Solve Three-Digit Subtraction: 936 minus 768 in Vertical Format

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

You need to borrow from the next column! Take 10 from the column to the left, add it to your current digit, then reduce the left column by 1.

Q: Why do we subtract from right to left?

We follow place value order - ones, then tens, then hundreds. This way, if we need to borrow, we're borrowing from the correct place value column.

Q: What if I need to borrow from a zero?

Look further left until you find a non-zero digit. Borrow from there, turning each zero into 9 as you work back to your original column.

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

Use addition to check! Add your answer to the bottom number (subtrahend). If you get the top number (minuend), your subtraction is correct.

Q: Do I always need to borrow in subtraction?

No! You only borrow when the top digit is smaller than the bottom digit. If 6 - 4, you don't need to borrow since 6 > 4.

Multi-Digit Subtraction with Borrowing

$\begin{aligned} &936 \\ -& \\ &768 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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

00:06 6 is less than 8

00:12 Therefore we'll subtract 1 from the tens and add this amount to the ones

00:20 So now instead of 6 we'll have 16

00:25 We'll subtract the ones from the ones plus ten

00:28 We'll place in the ones

00:34 2 is less than 6

00:44 Therefore we'll subtract 1 from the hundreds and add this amount to the tens

00:48 So now instead of 2 we'll have 12

00:52 We'll subtract the tens from the tens plus ten

00:59 We'll place in the tens

01:06 We'll subtract hundreds from hundreds, and place in hundreds

01:11 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &936 \\ -& \\ &768 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this subtraction problem, we'll perform vertical subtraction, which involves subtracting each corresponding pair of digits from right to left.

Step 1: Arrange the numbers vertically.
- Write 936 (the minuend) on top.
- Write 768 (the subtrahend) below it, aligning the digits by place value.
Step 2: Subtract the ones place.
Subtract 8 from 6. Since 8 is larger than 6, we need to borrow 1 from the tens place:
- Decrease the digit in the tens place (from 3 to 2).
- Increase the ones digit by 10 (making it 16).
- 16 - 8 = 8, write 8 below the line.
Step 3: Subtract the tens place.
Now subtract 6 from the adjusted tens digit (2):
- Since 6 is larger than 2, borrow 1 from the hundreds place (from 9 to 8).
- Increase the tens digit by 10 (making it 12).
- 12 - 6 = 6, write 6 below the line.
Step 4: Subtract the hundreds place.
Subtract 7 from the adjusted hundreds digit (8):
- 8 - 7 = 1, write 1 below the line.

Thus, the result of the subtraction $936 - 768$ is 168.

Final Answer

168

Key Points to Remember

Essential concepts to master this topic

Rule: Always align digits by place value when setting up
Technique: Borrow 10 from next column: 6 becomes 16 - 8 = 8
Check: Add your answer to subtrahend: 168 + 768 = 936 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to reduce the borrowed digit
Don't borrow 10 from the tens place but forget to reduce 3 to 2 = wrong calculations throughout! This creates errors that spread to every remaining column. Always reduce the borrowed digit by 1 immediately after borrowing.

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 do I do when the top digit is smaller than the bottom digit?

You need to borrow from the next column! Take 10 from the column to the left, add it to your current digit, then reduce the left column by 1.

Why do we subtract from right to left?

We follow place value order - ones, then tens, then hundreds. This way, if we need to borrow, we're borrowing from the correct place value column.

What if I need to borrow from a zero?

Look further left until you find a non-zero digit. Borrow from there, turning each zero into 9 as you work back to your original column.

How can I check if my subtraction is correct?

Use addition to check! Add your answer to the bottom number (subtrahend). If you get the top number (minuend), your subtraction is correct.

Do I always need to borrow in subtraction?

No! You only borrow when the top digit is smaller than the bottom digit. If 6 - 4, you don't need to borrow since 6 > 4.

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