Three-Digit Subtraction

Subtracting three-digit numbers is just like subtracting smaller numbers, but with an extra "hundreds" column. To make it easy, we use column subtraction.

Setting Up the Problem

Always line up your numbers vertically by their place value: hundreds over hundreds, tens over tens, and ones over ones. Always start subtracting from the right side (the ones column).

Borrowing (Regrouping)

Sometimes, the top digit is smaller than the bottom digit. When this happens, you need to "borrow" or "regroup" from the column to the left.

Example: $812 - 456$

1. Ones Column: $2 - 6$. Since $2$ is smaller than $6$, borrow from the tens column. The $1$ ten becomes $0$, and the $2$ ones become $12$. Now, $12 - 6 = 6$.
2. Tens Column: $0 - 5$. Since $0$ is smaller than $5$, borrow from the hundreds. The $8$ becomes $7$, and the $0$ becomes $10$. Now, $10 - 5 = 5$.
3. Hundreds Column: $7 - 4 = 3$.

Answer: $812 - 456 = 356$

Subtracting Across Zeros

What if you need to borrow, but the next number is a zero? You cannot borrow from nothing, so you have to move one more column to the left!

Example: $503 - 247$

1. Ones Column: $3 - 7$. You need to borrow, but the tens column is $0$.
2. Go to the Hundreds: Borrow from the $5$ hundreds. The $5$ becomes a $4$. The $0$ in the tens column becomes a $10$.
3. Borrow for the Ones: Now you can borrow from that new $10$ in the tens column. The $10$ becomes a $9$, and your $3$ ones become $13$.
4. Subtract:
   • Ones: $13 - 7 = 6$
   • Tens: $9 - 4 = 5$
   • Hundreds: $4 - 2 = 2$

Answer: $503 - 247 = 256$

Quick Tip for Double Zeros

When subtracting from a number ending in two zeros (like $600 - 358$), follow a simple shortcut:

• The hundreds digit goes down by one ($6 \rightarrow 5$).
• The middle zero becomes a $9$.
• The last zero becomes a $10$.

Then, just subtract straight down the columns: $10 - 8 = 2$, $9 - 5 = 4$, and $5 - 3 = 2$.

Answer: $600 - 358 = 242$