Solve Vertical Subtraction: 767 minus 9 Step-by-Step

Q: Why can't I just subtract 7 - 9 directly?

You can't subtract a larger number from a smaller one in basic subtraction! When the bottom digit is bigger, you must borrow from the column to the left first.

Q: How do I know when to borrow?

Look at each column from right to left. If the top digit is smaller than the bottom digit, you need to borrow 1 from the next column over.

Q: What happens to the number I borrow from?

When you borrow 1 from a column, that digit gets reduced by 1. In this problem, the 6 in the tens place became 5 after we borrowed from it.

Q: Can I borrow from any column?

You can only borrow from the column immediately to the left. If that column is 0, you'll need to borrow from further left columns first.

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

Add your answer to the number you subtracted: $ 758 + 9 = 767 $. If you get the original number, your subtraction is correct!

Vertical Subtraction with Regrouping

$\begin{aligned} &767 \\ -& \\ &~~~~9 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 consider a shortage of 2 digits, and then place

00:06 7 is less than 9

00:09 Therefore subtract 1 from the tens, and add this amount to the ones

00:14 Which means now instead of 7 we will have 17

00:19 Subtract the ones from the ones plus ten

00:22 Place in the ones

00:25 Place 0 in the missing digits

00:28 Subtract tens from tens, and place in tens

00:32 Subtract hundreds from hundreds, and place in hundreds

00:35 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

$\begin{aligned} &767 \\ -& \\ &~~~~9 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve the subtraction of 9 from 767, we will perform the following steps:

Step 1: Set up the subtraction in a vertical format:
$\begin{array}{c} 767 \\ - 9 \\ \hline \end{array}$
Step 2: Start with the units column (rightmost column). We have 7 in the units place of the number 767. Since 7 is greater than 9, we need to regroup.
Step 3: Regroup by borrowing 1 ten from the tens place (left to the units), changing the 6 in the tens column to a 5, and making the units 10 + 7 = 17.
Step 4: Now, subtract the units place: 17 - 9 = 8.
Step 5: Move to the tens column. After regrouping, we have 5 in the tens place. Subtract 0 (nothing was subtracted here beyond initial borrowing), so it remains 5.
Step 6: Finally, look at the hundreds column. Since no borrowing affected this column, simply bring the 7 down.

The resulting number after subtracting 9 from 767 is 758.

Therefore, the solution to the subtraction problem is $758$ .

Final Answer

758

Key Points to Remember

Essential concepts to master this topic

Regrouping Rule: Borrow 1 from left column when top digit is smaller
Technique: Change 7 to 17 by borrowing, making 17 - 9 = 8
Check: Add back: 758 + 9 = 767 to verify your answer ✓

Common Mistakes

Avoid these frequent errors

Subtracting smaller from larger without regrouping
Don't subtract 7 - 9 = -2 and ignore the negative! This creates impossible negative digits in your answer. Always borrow from the left column first, making 17 - 9 = 8.

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 can't I just subtract 7 - 9 directly?

You can't subtract a larger number from a smaller one in basic subtraction! When the bottom digit is bigger, you must borrow from the column to the left first.

How do I know when to borrow?

Look at each column from right to left. If the top digit is smaller than the bottom digit, you need to borrow 1 from the next column over.

What happens to the number I borrow from?

When you borrow 1 from a column, that digit gets reduced by 1. In this problem, the 6 in the tens place became 5 after we borrowed from it.

Can I borrow from any column?

You can only borrow from the column immediately to the left. If that column is 0, you'll need to borrow from further left columns first.

How do I check if my subtraction is correct?

Add your answer to the number you subtracted: $758 + 9 = 767$ . If you get the original number, your subtraction is correct!

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