How many feet are in 5.5 miles?
Conversion Factors: 1 mile = 1,760 yards 3 feet = 1 yard
First we need to set up the equation. 5.5 miles multiplied by a conversion factor (red box)
equals how many feet. Since we are starting with units of miles we know that our conversion
factor must have miles in the denominator.
5.5 miles
x
?
? miles
=
?
feet
We also know that since the final answer needs to be in feet we need to have feet in the
numerator of the conversion factor. Do we have a conversion factor to go from miles to feet?
No, but we have a conversion factor for miles to yards. So we put this conversion in factor in
the red box. Remember that the 1,760 goes with the yards and the 1 goes with the miles, not
the other way around.
5.5 miles
x
1,760 yards
1 mile
=
?
feet
The miles on the top cancel out the mile in the denominator of our conversion factor. If we
were to do the math now we would get our answer in yards because that’s the only unit we
have left in the equation. Since we need the answer in feet we need to use a 2nd conversion
factor. We know that yards have to be in the denominator of this 2 nd conversion factor to
cancel out the yards that are in the numerator of the 1st conversion factor.
5.5 miles
x
1,760 yards
1 mile
x
?
? yard
=
? feet
Do we have a conversion factor to convert yards to feet? Yes, so we put that conversion factor
in the 2nd red box. Remember that the 3 goes with the feet and the 1 goes with the yard.
5.5 miles
x
1,760 yards
1 mile
x
3 feet
1 yard
=
? feet
If we do the math now what will the units be in the answer? The units will be feet. Are we
ready to do the math? Yes! (5.5 x 1,760 x 3 = 29,040)
5.5 miles
x
1,760 yards
1 mile
x
3 feet
1 yard
=
29,040 feet