Lesson 1: Equivalence with Customary Units of Length

Property

The primary customary units of length are the inch, foot, yard, and mile.

Examples

• To convert 5 feet to inches: $5 \text{ ft} \times 12 \frac{\text{in}}{\text{ft}} = 60 \text{ in}$
• To convert 21 feet to yards: $21 \text{ ft} \div 3 \frac{\text{ft}}{\text{yd}} = 7 \text{ yd}$
• To convert 2 miles to feet: $2 \text{ mi} \times 5,280 \frac{\text{ft}}{\text{mi}} = 10,560 \text{ ft}$

Explanation

Length in the customary system is measured using inches, feet, yards, and miles. To convert from a larger unit to a smaller unit, you multiply by the appropriate conversion factor. For example, to change feet to inches, you multiply by 12. To convert from a smaller unit to a larger unit, you divide.

Property

To solve word problems involving fractional lengths, convert all measurements to the same smaller unit. Use the conversion factor to multiply both the whole number and the fraction.

Examples

• A piece of wood is $3\frac{1}{2}$ feet long. How long is it in inches?

• Sarah has a ribbon that is $2\frac{1}{3}$ yards long. She cuts off a piece that is $4$ feet long. How many feet of ribbon does she have left?

First, convert $2\frac{1}{3}$ yards to feet.

Then, subtract: $7 - 4 = 3$ feet.

Explanation

These problems require you to apply your knowledge of both fractions and customary unit conversions. First, identify the units used in the problem, such as feet, inches, or yards. Next, convert the measurements, including any fractions, into a common smaller unit by multiplying. Once all measurements are in the same unit, you can perform the necessary calculations like addition or subtraction to solve the problem.