BB.3 Convert and compare customary units of length
What is length?
Length is the measurement of how long an object is from one end to the other. It tells you the distance between two points. In the United States, we often measure length using customary units. The customary units of length are inch, foot, yard, and mile. These units are part of the U.S. customary system, which is different from the metric system used in most other countries.
- A pencil is about 7 inches long.
- A school bus is about 40 feet long.
- A football field is 100 yards long.
- The distance between two towns might be 15 miles.
When you measure length, always choose the unit that makes the most sense for the object. You would not measure the length of a pencil in miles!
Customary units of length
There are four main customary units of length: inch (in.), foot (ft), yard (yd), and mile (mi). Each unit is a different size. Knowing how they relate to each other helps you convert and compare lengths.
- Inch – about the length of a quarter from top to bottom.
- Foot – about the length of a ruler. 1 foot = 12 inches.
- Yard – about the width of a door. 1 yard = 3 feet = 36 inches.
- Mile – about the length of 15 football fields. 1 mile = 5,280 feet = 1,760 yards.
The abbreviations for these units are in., ft, yd, and mi. You will see them in math problems and in real life.
Customary length conversion rules
Converting means changing a measurement from one unit to another without changing the actual length. To convert, you multiply or divide using the relationships between units. Here are the key rules:
- Inches to feet: Divide by 12.
Feet to inches: Multiply by 12. - Feet to yards: Divide by 3.
Yards to feet: Multiply by 3. - Yards to inches: Multiply by 36.
Inches to yards: Divide by 36. - Feet to miles: Divide by 5,280.
Miles to feet: Multiply by 5,280. - Yards to miles: Divide by 1,760.
Miles to yards: Multiply by 1,760.
- Convert 3 feet to inches: 3 × 12 = 36 inches.
- Convert 24 inches to feet: 24 ÷ 12 = 2 feet.
- Convert 2 miles to feet: 2 × 5,280 = 10,560 feet.
- Convert 3,520 yards to miles: 3,520 ÷ 1,760 = 2 miles.
When converting from a larger unit to a smaller unit, you multiply. When converting from a smaller unit to a larger unit, you divide. This is because you need more small units to make one large unit.
Converting between inches, feet, and yards
Inches, feet, and yards are used for measuring smaller lengths, such as the length of a book, a room, or a piece of fabric. To convert between them, use these facts:
- 1 foot = 12 inches
- 1 yard = 3 feet
- 1 yard = 36 inches
- How many inches are in 4 feet? 4 × 12 = 48 inches.
- How many feet are in 7 yards? 7 × 3 = 21 feet.
- How many inches are in 2 yards? 2 × 36 = 72 inches.
- How many yards are in 108 inches? 108 ÷ 36 = 3 yards.
Remember that a yard is longer than a foot, and a foot is longer than an inch. So, 1 yard is greater than 1 foot, and 1 foot is greater than 1 inch.
Converting between feet, yards, and miles
Miles are used for measuring long distances, such as the distance between cities or the length of a road. To convert between feet, yards, and miles, use these facts:
- 1 mile = 5,280 feet
- 1 mile = 1,760 yards
- 1 yard = 3 feet
- How many feet are in 3 miles? 3 × 5,280 = 15,840 feet.
- How many yards are in 2 miles? 2 × 1,760 = 3,520 yards.
- How many miles are in 10,560 feet? 10,560 ÷ 5,280 = 2 miles.
- How many miles are in 5,280 yards? 5,280 ÷ 1,760 = 3 miles.
The numbers 5,280 and 1,760 are important to memorize. They are the number of feet and yards in one mile. Also, notice that 5,280 is a large number, so we write it with a comma: 5,280.
Comparing customary units of length
Comparing lengths means deciding which measurement is longer, shorter, or if they are equal. To compare, you must first convert the measurements to the same unit. Then you can compare the numbers.
- Compare 2 feet and 20 inches.
Convert 2 feet to inches: 2 × 12 = 24 inches.
24 inches > 20 inches, so 2 feet > 20 inches. - Compare 1 yard and 4 feet.
Convert 1 yard to feet: 1 × 3 = 3 feet.
3 feet < 4 feet, so 1 yard < 4 feet. - Compare 1 mile and 1,000 yards.
Convert 1 mile to yards: 1 × 1,760 = 1,760 yards.
1,760 yards > 1,000 yards, so 1 mile > 1,000 yards.
Always convert to the same unit before comparing. If you don't, you might make a mistake. For example, 2 feet is not the same as 2 inches, even though the number 2 is the same.
Using conversion tables
A conversion table is a helpful tool that shows how units relate to each other. You can use it to quickly change from one unit to another. Here is a table for customary units of length:
- 1 foot = 12 inches
- 1 yard = 3 feet
- 1 yard = 36 inches
- 1 mile = 5,280 feet
- 1 mile = 1,760 yards
- Use the table to find how many inches are in 3 yards.
1 yard = 36 inches, so 3 × 36 = 108 inches. - Use the table to find how many feet are in 2 miles.
1 mile = 5,280 feet, so 2 × 5,280 = 10,560 feet.
You can make your own conversion table on a piece of paper. Keep it handy when you solve problems. It will help you remember the relationships between units.
Solving real-world problems with customary units
In real life, you often need to convert and compare lengths. For example, if you are building a fence, you might need to know how many feet of wood to buy. If you are planning a trip, you might need to know how many miles you will travel. Using the correct unit and converting when necessary helps you solve these problems.
- A rope is 5 yards long. How many feet is that?
5 × 3 = 15 feet. - A trail is 2 miles long. How many yards is that?
2 × 1,760 = 3,520 yards. - A board is 48 inches long. How many feet is that?
48 ÷ 12 = 4 feet. - Which is longer: 3 feet or 30 inches?
3 feet = 36 inches, so 3 feet > 30 inches.
When solving word problems, read carefully to see which unit the answer should be in. Sometimes you need to convert before you can add, subtract, multiply, or divide.
Common mistakes to avoid
When working with customary units of length, students sometimes make mistakes. Here are a few common ones and how to avoid them:
- Forgetting to convert before comparing. Always change to the same unit first.
- Multiplying when you should divide. Remember: larger to smaller = multiply; smaller to larger = divide.
- Mixing up the numbers. For example, 1 mile is 5,280 feet, not 5,280 yards.
- Using the wrong unit. Do not measure a pencil in miles or a road in inches.
- Mistake: 2 feet = 2 inches.
Correct: 2 feet = 24 inches. - Mistake: 1 mile = 1,760 feet.
Correct: 1 mile = 5,280 feet.
Double-check your work. Ask yourself if the answer makes sense. If you convert 1 mile to feet, you should get a large number because feet are much smaller than miles.
Practice converting and comparing
The more you practice, the better you will become at converting and comparing customary units of length. Try these problems on your own:
- Convert 6 feet to inches.
- Convert 4 yards to feet.
- Convert 2 miles to yards.
- Compare 5 feet and 50 inches.
- Compare 1 mile and 2,000 yards.
- 6 × 12 = 72 inches
- 4 × 3 = 12 feet
- 2 × 1,760 = 3,520 yards
- 5 feet = 60 inches, so 5 feet > 50 inches
- 1 mile = 1,760 yards, so 1 mile < 2,000 yards
Keep practicing with different numbers. You can also measure objects around your home and convert their lengths to different units.
Common Core alignment: CCSS.MATH.CONTENT.4.MD.A.1 – Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
Notes for teachers
All content is 100% free, student-safe, aligned with CCSS.MATH.CONTENT.4.MD.A.1. Use it for whole-class instruction, independent practice, or homework.