Solve the Vertical Subtraction: 8314 minus 5278

Q: What happens to the digit I borrow from?

The digit you borrow from gets reduced by 1. If you borrow from 3, it becomes 2. If you borrow from 1, it becomes 0. This is crucial for getting the right answer!

Q: Do I always start subtracting from the right?

Yes! Always start from the units column (rightmost) and work your way left. This ensures borrowing works correctly through each column.

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

Use addition to check! Add your answer to the number you subtracted. If you get the original number back, you're correct: $3036 + 5278 = 8314$ ✓

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

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

Q: Is there a pattern to borrowing in subtraction?

Yes! When you borrow: the digit you're working with gets +10, and the digit you borrow from gets -1. This pattern helps you stay organized.

Multi-Digit Subtraction with Borrowing

$\begin{aligned} &8314 \\ -& \\ &5278 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Each time we consider a deficit of 2 digits, and then we place

00:06 4 is less than 8

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

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

00:19 We subtract the ones from the ones plus ten

00:22 We place in the ones

00:29 0 is less than 7

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

00:38 So now instead of 0 we will have 10

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

00:46 We place in the tens

00:50 We subtract hundreds from hundreds, and place in hundreds

00:56 We subtract thousands from thousands, and place in thousands

00:59 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

$\begin{aligned} &8314 \\ -& \\ &5278 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve the problem of subtracting 5278 from 8314, we'll follow these steps:

Step A: Subtract the units: $4 - 8$ . Since 4 is less than 8, we need to borrow 1 from the tens column, making it $14 - 8 = 6$ .
Step B: After borrowing, the tens column is $0$ (since the 1 we borrowed from 1 in 31 becomes 30). So, $0 - 7$ again requires borrowing from hundreds, making it $10 - 7 = 3$ .
Step C: The hundreds column reduces to 2 after borrowing, leading to $2 - 2 = 0$ .
Step D: Finally, the thousands column, $8 - 5$ , gives us $3$ .

Therefore, the result of the subtraction $8314 - 5278$ is $3036$ .

Final Answer

3036

Key Points to Remember

Essential concepts to master this topic

Borrowing Rule: When top digit is smaller, borrow 1 from the next column
Column Method: Start from units: 14 - 8 = 6 after borrowing from tens
Check Work: Add your answer to the subtracted number: 3036 + 5278 = 8314 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to reduce the borrowed-from digit
Don't borrow 1 from tens but forget to change 1 to 0 = wrong calculation! This leaves the borrowed digit unchanged, giving incorrect results in that column. Always reduce the borrowed-from digit by 1 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

Why do I need to borrow when the top number is smaller?

When the top digit is smaller than the bottom digit, you can't subtract directly. Borrowing lets you 'take' 10 from the next column, making subtraction possible. For example, 4 becomes 14 when you borrow.

What happens to the digit I borrow from?

The digit you borrow from gets reduced by 1. If you borrow from 3, it becomes 2. If you borrow from 1, it becomes 0. This is crucial for getting the right answer!

Do I always start subtracting from the right?

Yes! Always start from the units column (rightmost) and work your way left. This ensures borrowing works correctly through each column.

How can I check if my subtraction is correct?

Use addition to check! Add your answer to the number you subtracted. If you get the original number back, you're correct: $3036 + 5278 = 8314$ ✓

What if I need to borrow from a zero?

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

Is there a pattern to borrowing in subtraction?

Yes! When you borrow: the digit you're working with gets +10, and the digit you borrow from gets -1. This pattern helps you stay organized.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Arithmetic Operations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime