Why do we regroup tens in 3-digit subtraction? A simple explanation

📚 Why We Regroup Tens in 3-Digit Subtraction

Regrouping, also known as borrowing, is a crucial technique in subtraction that allows us to subtract when a digit in the number we're subtracting from (the minuend) is smaller than the corresponding digit in the number we're subtracting (the subtrahend). Let's break it down with an example.

🔢 Understanding Place Value

• 🌍 Hundreds, Tens, and Ones: Remember that in a 3-digit number, each digit represents a different place value. For example, in the number 352, the 3 is in the hundreds place, the 5 is in the tens place, and the 2 is in the ones place.
• 🧮 Decomposing Numbers: We can decompose 352 as $300 + 50 + 2$. This understanding is key to understanding regrouping.

➖ The Regrouping Process Explained

Let's say we want to subtract 175 from 352 ($352 - 175$).

1. Start with the Ones Place: We try to subtract 5 from 2 in the ones place. But, we can't subtract a larger number (5) from a smaller number (2).
2. Regrouping: This is where regrouping comes in. We borrow 1 ten from the tens place (50). So, 50 becomes 40, and we add that 10 to the ones place. Now, the 2 in the ones place becomes 12.
3. Subtraction in the Ones Place: Now we can subtract: $12 - 5 = 7$.
4. Subtraction in the Tens Place: Next, we subtract the tens place. We now have $4 - 7$. Again, we can't subtract a larger number from a smaller number.
5. Regrouping Again: So, we borrow 1 hundred from the hundreds place (300). 300 becomes 200, and we add that 100 (which is 10 tens) to the tens place. Now, the 4 in the tens place becomes 14.
6. Subtraction in the Tens Place: Now we can subtract: $14 - 7 = 7$.
7. Subtraction in the Hundreds Place: Finally, we subtract the hundreds place: $2 - 1 = 1$.

Therefore, $352 - 175 = 177$.

🔑 Why Regrouping Works: The 'Why'

• ➕ Maintaining Value: Regrouping doesn't change the overall value of the original number. We're just rearranging it. We're essentially using the identity property. For example, in $352 - 175$, when regrouping, we are rewriting 352 as $300 + 50 + 2 = 200 + 140 + 12$.
• 💡 Facilitating Subtraction: It allows us to perform subtraction in each place value column, even when the digit in the minuend is smaller than the digit in the subtrahend.

✍️ Example

Let's calculate $523 - 247$:

1. Ones Place: We can't subtract 7 from 3, so we borrow 1 ten from the tens place. 2 becomes 1, and 3 becomes 13. $13 - 7 = 6$.
2. Tens Place: We can't subtract 4 from 1, so we borrow 1 hundred from the hundreds place. 5 becomes 4, and 1 becomes 11. $11 - 4 = 7$.
3. Hundreds Place: $4 - 2 = 2$.

Result: $523 - 247 = 276$.

🧠 Practice Quiz

Solve the following subtraction problems:

1. $456 - 178$
2. $682 - 395$
3. $913 - 546$
4. $721 - 453$
5. $500 - 237$
6. $834 - 659$
7. $367 - 188$