Basic Mathematics for College Students

Convert from one American unit of length to another.

To convert from one unit of length to another, we use unit conversion factors.To find
the unit conversion factor between yards and feet, we begin with this fact:

If we divide both sides of this equation by 1 yard, we get

Simplify the right side of the equation. A number divided by itself is 1:.

The fraction is called a unit conversion factor,because its value is 1. It can be
read as “3 feet per yard.” Since this fraction is equal to 1, multiplying a length by this
fraction does not change its measure; it changes only the unitsof measure.

To convert units of length in the American system of measurement, we use the
following unit conversion factors. Each conversion factor shown below is a form of 1.

3 ft

1 yd

1 yd

(^) 1 yd 1
3 ft
1 yd

 1

3 ft

1 yd



1 yd

1 yd

3 ft1 yd

3

5.3 American Units of Measurement 445

Self Check 3

Convert 9 yards to feet.

Now TryProblem 35

Use the unit Use the unit

To convert from conversion factor To convert from conversion factor

feet to inches inches to feet

yards to feet feet to yards

yards to inches inches to yards

miles to feet 5,280 ft1 mi feet to miles 5,280 ft1 mi

1 yd

36 in.

36 in.

1 yd

1 yd

3 ft

3 ft

1 yd

1 ft

12 in.

12 in.

1 ft

EXAMPLE (^3) Convert 8 yards to feet.
StrategyWe will multiply 8 yards by a carefully chosen unit conversion factor.
WHYIf we multiply by the proper unit conversion factor, we can eliminate the
unwanted units of yards and convert to feet.
Solution
To convert from yards to feet, we must use a unit conversion factor that relates
feet to yards. Since there are 3 feet per yard, we multiply 8 yards by the unit
conversion factor.
Write 8 yd as a fraction:.
Then multiply by a form of 1:.
Simplify.
Multiply: 8  3 24.
8 yards is equal to 24 feet.
 24 ft
 8 3 ft
Remove the common units of yards from the numerator
 (^) and denominator. Notice that the units of feet remain.
8 yd
1



3 ft

1 yd

3 ft

1 yd

8 yd

8 yd

8 yd8 yd^1

1



3 ft

1 yd

3 ft

1 yd

Success Tip Notice that in Example 3, we eliminated the units of yards and

introduced the units of feet by multiplying by the appropriate unit conversion

factor. In general, a unit conversion factor is a fraction with the following form:

Numerator

 Denominator

Unit we want to introduce

Unit we want to eliminate