Customary length subtraction word problems with solutions Grade 3

📚 Understanding Customary Length Subtraction

Customary length subtraction involves finding the difference between two lengths expressed in customary units such as inches, feet, yards, and miles. These problems often appear in word problems where you need to determine how much shorter or longer one object is compared to another.

• 📏 Units of Length: Understanding the relationships between inches, feet, yards, and miles is crucial. Remember: 1 foot = 12 inches, 1 yard = 3 feet, and 1 mile = 5280 feet.
• ➕ Conversion: Sometimes, you'll need to convert lengths to the same unit before subtracting. For example, you might need to convert feet to inches.
• ➖ Subtraction: Once the units are the same, subtract the smaller length from the larger length.

📜 History and Background

The customary system of measurement has roots in ancient Roman, Anglo-Saxon, and medieval English traditions. These units were often based on human anatomy or everyday objects. While many parts of the world use the metric system, the United States continues to use the customary system, making it important for students to learn.

📌 Key Principles

• 🔍 Read Carefully: Understand what the problem is asking before you start solving. Identify the lengths you need to subtract.
• 🧮 Align Units: Make sure all lengths are in the same unit before subtracting. If not, convert them.
• ✍️ Show Your Work: Write down each step to avoid mistakes and make it easier to check your answer.
• ✅ Check Your Answer: Does the answer make sense in the context of the problem?

💡 Real-World Examples

Let's look at some examples of customary length subtraction word problems:

1. Example 1:
   A ribbon is 2 feet long. Sarah cuts off 9 inches. How much ribbon is left?
   Solution:
   First, convert 2 feet to inches: $2 \times 12 = 24$ inches. Then, subtract: $24 - 9 = 15$ inches.
2. Example 2:
   A table is 6 feet long and a bench is 4 feet long. How much longer is the table than the bench?
   Solution:
   Subtract: $6 - 4 = 2$ feet.
3. Example 3:
   John walks 1 mile to school. He has already walked 3520 feet. How many more feet does he need to walk?
   Solution:
   Since 1 mile = 5280 feet, subtract: $5280 - 3520 = 1760$ feet.

🧪 Practice Quiz

1. A carpenter has a wooden plank that is 8 feet long. He cuts off a piece that is 2 feet and 7 inches long. How long is the remaining plank?
2. A garden is 15 feet long. If you plant flowers along 8 feet and 9 inches of the garden, how much length is left for vegetables?
3. A roll of fabric contains 10 yards. If a tailor uses 4 yards and 2 feet, how much fabric remains on the roll?
4. A bookshelf is 5 feet tall. A stack of books is 2 feet and 5 inches tall. How much space is left above the books on the shelf?
5. A park trail is 2 miles long. If someone has walked 1 mile and 2640 feet, how much further do they need to walk to complete the trail?
6. A room is 12 feet wide. A rug is placed in the center that is 8 feet and 6 inches wide. How much of the floor remains uncovered on each side of the rug?
7. A painter has a ladder that extends to 15 feet. He only needs to reach a height of 9 feet and 8 inches. How much longer is the ladder than the height he needs to reach?

🔑 Conclusion

Mastering customary length subtraction is essential for solving real-world problems involving measurements. By understanding the relationships between different units and practicing regularly, you can confidently tackle any length subtraction problem. Keep practicing, and you'll become a pro in no time!