How to subtract using the decomposition strategy (Grade 3 step-by-step guide).

📚 Understanding Decomposition in Subtraction

Decomposition, also known as borrowing or regrouping, is a strategy used in subtraction when the digit in the ones place of the number you're subtracting from (the minuend) is smaller than the digit in the ones place of the number you're subtracting (the subtrahend). In simpler terms, it's like needing more ones than you have, so you 'borrow' from the tens place.

📜 A Little History

The concept of borrowing has been around for centuries! Different cultures developed various methods for performing subtraction, and decomposition is one of the most common and efficient. It helps us handle subtraction problems, even with large numbers, by breaking them down into smaller, more manageable parts.

🧠 Key Principles of Decomposition

• 🔢 Place Value: Understanding that each digit in a number has a specific value based on its position (ones, tens, hundreds, etc.) is crucial.
• ➕ Regrouping: This involves changing a ten into ten ones, or a hundred into ten tens, and so on.
• ➖ Subtracting Column by Column: Start with the ones place, then the tens place, and so on, regrouping when necessary.

🪜 Step-by-Step Guide to Decomposition

Let's go through an example: 42 - 27

1. 📝 Write the problem vertically: $$\begin{array}{@{}c@{\,}c@{}c} & 4 & 2 \\ - & 2 & 7 \\ \hline \end{array}$$
2. 🧐 Look at the ones place: We need to subtract 7 from 2. But 2 is smaller than 7, so we need to regroup.
3. 🤝 Borrow from the tens place: We borrow 1 ten from the 4 in the tens place. This leaves us with 3 tens. The 1 ten we borrowed becomes 10 ones.
4. ✨ Add to the ones place: Add the 10 ones to the 2 ones we already have, giving us 12 ones. $$\begin{array}{@{}c@{\,}c@{}c} & \stackrel{3}{\cancel{4}} & \stackrel{12}{\cancel{2}} \\ - & 2 & 7 \\ \hline \end{array}$$
5. ➖ Subtract the ones: Now we can subtract 7 from 12. 12 - 7 = 5. $$\begin{array}{@{}c@{\,}c@{}c} & \stackrel{3}{\cancel{4}} & \stackrel{12}{\cancel{2}} \\ - & 2 & 7 \\ \hline & & 5 \end{array}$$
6. ➖ Subtract the tens: Subtract 2 from 3. 3 - 2 = 1. $$\begin{array}{@{}c@{\,}c@{}c} & \stackrel{3}{\cancel{4}} & \stackrel{12}{\cancel{2}} \\ - & 2 & 7 \\ \hline & 1 & 5 \end{array}$$
7. ✅ The answer: 42 - 27 = 15

➕ More Examples

• 🍎 Example 1: 61 - 34 $$\begin{array}{@{}c@{\,}c@{}c} & \stackrel{5}{\cancel{6}} & \stackrel{11}{\cancel{1}} \\ - & 3 & 4 \\ \hline & 2 & 7 \end{array}$$ So, 61 - 34 = 27
• 🍌 Example 2: 83 - 56 $$\begin{array}{@{}c@{\,}c@{}c} & \stackrel{7}{\cancel{8}} & \stackrel{13}{\cancel{3}} \\ - & 5 & 6 \\ \hline & 2 & 7 \end{array}$$ So, 83 - 56 = 27
• 🍇 Example 3: 95 - 18 $$\begin{array}{@{}c@{\,}c@{}c} & \stackrel{8}{\cancel{9}} & \stackrel{15}{\cancel{5}} \\ - & 1 & 8 \\ \hline & 7 & 7 \end{array}$$ So, 95 - 18 = 77

💡 Tips and Tricks

• ✍️ Practice Regularly: The more you practice, the easier it will become.
• 📃 Use Visual Aids: Draw pictures or use manipulatives (like blocks) to help you visualize the regrouping process.
• 🗣️ Explain Aloud: Talking through the steps can help solidify your understanding.

📝 Practice Quiz

Solve these problems using the decomposition strategy:

1. ❓ 54 - 28 = ?
2. ❓ 71 - 35 = ?
3. ❓ 92 - 46 = ?
4. ❓ 63 - 17 = ?
5. ❓ 85 - 59 = ?
6. ❓ 46 - 27 = ?
7. ❓ 73 - 45 = ?

🏁 Conclusion

Decomposition is a valuable strategy for mastering subtraction. By understanding place value and practicing regularly, you'll become a subtraction superstar! Keep practicing, and don't be afraid to ask for help when you need it. You've got this! 💪