Definition of 4-digit by 1-digit multiplication in Grade 4 math

📚 Definition of 4-Digit by 1-Digit Multiplication

4-digit by 1-digit multiplication in Grade 4 math refers to the process of multiplying a number that has four digits (thousands, hundreds, tens, and ones) by a single-digit number (from 1 to 9). This involves multiplying each digit of the 4-digit number by the 1-digit number, taking into account place value and carrying over when necessary. The result is a product that can be four or five digits long.

📜 Historical Context and Background

Multiplication as a concept has been around for millennia, with evidence of its use found in ancient civilizations like Egypt and Mesopotamia. However, the specific algorithms and notations we use today evolved over time. The development of place value systems and efficient multiplication methods made working with larger numbers, like 4-digit numbers, more manageable. The distributive property is a key concept that makes multi-digit multiplication possible.

🔑 Key Principles

• 🔢 Place Value: Understanding the value of each digit in the 4-digit number (thousands, hundreds, tens, ones) is crucial.
• ➗ Distributive Property: Breaking down the multiplication into smaller parts (e.g., multiplying the 1-digit number by each digit of the 4-digit number separately).
• ➕ Carrying Over: If the product of a digit and the 1-digit number is greater than 9, carry the tens digit to the next place value column.
• 📐 Algorithm: Following a systematic approach or algorithm ensures accuracy. Typically, multiplication starts from the rightmost digit (ones place) and proceeds to the left.

🧮 Step-by-Step Example

Let's multiply 2,345 by 6:

1. Multiply 6 by the ones digit (5): $6 \times 5 = 30$. Write down 0 and carry over 3.
2. Multiply 6 by the tens digit (4): $6 \times 4 = 24$. Add the carry-over 3: $24 + 3 = 27$. Write down 7 and carry over 2.
3. Multiply 6 by the hundreds digit (3): $6 \times 3 = 18$. Add the carry-over 2: $18 + 2 = 20$. Write down 0 and carry over 2.
4. Multiply 6 by the thousands digit (2): $6 \times 2 = 12$. Add the carry-over 2: $12 + 2 = 14$. Write down 14.

Therefore, $2345 \times 6 = 14070$.

➕ Real-World Examples

• 📦 Inventory Calculation: A toy factory produces 1,250 toy cars each day. How many toy cars are produced in 7 days? ($1250 \times 7$)
• 💰 Savings: If you save $2,575 each year, how much will you save in 4 years? ($2575 \times 4$)
• 🚌 Travel Distance: A school bus travels 1,852 miles each month. How far does it travel in 9 months? ($1852 \times 9$)

📝 Practice Quiz

Solve these multiplication problems:

1. $1,234 \times 2 = ?$
2. $3,456 \times 3 = ?$
3. $5,678 \times 4 = ?$
4. $7,890 \times 5 = ?$
5. $9,012 \times 6 = ?$

💡 Conclusion

Understanding 4-digit by 1-digit multiplication is a fundamental skill in mathematics. By mastering place value, the distributive property, and a systematic approach, students can confidently solve these problems. These skills build a solid foundation for more advanced mathematical concepts.