How to Divide 3-Digit by 2-Digit Numbers Using the Standard Algorithm (Grade 5)

📚 Understanding 3-Digit by 2-Digit Division

Dividing a 3-digit number by a 2-digit number involves breaking down the problem into smaller, manageable steps using the standard algorithm. This method relies on repeated subtraction and estimation to find the quotient and remainder.

📜 A Brief History of Division Algorithms

The standard division algorithm has evolved over centuries. Its roots can be traced back to ancient civilizations, where mathematicians developed various methods for dividing numbers. The modern algorithm we use today is a refinement of these earlier techniques, designed for efficiency and accuracy.

➗ Key Principles of the Standard Algorithm

• 🔢 Divide: Determine how many times the divisor goes into the first digit(s) of the dividend.
• ✖️ Multiply: Multiply the quotient by the divisor.
• ➖ Subtract: Subtract the product from the corresponding part of the dividend.
• ⬇️ Bring Down: Bring down the next digit of the dividend.
• 🔁 Repeat: Repeat the steps until all digits of the dividend have been used.

➗ Step-by-Step Example: 456 ÷ 12

Let's walk through an example to illustrate the process:

1. Step 1: How many times does 12 go into 45? It goes 3 times. Write 3 above the 5 in 456.
2. Step 2: Multiply 3 by 12. $3 \times 12 = 36$. Write 36 below 45.
3. Step 3: Subtract 36 from 45. $45 - 36 = 9$.
4. Step 4: Bring down the next digit, 6, to make 96.
5. Step 5: How many times does 12 go into 96? It goes 8 times. Write 8 above the 6 in 456.
6. Step 6: Multiply 8 by 12. $8 \times 12 = 96$. Write 96 below 96.
7. Step 7: Subtract 96 from 96. $96 - 96 = 0$. The remainder is 0.

Therefore, $456 \div 12 = 38$.

➕ Another Example: 789 ÷ 23

Here's another example to solidify your understanding:

1. Step 1: How many times does 23 go into 78? It goes 3 times. Write 3 above the 8 in 789.
2. Step 2: Multiply 3 by 23. $3 \times 23 = 69$. Write 69 below 78.
3. Step 3: Subtract 69 from 78. $78 - 69 = 9$.
4. Step 4: Bring down the next digit, 9, to make 99.
5. Step 5: How many times does 23 go into 99? It goes 4 times. Write 4 above the 9 in 789.
6. Step 6: Multiply 4 by 23. $4 \times 23 = 92$. Write 92 below 99.
7. Step 7: Subtract 92 from 99. $99 - 92 = 7$. The remainder is 7.

Therefore, $789 \div 23 = 34$ with a remainder of 7.

💡 Tips for Success

• ✅ Estimate: Before dividing, estimate the quotient to make sure your answer is reasonable.
• 📝 Check Your Work: Multiply the quotient by the divisor and add the remainder to ensure it equals the dividend.
• 📊 Practice Regularly: The more you practice, the more comfortable you'll become with the standard algorithm.

🌍 Real-World Applications

Division is used in many real-world scenarios, such as:

• 🍕 Sharing Pizza: Dividing a pizza equally among friends.
• 🍪 Baking: Adjusting recipe amounts for a different number of servings.
• 💰 Finance: Calculating monthly payments for a loan.

✍️ Practice Quiz

Solve the following division problems using the standard algorithm:

1. $123 \div 15 =$ ?
2. $234 \div 11 =$ ?
3. $345 \div 12 =$ ?
4. $456 \div 13 =$ ?
5. $567 \div 14 =$ ?
6. $678 \div 15 =$ ?
7. $789 \div 16 =$ ?

⭐ Conclusion

Mastering the standard algorithm for dividing 3-digit numbers by 2-digit numbers takes practice, but with these steps and tips, you'll be well on your way to becoming a division pro! Keep practicing, and remember that every problem you solve builds your understanding and confidence.