How to borrow in subtraction?

Borrowing in subtraction, also known as regrouping, is a technique used when the digit you're subtracting in a column is larger than the digit you're subtracting from in that same column. It's a way to make subtraction possible when you don't have enough in one place value to subtract from.

Here's a breakdown of how to borrow:

The Borrowing Process:

1. Identify the Problem: Look at the rightmost column (the ones place). If the bottom number is bigger than the top number, you need to borrow.

2. Borrow from the Neighbor: Move to the column immediately to the left of the column where you need to borrow (e.g., the tens place if you needed to borrow from the ones place).

3. Subtract One: Subtract 1 from the digit in this neighbor column. Cross out the original number and write the new, reduced number above it. This represents taking one "ten" (or one "hundred," etc., depending on the column you're borrowing from).

4. Give to the Needy: Add 10 to the digit in the column where you needed to borrow. Write this new number above the original digit in that column. You are essentially converting the "one ten" (or "one hundred") into ten "ones."

5. Subtract as Usual: Now that you've borrowed, the top number in the column is large enough to subtract from. Perform the subtraction in that column, and continue subtracting in the remaining columns as normal.

Example:

Let's say we want to solve 42 - 17.

• Ones Column (2 - 7): We can't subtract 7 from 2, so we need to borrow.
• Borrow from Tens Column: We move to the tens column, which has a 4. We subtract 1 from 4, making it 3. We cross out the 4 and write a 3 above it.
• Give to Ones Column: We add 10 to the 2 in the ones column, making it 12. We cross out the 2 and write a 12 above it.
• Subtract: Now we have 12 - 7 = 5 in the ones column, and 3 - 1 = 2 in the tens column.

So, 42 - 17 = 25.

When to Borrow Multiple Times:

Sometimes you need to borrow multiple times in a single subtraction problem. Just repeat the borrowing process as needed, moving from right to left, until you have numbers large enough to subtract in each column.

Borrowing When the Next Column is Zero:

If the column you need to borrow from has a zero, you need to "borrow through" the zero.

1. Move one column to the left of the zero.
2. Borrow from that column.
3. The zero becomes a 10.
4. Now you can borrow from the 10, making it a 9, and adding 10 to the column where you originally needed to borrow.

Example: 304 - 186

1. We can't subtract 6 from 4, so we need to borrow from the tens column.
2. The tens column is a 0, so we borrow from the hundreds column (the 3). The 3 becomes a 2.
3. The 0 in the tens column becomes a 10.
4. Now, we borrow from the 10 in the tens column, making it a 9. We add 10 to the 4 in the ones column, making it a 14.
5. 14 - 6 = 8, 9 - 8 = 1, and 2 - 1 = 1. Therefore, 304 - 186 = 118.

In summary, borrowing is a crucial skill for subtraction, enabling you to subtract numbers even when the digits in the subtrahend are larger than the corresponding digits in the minuend. By following these steps, you can successfully navigate any subtraction problem that requires borrowing.