Solve the Subtraction Problem: 8651 minus 7740

Q: What does borrowing mean in subtraction?

Borrowing means taking 10 from the digit to the left and adding it to the current digit. For example, when 6 can't subtract 7, we borrow 1 from the 8 (making it 7) and turn 6 into 16.

Q: Why can't I just subtract the smaller number from the larger one?

Because place value matters! In $8651 - 7740$, the 6 in the hundreds place represents 600, not just 6. You must respect each digit's position when subtracting.

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. Look at each place value from right to left and check if borrowing is needed.

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

When borrowing from 0, you must keep borrowing left until you find a non-zero digit. Turn that digit into 9s as you work back to your original column.

Q: What should I do if my answer seems too big or too small?

Double-check your borrowing steps! Common errors include forgetting to reduce the borrowed-from digit or not carrying the borrowing through multiple columns.

Multi-Digit Subtraction with Borrowing

$\begin{aligned} &8651 \\ -& \\ &7740 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 subtract 2 digits, and then we'll place

00:06 Subtract ones from ones, and place in ones

00:09 Subtract tens from tens, and place in tens

00:14 6 is less than 7

00:20 Therefore we subtract 1 from thousands, and add this amount to hundreds

00:25 Meaning now instead of 6 we will have 16

00:30 Subtract the hundreds from hundreds plus the hundred

00:33 Place in hundreds

00:36 Subtract thousands from thousands, and place in thousands

00:39 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

$\begin{aligned} &8651 \\ -& \\ &7740 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

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

Step 1: Align the numbers by place value.
Step 2: Subtract each digit starting from the rightmost side.
Step 3: Perform borrowing where necessary.

Now, let's go through each step:
Step 1: Align the numbers:
$\begin{array}{c} 8651 \\ -7740 ~~~\\ \hline \end{array}$

Step 2: Begin with the unit place.
From the rightmost digit (units), subtract: $1 - 0 = 1$ .

Step 3: Move to the tens place. Subtract $5 - 4 = 1$ .

Step 4: Move to the hundreds place. Subtract $6 - 7$ . Since 6 is less than 7, we borrow 1 from the thousands place:
Change 8 (thousands) to 7, and 6 becomes 16.
Now, subtract $16 - 7 = 9$ .

Step 5: For the thousands place, after borrowing, subtract $7 - 7 = 0$ .

Putting it all together, the result of the subtraction is $911$ .

Therefore, the solution to the problem is $911$ .

Final Answer

911

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers by place value before subtracting digits
Borrowing: When top digit is smaller, borrow 10 from left neighbor: 6 becomes 16
Verification: Add your answer to the subtracted number: 911 + 7740 = 8651 ✓

Common Mistakes

Avoid these frequent errors

Subtracting smaller from larger regardless of position
Don't subtract 6 - 7 = 1 by switching to 7 - 6 = wrong answer! This ignores place value and gives incorrect results. Always borrow from the left when the top digit is smaller than the bottom digit.

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 does borrowing mean in subtraction?

Borrowing means taking 10 from the digit to the left and adding it to the current digit. For example, when 6 can't subtract 7, we borrow 1 from the 8 (making it 7) and turn 6 into 16.

Why can't I just subtract the smaller number from the larger one?

Because place value matters! In $8651 - 7740$ , the 6 in the hundreds place represents 600, not just 6. You must respect each digit's position when subtracting.

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. Look at each place value from right to left and check if borrowing is needed.

What if I need to borrow from a zero?

When borrowing from 0, you must keep borrowing left until you find a non-zero digit. Turn that digit into 9s as you work back to your original column.

How can I check if my subtraction answer is correct?

Add your answer to the number you subtracted. If you get the original number, you're correct! For example: $911 + 7740 = 8651$ ✓

What should I do if my answer seems too big or too small?

Double-check your borrowing steps! Common errors include forgetting to reduce the borrowed-from digit or not carrying the borrowing through multiple columns.

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