Solve: 3732 minus 2865 Using Vertical Subtraction

Q: What happens when the top digit is smaller than the bottom digit?

You need to borrow from the next column to the left! Add 10 to the current digit and subtract 1 from the digit you borrowed from.

Q: Why do we start from the right side?

We start from the ones place because any borrowing affects the next column to the left. This prevents confusion and ensures we handle all borrowing correctly.

Q: How can I check if my subtraction is correct?

Add your answer to the number you subtracted. If you get the original number back, your subtraction is correct! For this problem: 867 + 2865 = 3732 ✓

Q: Is there a pattern to borrowing?

Yes! When you borrow: the current digit gets +10, and the next digit gets -1. Remember this pattern and you'll never forget to adjust both digits.

Vertical Subtraction with Borrowing

$\begin{aligned} &3732 \\ -& \\ &2865 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Each time we consider a shortage of 2 digits, and then we'll place

00:09 2 is less than 5

00:13 Therefore we'll subtract 1 from the tens, and add this amount to the ones

00:17 Meaning now instead of 2 we'll have 12

00:20 We'll subtract the ones from the ones plus ten

00:23 We'll place in the ones

00:29 2 is less than 6

00:33 Therefore we'll subtract 1 from the hundreds, and add this amount to the tens

00:36 Meaning now instead of 2 we'll have 12

00:42 We'll subtract the tens from the tens plus ten

00:45 We'll place in the tens

00:50 6 is less than 8

00:54 Therefore we'll subtract 1 from the thousands, and add this amount to the hundreds

00:59 Meaning now instead of 6 we'll have 16

01:04 We'll subtract the hundreds from the hundreds plus hundred

01:07 We'll place in the hundreds

01:10 We'll subtract thousands from thousands, and place in thousands

01:13 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &3732 \\ -& \\ &2865 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve the subtraction problem $3732 - 2865$ , we will use the vertical subtraction method and ensure proper borrowing where needed:

Step 1: Subtract the units digit: $2 - 5$ . Since 2 is less than 5, we borrow 10 from the tens column, making it $12$ . Then, $12 - 5 = 7$ .
Step 2: Move to the tens digit: Due to borrowing, we now have $2$ (from the original 3) in the tens column. Subtract $6$ , i.e., $2 - 6$ . We need to borrow from the hundreds column, so $12 - 6 = 6$ .
Step 3: Hundreds digit: Originally, we have $7$ but reduced to $6$ due to prior borrowing. Subtract $8$ , i.e., $6 - 8$ . We borrow from the thousands: $16 - 8 = 8$ .
Step 4: Thousands digit: Now having $2$ (from the original 3 due to borrowing), subtract $2$ : $2 - 2 = 0$ .

The solution to the subtraction of $3732 - 2865$ is $867$ .

Final Answer

867

Key Points to Remember

Essential concepts to master this topic

Rule: Work from right to left, borrowing when needed
Technique: When borrowing, add 10 to current digit and subtract 1 from next
Check: Add your answer to the subtrahend: 867 + 2865 = 3732 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to reduce borrowed digit
Don't borrow 10 without reducing the next column by 1 = wrong calculations! When you borrow, the lending digit becomes 1 less. Always remember to subtract 1 from the digit you borrowed from.

Practice Quiz

Test your knowledge with interactive questions

$\begin{aligned} &105 \\ -& \\ &~~~~3 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

FAQ

Everything you need to know about this question

What happens when the top digit is smaller than the bottom digit?

You need to borrow from the next column to the left! Add 10 to the current digit and subtract 1 from the digit you borrowed from.

Why do we start from the right side?

We start from the ones place because any borrowing affects the next column to the left. This prevents confusion and ensures we handle all borrowing correctly.

What if I need to borrow from a zero?

First borrow from the next non-zero digit, making all zeros become 9s along the way. For example: $1002$ becomes $0\underline{9}\underline{9}12$ after borrowing.

How can I check if my subtraction is correct?

Add your answer to the number you subtracted. If you get the original number back, your subtraction is correct! For this problem: 867 + 2865 = 3732 ✓

Is there a pattern to borrowing?

Yes! When you borrow: the current digit gets +10, and the next digit gets -1. Remember this pattern and you'll never forget to adjust both digits.

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