Subtraction with Four and Five Digit Numbers

When you subtract larger numbers, like those in the thousands (4 digits) or ten-thousands (5 digits), you use the exact same steps you learned for smaller numbers. The secret to success is keeping your numbers lined up perfectly and borrowing carefully!

Setting Up the Problem

Always use column subtraction. Write the larger number on top and the smaller number on the bottom. Make sure to line up the place values on the right side: ones under ones, tens under tens, hundreds under hundreds, and so on.

Borrowing Across Zeros

Sometimes, the top digit is smaller than the bottom digit, so you have to borrow (or regroup) from the next column to the left. This can get tricky when you have to borrow across zeros. Let's look at an example:

$5{,}002 - 3{,}478$

Step 1: Try to subtract the ones. $2 - 8$. We can't do this, so we need to borrow from the tens.

Step 2: Borrowing across zeros.

• Look at the tens column: It's a $0$. We can't borrow from $0$.
• Look at the hundreds column: It's also a $0$. We can't borrow here either.
• Look at the thousands column: It's a $5$. We can borrow from here!

Step 3: Regroup.

• Borrow $1$ from the thousands ($5$ becomes $4$). The hundreds column becomes $10$.
• Now borrow from the hundreds ($10$ becomes $9$). The tens column becomes $10$.
• Finally, borrow from the tens ($10$ becomes $9$). The ones column becomes $12$.

Step 4: Subtract straight down.

• Ones: $12 - 8 = 4$
• Tens: $9 - 7 = 2$
• Hundreds: $9 - 4 = 5$
• Thousands: $4 - 3 = 1$

The answer is $1{,}524$.

Subtracting from 10,000

Let's try a 5-digit number with even more zeros:

$10{,}000 - 4{,}567$

Because $10{,}000$ is a $1$ followed by all zeros, we have to borrow all the way across!

1. The $1$ in the ten-thousands place becomes $0$.
2. The thousands place becomes $10$, but we borrow from it, so it becomes $9$.
3. The hundreds place becomes $10$, we borrow, it becomes $9$.
4. The tens place becomes $10$, we borrow, it becomes $9$.
5. The ones place becomes $10$.

Now, subtract the columns:

• Ones: $10 - 7 = 3$
• Tens: $9 - 6 = 3$
• Hundreds: $9 - 5 = 4$
• Thousands: $9 - 4 = 5$

The answer is $5{,}433$.

Quick Tips for Success

• Keep it neat: Write your numbers clearly and leave enough space to cross things out.
• Cross out cleanly: When you borrow, cross out the old number and write the new number directly above it so you don't forget.
• Check your work: You can always check a subtraction problem by adding! If $10{,}000 - 4{,}567 = 5{,}433$, then $5{,}433 + 4{,}567$ should equal $10{,}000$.