Measurement
Page 13
Linear Measurement: U.S. or English System
In the United States it is common, outside of science applications, to use the U.S. or English system
of measurements for length. This system starts with defining how long an inch is and then defines the
length of a foot, yard, or mile. The following list shows the relationship between these units. The
common abbreviations are also shown. You may use the abbreviations in your work if you like.
1 foot (ft.) = 12 inches (in.)
1 yard (yd.) = 3 feet (ft.)
1 mile = 5280 feet (ft.)
Unit Fractions
A unit fraction is a fraction that has the value of 1. In this chapter we will create unit fractions that are
rates that are equal to 1.
If 1 foot = 12 inch
we can divide both side of
the equation by 12 inch
to get a unit fraction
If 1 yard = 3 feet
we can divide both side of
the equation by 3 feet
to get a unit fraction
If 1 mile = 5280 feet.
we can divide both side of
the equation by 5280 feet
to get a unit fraction
1 ft.
12 in.
=
12 in.
12 in.
1 yd.
3 ft.
=
3 ft.
3 ft.
1 mile
5280 ft.
=
5280 ft.
5280 ft.
1 ft.
= 1
12 in.
1 yd.
= 1
3 ft.
1 mile
= 1
5280 ft.
If 1 foot = 12 inch
we can divide both side of
the equation by 1 foot
to get a unit fraction
If 1 yard = 3 feet
we can divide both side of
the equation by 1 yard
to get a unit fraction
If 1 mile = 5280 feet
we can divide both side of
the equation by 1 mile
to get a unit fraction
1 ft.
12 in.
=
1ft.
1 ft.
1 yd.
3 ft.
=
1 yd.
1 yd.
1 mile
5280 ft.
=
1 mile
1 mile
1=
12 in.
1 ft.
1=
3 ft.
1 yd.
1 =
5280 ft.
1 mile
Each of the fractions listed as equal to 1 is a unit fraction. Each unit fraction has a numerical value of 1
but the units of measure (in., ft., yd.) must accompany the unit fraction. It may seem that
12 in.
1 ft.
and
are the same rate since they both equal 1 but the first is the rate of inches per
1 ft.
12 in.
foot and the second is the rate of feet per inch.
Chapter 2
© 2015 Eitel
Unit Fractions
For feet and inches
for yards and feet
for miles and feet
1 ft.
12 in.
=
= 1
12 in.
1 ft.
1 yd.
3 ft.
=
= 1
3 ft.
1 yd.
1 miles
5280 ft.
=
= 1
5280 ft.
1 miles
Using Unit Fractions to convert from one unit measurement to another
Converting feet to inches
To convert feet to inches we need to multiply by a unit fraction that will cancel out the feet in the
original problem and produce inches in the answer. We will use a unit fraction that has inches in
the numerator and feet in the denominator so that the feet units divide out.
Example 1
Example 2
Convert 4 feet to ____ inches
Convert 8 feet to ____ inches
4 f/t/. 12 in.
•
= 48 in.
1
1 f//t.
12 in.
(we use
so the feet divide out)
1 ft.
8 f/t/. 12 in.
•
= 96 in.
1
1 f//t.
12 in.
(we use
so the feet divide out)
1 ft.
4 feet = 48 inches
8 feet = 96 inches
Converting inches to feet
To convert inches to feet we need to multiply by a unit fraction that will cancel out the inches in the
original problem and produce feet in the answer. We will use a unit fraction that has feet in the
numerator and inches in the denominator so that the feet units divide out.
Example 3
Example 4
Convert 60 inches to ____ feet
Convert 42 inches to ____ feet
60 /i n/ . 1 ft.
•
1
12 /in/ .
1 ft.
(we use
so the inches divide out)
12 in.
60 ft.
= 5 ft.
12
42 /in/ . 1 ft.
•
1
12 /in/ .
1 ft.
(we use
so the inches divide out)
12 in.
42 ft. 7
=
= 3.5 ft.
12
2
60 in. = 5 ft.
42 in. = 3.5 ft.
Chapter 2
© 2015 Eitel
Converting feet to yards
Converting yards to feet
Example 5
Example 6
Convert 36 feet to ____ yards
Convert 5 yards to ____ feet
36 f//t. 1 yd.
•
= 12 yd.
1
3 f/t/.
1 yd.
(we use
so the ft. divide out)
3 ft.
5 y/ d/ . 3 ft.
•
= 15 ft.
1
1 y/ d/ .
3 ft.
(we use
so the yd. divide out)
1 yd.
36 ft. = 12 yd.
5 • 3 ft. = 15 ft.
Converting feet to miles
Converting miles to feet
Example 7
Example 8
Convert 10560 ft. to ____ miles
Convert 3 miles to ____ ft.
10560 f//t.
1 mile
•
1
5280 f/t/.
1 miles
(we use
so the ft. divide out)
5280 ft.
=
10560 miles
5280
= 2 miles
3m
/ /i/le/ /s 5280 ft.
•
1
1m
/ /i/le/ /s
5280 ft.
(we use
so the miles divide out)
1 mi.
3• 5280 ft. = 15840 ft.
Conversions that require Two Steps
Converting yards to inches
Converting inches to yards
Example 9
Convert 5 yards to ____ inches
5 y/ d/ . 3 f/t/. 12 in.
•
•
.
1
1 y/ d/ . 1 f//t.
= 5• 3• 12 in.
= 180 in.
Chapter 2
Example 10
Convert 72 inches to ____ yards
72 /in/ . 1 f//t. 1 yd.
•
•
1
12 /in/ . 3 f//t.
=
72 yd.
36
= 2 yd.
© 2015 Eitel
page 16
Converting Linear Measurement: Show the set up and the answer.
1 foot (ft.) = 12 inches (in.)
1 yard (yd.) = 3 feet (ft.)
1 mile = 5280 feet (ft.)
1. Convert 36 inches to feet
2. Convert 6 feet to inches
3. Convert 3 yd. to feet
4. Convert 27 feet to yards
5. Convert 84 inches to feet
6. Convert 8 feet to inches
Page 16 answers
1. 3 feet
2. 72 inches
Chapter 2
3. 9 feet
4. 9 yards
5. 7 feet
6. 96 inches
© 2015 Eitel
Chapter 2
© 2015 Eitel