ft's: 

{{{1300yd/1}}}{{{"×"}}}{{{1300yd/1}}}{{{"×"}}}{{{3ft/(1yd)}}}{{{"×"}}}{{{3ft/(1yd)}}}

Multiply by unit multiplier {{{1mi/(5280ft)}}} twice to cancel away the
ft's and bring in mi's:

{{{1300yd/1}}}{{{"×"}}}{{{1300yd/1}}}{{{"×"}}}{{{3ft/(1yd)}}}{{{"×"}}}{{{3ft/(1yd)}}}{{{"×"}}}{{{1mi/(5280ft)}}}{{{1mi/(5280ft)}}}

Cancel the yd's

{{{1300cross(yd)/1}}}{{{"×"}}}{{{1500cross(yd)/1}}}{{{"×"}}}{{{3ft/(1cross(yd))}}}{{{"×"}}}{{{3ft/(1cross(yd))}}}{{{"×"}}}{{{1mi/(5280ft)}}}{{{1mi/(5280ft)}}}

Cancel the ft's

{{{1300cross(yd)/1}}}{{{"×"}}}{{{1500cross(yd)/1}}}{{{"×"}}}{{{3cross(ft)/(1cross(yd))}}}{{{"×"}}}{{{3cross(ft)/(1cross(yd))}}}{{{"×"}}}{{{1mi/(5280cross(ft))}}}{{{1mi/(5280cross(ft))}}}

All that's left is

{{{(1300*1500*3*3*mi*mi)/(5280*5280)}}}

or

{{{(17550000mi^2)/27876400}}}

which reduces to

{{{4875mi^2/7744}}}

or as a decimal

{{{0.6295196281mi^2}}}

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</pre></b>
b) What is the area in acres?
<pre><b>
There are 640 acres in a square mile.

So we start with

{{{4875mi^2/7744}}}

Multiply by unit multiplier {{{640acres/(1mi^2)}}} once to cancel away the
mi²'s and bring in acres:

{{{4875mi^2/7744}}}{{{"×"}}}{{{640acres/(1mi^2)}}}

Cancel the mi²'s

{{{4875cross(mi^2)/7744}}}{{{"×"}}}{{{640acres/(1cross(mi^2))}}}

All that's left is

{{{(4875*640acres)/7744}}}

or

{{{(3120000acres)/7744}}}

which reduces to

{{{(48750acres)/121}}}

or as a decimal:

{{{402.892562acres}}}

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[Be sure to round off these numbers as your teacher told you.]

Edwin</pre>