# US Customary units of length review (in, ft, yd, & mi)

CCSS Math: 5.MD.A.1
Review the size of inches, feet, yards, and miles and how to convert between them.  Then, try some practice problems.

## Summary of customary units of distance

InchesFeetYardsMiles
$63, 360$$5,280$$1,760$$\goldD1$
$36$$3$$\goldD1$$\dfrac{1}{1,760}$
$12$$\goldD1$$\dfrac13$$\dfrac{1}{5,280}$
$\goldD1$$\dfrac{1}{12}$$\dfrac{1}{36}$$\dfrac{1}{63,360}$

## What is distance?

Distance measures length. For example, the length of a snake is how long the snake is.
In the US customary system of measurement, the most common units of distance are inches, feet, yards, and miles.

### How big are customary units of distance?

The length of a quarter is about $1$ inch.
The length of a man's shoe is about $1$ foot.
The length of a guitar is about $1$ yard.
The length of a runway at a large airport is about $1$ mile.

## Practice set 1: Estimating distance

Problem 1A
Identify the most reasonable unit to measure the length of a banana.
Want to try more problems like this? Check out this exercise.

## Converting larger units to smaller units

$1 \text{ foot} = \greenD{12}\text{ inches}$
$1 \text{ yard} = \greenD{3}\text{ feet}$
$1 \text{ yard} = \greenD{36}\text{ inches}$
$1 \text{ mile} = \greenD{1760}\text{ yards}$
To convert larger units to smaller units we multiply the number of larger units by the green conversion factor for the appropriate smaller units.
Example: Converting feet to inches
$1 \text{ foot} = \greenD{12}\text{ inches}$
$\blueD{5} \text{ feet} = \blueD{5}\times \greenD{12}=60\text{ inches}$

## Converting smaller units to larger units

$1\text{ inch}= \dfrac1{\green{12}} \text{ foot}$
$1\text{ foot}= \dfrac1{\green{3}} \text{ yard}$
$1\text{ yard}= \dfrac1{\green{1760}} \text{ mile}$
To convert smaller units to larger units we divide the number of smaller units by the green conversion factor for the appropriate larger units.
Example: Converting inches to feet
$1\text{ inch}= \dfrac1{\green{12}} \text{ foot}$
$\pink{72} \text{ inches}= \dfrac{\pink{72}}{\green{12}}= \pink{72}\div\green{12}=\blue{6}\text{ feet}$
Example: Converting yards to miles
$1\text{ yard}= \dfrac1{\green{1760}} \text{ mile}$
$\pink{17{,}600} \text{ yards}= \dfrac{\pink{17{,}600}}{\green{1760}}= \pink{17{,}600}\div\green{1760}=\blue{10}\text{ miles}$
$3$ yards $=$