Subtract 8571 from 66742: Multi-Digit Subtraction Practice

Q: What happens when I need to borrow from a zero?

When you need to borrow from 0, you have to borrow from the next digit to the left first. The 0 becomes 10, then you can borrow 1 from it, making it 9.

Q: How do I know when to borrow?

You need to borrow when the top digit is smaller than the bottom digit in any column. For example, in this problem, 4

Q: Why do we start from the right side?

We start from the ones place (rightmost) because borrowing affects the columns to the left. Working right to left ensures we handle all borrowing correctly!

Q: Can I check my answer without doing the whole addition?

Yes! You can use estimation: 66,742 is about 67,000 and 8,571 is about 9,000. So 67,000 - 9,000 = 58,000, which is close to our answer 58,171.

Q: What if I make a borrowing mistake?

If your final answer doesn't check out when you add it back, look for borrowing errors. Make sure each digit you borrowed from is reduced by 1, and each digit you borrowed to is increased by 10.

Multi-Digit Subtraction with Borrowing

$\begin{aligned} &66742 \\ -& \\ &~~8571 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 we consider a shortage of 2 digits, and then we'll place

00:06 Now we subtract ones from ones, and we'll place in ones

00:09 4 is less than 7

00:14 And now we'll borrow ten from hundreds for the tens

00:19 Which will change the hundreds from 7 to 6

00:22 In other words, now instead of 4 we'll have 14, in tens!

00:28 Subtract tens from tens, and we'll place in tens

00:32 Subtract hundreds from hundreds, and we'll place in hundreds

00:37 6 is less than 8

00:42 We'll borrow one hundred thousand from hundred thousands for the thousands

00:47 In other words, now instead of 6 we'll have 16, in thousands!

00:52 Subtract thousands from thousands, and we'll place in thousands

00:57 Place 0 in the missing digits

01:02 Subtract tens of thousands from tens of thousands, and we'll place

01:06 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

$\begin{aligned} &66742 \\ -& \\ &~~8571 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

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

Step 1: Write the numbers 66,742 and 8,571 vertically, aligning them by their right-hand digits.
Step 2: Start subtracting from the rightmost column (units):
- Subtract 1 from 2: The result is 1.
Step 3: Move to the tens column:
- Subtract 7 from 4. Since 4 is less than 7, we need to borrow 1 from the hundreds place, making it 14.
- Subtract 7 from 14: The result is 7.
Step 4: Move to the hundreds column, remembering we borrowed 1, leaving us with 6 in the hundreds place:
- Subtract 5 from 6: The result is 1.
Step 5: Move to the thousands column:
- Subtract 8 from 6. Since 6 is less than 8, borrow 1 from the ten-thousands place, making it 16.
- Subtract 8 from 16: The result is 8.
Step 6: Move to the ten-thousands column, remembering we borrowed 1, leaving us with 5:
- Subtract 0 from 5: The result is 5.

Therefore, the solution to the problem is $58,171$ .

Final Answer

58171

Key Points to Remember

Essential concepts to master this topic

Borrowing Rule: When the top digit is smaller, borrow from the left
Column Method: Start from rightmost digit: 2-1=1, then 14-7=7
Verification: Add your answer to the subtrahend: 58,171 + 8,571 = 66,742 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to reduce the borrowed-from digit
Don't leave 7 as 7 after borrowing 1 from it = wrong calculation! When you borrow 1 from a digit, that digit becomes 1 less. Always reduce the digit you borrowed from and remember this change for the next column.

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 happens when I need to borrow from a zero?

When you need to borrow from 0, you have to borrow from the next digit to the left first. The 0 becomes 10, then you can borrow 1 from it, making it 9.

How do I know when to borrow?

You need to borrow when the top digit is smaller than the bottom digit in any column. For example, in this problem, 4 < 7 in the tens place, so we borrowed from the hundreds.

Why do we start from the right side?

We start from the ones place (rightmost) because borrowing affects the columns to the left. Working right to left ensures we handle all borrowing correctly!

Can I check my answer without doing the whole addition?

Yes! You can use estimation: 66,742 is about 67,000 and 8,571 is about 9,000. So 67,000 - 9,000 = 58,000, which is close to our answer 58,171.

What if I make a borrowing mistake?

If your final answer doesn't check out when you add it back, look for borrowing errors. Make sure each digit you borrowed from is reduced by 1, and each digit you borrowed to is increased by 10.

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