Solve: 5421 minus 3675 in Vertical Subtraction Format

Q: Why do I need to borrow multiple times in this problem?

In 5421 - 3675, you need to borrow three times because the top digits (1, 2, 4) are all smaller than the bottom digits (5, 7, 6) in their respective places. Each borrowing is independent - handle one column at a time!

Q: What happens to the digit I borrow from?

When you borrow 1 from a digit, that digit becomes 1 less. For example, when borrowing from the tens place (4), it becomes 3. Always remember to update the digit you borrowed from!

Q: How do I know when I need to borrow?

You need to borrow whenever the top digit is smaller than the bottom digit in any column. In our problem: 1

Q: What if I borrow from a zero?

When borrowing from 0, it becomes 10, but you also need to borrow from the next column to the left. This creates a chain reaction - keep borrowing until you reach a non-zero digit.

Q: Can I check my subtraction answer?

Yes! Add your answer to the number you subtracted: $ 1746 + 3675 = 5421 $. If you get the original number, your subtraction is correct!

Q: Why does borrowing turn 1 into 11?

Borrowing 1 from the tens place gives you 10 more units. So 1 unit + 10 units = 11 units total. Think of it as trading one ten-dollar bill for ten one-dollar bills!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve this problem together.

00:11 We'll borrow a group of 10 to help us subtract.

00:15 First, notice that 1 is less than 5.

00:18 So, we'll take 1 from the tens place, and add 10 to the ones.

00:23 Now, we have 11 in the ones place.

00:26 Subtract the smaller digit from the larger one and write the answer in the ones column.

00:31 Next, let's check the tens place. 1 is less than 7.

00:35 Again, we'll borrow, taking 1 from the hundreds and adding 10 to the tens.

00:41 Now, we have 11 in the tens place.

00:45 Subtract and write your result in the tens column.

00:48 Check the hundreds. Is 3 less than 6? Yes, it is.

00:54 So, we'll take 1 from the thousands, adding 10 to the hundreds.

01:00 Now we have 13 in the hundreds place.

01:06 Subtract as before, and place your answer in the hundreds.

01:11 Finally, subtract the thousands the same way.

01:15 And there you have it! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\begin{aligned} &5421 \\ -& \\ &3675 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

2

Step-by-step solution

To solve this problem, we'll execute vertical subtraction with regrouping as follows:

Let's start by aligning the numbers one above the other:
$\begin{array}{c} && 5 & 4 & 2 & 1 \\ - & & 3 & 6 & 7 & 5 \\ \hline \end{array}$

We begin subtraction from the rightmost digits (units place):

Units: $1 - 5$ requires borrowing because 1 is less than 5. Borrow 1 from the tens (making it 3), turning 1 into 11. Now, $11 - 5 = 6$ .

Next, subtract the tens:

Tens: $2 - 7$ requires borrowing because 2 is less than 7. Borrow 1 from the hundreds (making it 3), turning 2 into 12. Now, $12 - 7 = 5$ .

Then, subtract the hundreds:

Hundreds: $3 - 6$ requires borrowing because 3 is less than 6. Borrow 1 from the thousands (making it 4), turning 3 into 13. Now, $13 - 6 = 7$ .

Finally, subtract the thousands:

Thousands: $4 - 3 = 1$ .

Putting it all together, the result is:

$\begin{array}{c} & 5 & 4 & 2 & 1 \\ - & 3 & 6 & 7 & 5 \\ \hline & 1 & 7 & 4 & 6 \\ \end{array}$

Therefore, the solution to the problem is $1746$ .

3

Final Answer

1746

Key Points to Remember

Essential concepts to master this topic

Borrowing Rule: Start from rightmost digit and borrow from next higher place value
Technique: When 1 < 5, borrow from tens: 11 - 5 = 6
Check: Add your answer to subtrahend: 1746 + 3675 = 5421 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to reduce the borrowed-from digit
Don't borrow 1 from the tens place but forget to change 4 to 3 = wrong calculation in next column! This creates incorrect values that multiply through remaining steps. Always reduce the digit you borrowed from by 1.

Practice Quiz

Test your knowledge with interactive questions

$\begin{aligned} &15 \\ -& \\ &~~4 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

FAQ

Everything you need to know about this question

Why do I need to borrow multiple times in this problem?

+

In 5421 - 3675, you need to borrow three times because the top digits (1, 2, 4) are all smaller than the bottom digits (5, 7, 6) in their respective places. Each borrowing is independent - handle one column at a time!

What happens to the digit I borrow from?

+

When you borrow 1 from a digit, that digit becomes 1 less. For example, when borrowing from the tens place (4), it becomes 3. Always remember to update the digit you borrowed from!

How do I know when I need to borrow?

+

You need to borrow whenever the top digit is smaller than the bottom digit in any column. In our problem: 1 < 5, 2 < 7, and 4 < 6, so we borrow three times.

What if I borrow from a zero?

+

When borrowing from 0, it becomes 10, but you also need to borrow from the next column to the left. This creates a chain reaction - keep borrowing until you reach a non-zero digit.

Can I check my subtraction answer?

+

Yes! Add your answer to the number you subtracted: $1746 + 3675 = 5421$ . If you get the original number, your subtraction is correct!

Why does borrowing turn 1 into 11?

+

Borrowing 1 from the tens place gives you 10 more units. So 1 unit + 10 units = 11 units total. Think of it as trading one ten-dollar bill for ten one-dollar bills!

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Solve: 5421 minus 3675 in Vertical Subtraction Format

Vertical Subtraction with Multi-Digit Borrowing

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