Subtract 4272 from 51843: Vertical Format Multi-digit Subtraction

Q: What does it mean to 'borrow' in subtraction?

Borrowing means taking 1 from the next higher place value to make subtraction possible. For example, when subtracting 4 - 7, we borrow 1 from the hundreds place, making it 14 - 7 = 7.

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. Like 4 - 7 or 1 - 4 in this problem.

Q: What happens to the digit I borrow from?

The digit you borrow from decreases by 1. In this problem, when we borrowed from 8 in the hundreds place, it became 7. When we borrowed from 5 in the ten-thousands place, it became 4.

Q: Can I borrow from a zero?

You can't directly borrow from 0. Instead, you need to borrow from the next non-zero digit to the left, which creates a chain of borrowing across multiple columns.

Q: Why do we subtract from right to left?

We work right to left because borrowing affects the next column to the left. Starting from the units place ensures we handle all borrowing correctly before moving to the next column.

Column Subtraction with Multi-digit Borrowing

$\begin{aligned} &51843\\ -& \\ &~~4272 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve this together!

00:11 First, subtract two digits each time.

00:15 Subtract the ones digit from the ones place.

00:18 Notice, 4 is less than 7.

00:21 We need to borrow from the hundreds to help the tens.

00:25 The hundreds change from 8 to 7.

00:29 Now, instead of 4, we have 14 in the tens place.

00:34 Subtract the tens digits and place the result in tens.

00:39 Subtract the hundreds digits and place the result in hundreds.

00:44 See, 1 is less than 4.

00:49 We borrow from hundred thousands for the thousands.

00:55 So, now instead of 1, we have 11 in the thousands place.

01:00 Subtract the thousands digits and place in thousands.

01:05 Remember to place 0 in any missing digits.

01:08 Finally, subtract the ten thousands and place the result.

01:13 And there you have it, the solution to the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &51843\\ -& \\ &~~4272 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll use the column subtraction method:

Step 1: Write the numbers vertically, aligning them by place value:
Step 2: Subtract each digit starting from the rightmost (units) place:

$\begin{array}{c} \phantom{12\ } 51843 \\ - \phantom{10} 4272 \\ \hline \end{array}$

Step 3: Units place: $3 - 2 = 1$ .

Step 4: Tens place: $4 - 7$ . Here, we need to borrow 1 from the hundreds place, so it becomes $14 - 7 = 7$ . After borrowing, the hundreds digit from 8 becomes 7.

Step 5: Hundreds place: $7 - 2 = 5$ .

Step 6: Thousands place: $1 - 4$ . Again, we borrow 1 from the ten-thousands place, so it becomes $11 - 4 = 7$ . After borrowing, the ten-thousands digit from 5 becomes 4.

Step 7: Ten-thousands place: $4 - 0 = 4$ .

The completed subtraction is:

$\begin{array}{c} \phantom{12\ } 51843 \\ - \phantom{10} 4272 \\ \hline \phantom{10\ } 47571 \\ \end{array}$

Therefore, the solution to the problem is $47571$ .

Final Answer

47571

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers by place value with larger number on top
Borrowing: When 4 - 7 is impossible, borrow 1 from hundreds: 14 - 7 = 7
Check: Add your answer to the subtracted number: 47571 + 4272 = 51843 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to adjust the borrowed-from digit
Don't subtract 4 - 7 by borrowing but leave the hundreds place as 8 = wrong answer 48571! When you borrow 1 from the hundreds place, that digit decreases by 1. Always reduce the borrowed-from digit after borrowing.

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

What does it mean to 'borrow' in subtraction?

Borrowing means taking 1 from the next higher place value to make subtraction possible. For example, when subtracting 4 - 7, we borrow 1 from the hundreds place, making it 14 - 7 = 7.

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. Like 4 - 7 or 1 - 4 in this problem.

What happens to the digit I borrow from?

The digit you borrow from decreases by 1. In this problem, when we borrowed from 8 in the hundreds place, it became 7. When we borrowed from 5 in the ten-thousands place, it became 4.

Can I borrow from a zero?

You can't directly borrow from 0. Instead, you need to borrow from the next non-zero digit to the left, which creates a chain of borrowing across multiple columns.

How can I check if my subtraction is correct?

Add your answer to the number you subtracted. If you get the original larger number, you're correct! 47571 + 4272 = 51843 ✓

Why do we subtract from right to left?

We work right to left because borrowing affects the next column to the left. Starting from the units place ensures we handle all borrowing correctly before moving to the next column.

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