Subtract 667 from 756: Vertical Format Three-Digit Subtraction

Q: Why can't I just subtract 7 from 6 in the ones place?

You cannot subtract a larger number from a smaller number in standard subtraction! When the top digit is smaller, you must borrow from the next column to make it larger.

Q: What does borrowing actually mean?

Borrowing means taking 1 from the next column (worth 10 in the current column) and adding it to make subtraction possible. For example, borrowing 1 from tens makes 6 become 16 in the ones place.

Q: Do I always need to borrow in subtraction?

No! You only borrow when the top digit is smaller than the bottom digit in any column. If 8 - 3, no borrowing needed. If 3 - 8, then you must borrow.

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

Add your answer to the number you subtracted. If you get the original number, you're right! $ 89 + 667 = 756 $ ✓

Q: What if I need to borrow from zero?

When borrowing from 0, you need to borrow from the next non-zero digit to the left first. The 0 becomes 10, then you can borrow 1 from it, leaving 9.

Q: Can the answer have fewer digits than the original number?

Yes! When subtracting, your answer can have fewer digits than the original number. Like $ 756 - 667 = 89 $ (3 digits become 2 digits).

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Each time we consider borrowing 2 digits, and then we place

00:06 6 is less than 7

00:10 Therefore we subtract 1 from the tens and add this amount to the ones

00:14 So now instead of 6 we will have 16

00:17 We subtract the ones from the ones plus ten

00:20 We place in the ones

00:25 4 is less than 6

00:29 Therefore we subtract 1 from the hundreds and add this amount to the tens

00:32 So now instead of 4 we will have 14

00:36 We subtract the tens from the tens plus ten

00:42 We place in the tens

00:47 We subtract hundreds from hundreds, and place in hundreds

00:53 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\begin{aligned} &756 \\ -& \\ &667 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

2

Step-by-step solution

To solve this problem, we'll follow these steps in vertical subtraction:

Step 1: Write down the numbers aligning them by their place values:

$\begin{aligned} & 756 \\ - & 667 \\ \hline \phantom{0} \end{aligned}$

Step 2: Subtract the units digit:

The units digit of 756 is 6, and the units digit of 667 is 7. Since 6 < 7, we need to regroup. We borrow 1 from the tens column, turning the 5 into a 4, and make the 6 into 16. Now $16 - 7 = 9$ .

Step 3: Subtract the tens digit:

After regrouping, the tens digit of 756 became 4, and we subtract the tens digit of 667, which is 6. Again, since 4 < 6, we need to regroup from the hundreds column. Borrowing 1, we turn the 7 into a 6, and the 4 into 14. Now $14 - 6 = 8$ .

Step 4: Subtract the hundreds digit:

The hundreds digit of 756 after regrouping is now 6, and for 667, it is 6 as well. So, $6 - 6 = 0$ .

After completing the subtraction, we have:

$\begin{aligned} & 756 \\ - & 667 \\ \hline & 089 \end{aligned}$

Therefore, the solution to the subtraction problem is $\boldsymbol{89}$ .

3

Final Answer

89

Key Points to Remember

Essential concepts to master this topic

Regrouping Rule: Borrow from the next column when top digit is smaller
Technique: Turn 6 into 16 by borrowing 1 from tens place
Check: Add answer to subtrahend: 89 + 667 = 756 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to reduce borrowed digit
Don't borrow 1 from tens place but forget to reduce 5 to 4 = wrong calculation in tens column! This creates errors that cascade through remaining columns. Always reduce the digit you borrowed from by 1.

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

Why can't I just subtract 7 from 6 in the ones place?

+

You cannot subtract a larger number from a smaller number in standard subtraction! When the top digit is smaller, you must borrow from the next column to make it larger.

What does borrowing actually mean?

+

Borrowing means taking 1 from the next column (worth 10 in the current column) and adding it to make subtraction possible. For example, borrowing 1 from tens makes 6 become 16 in the ones place.

Do I always need to borrow in subtraction?

+

No! You only borrow when the top digit is smaller than the bottom digit in any column. If 8 - 3, no borrowing needed. If 3 - 8, then you must borrow.

How do I check if my subtraction is correct?

+

Add your answer to the number you subtracted. If you get the original number, you're right! $89 + 667 = 756$ ✓

What if I need to borrow from zero?

+

When borrowing from 0, you need to borrow from the next non-zero digit to the left first. The 0 becomes 10, then you can borrow 1 from it, leaving 9.

Can the answer have fewer digits than the original number?

+

Yes! When subtracting, your answer can have fewer digits than the original number. Like $756 - 667 = 89$ (3 digits become 2 digits).

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Subtract 667 from 756: Vertical Format Three-Digit Subtraction

Three-Digit Subtraction with Regrouping

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