Solve Vertical Subtraction: 867 minus 578

Q: Why do I need to borrow when doing 867 - 578?

You need to borrow because 7 is smaller than 8 in the ones place, and 6 is smaller than 7 in the tens place. Borrowing lets you make these digits big enough to subtract!

Q: What happens to the number I borrow from?

When you borrow 1 ten from the tens place, that digit gets reduced by 1. So the 6 in 867 becomes 5 after you borrow 1 ten for the ones place.

Q: How do I remember which direction to borrow?

Always borrow from the left! Think of it like borrowing money from a friend - you take from the bigger amount (left column) to help the smaller amount (current column).

Q: What if I need to borrow from zero?

If the column to the left has 0, you need to keep borrowing left until you find a non-zero digit. Then work your way back right, turning each 0 into 9.

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

Use addition to check! Add your answer to the number you subtracted: $ 289 + 578 = 867 $. If you get the original top number, you're right!

Subtraction with Borrowing Across Places

$\begin{aligned} &867 \\ -& \\ &578 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 place

00:06 7 is less than 8

00:11 Therefore we subtract 1 from the tens and add this amount to the ones

00:18 So now instead of 7 we will have 17

00:24 We subtract the ones from the ones plus ten

00:29 We place in the ones

00:35 5 is less than 7

00:41 Therefore we subtract 1 from the hundreds and add this amount to the tens

00:46 So now instead of 5 we will have 15

00:51 We subtract the tens from the tens plus ten

00:56 We place in the tens

01:00 We subtract hundreds from hundreds, and place in hundreds

01:03 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

$\begin{aligned} &867 \\ -& \\ &578 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we’ll perform vertical subtraction:

Step 1: Subtract the units digit: $7$ (in 867) - $8$ (in 578) requires borrowing. Borrow 1 ten from the tens place of 867, making the units place $17$ and the tens place $5$ .
Step 2: Now, $17 - 8 = 9$ . The digit in the units place of the answer is 9.
Step 3: Subtract the tens digit: With the new tens digit, $5 - 7$ also requires borrowing. Borrow 1 from the hundreds place, making the tens place $15$ and the hundreds place $7$ .
Step 4: Now, $15 - 7 = 8$ . The digit in the tens place of the answer is 8.
Step 5: Subtract the hundreds digit: $7 - 5 = 2$ . The digit in the hundreds place of the answer is 2.

Therefore, the final answer after subtraction is $289$ .

Final Answer

289

Key Points to Remember

Essential concepts to master this topic

Borrowing Rule: When top digit is smaller, borrow from the left column
Place Value Method: Transform 7 to 17 by borrowing 1 ten from 60s place
Verification Check: Add your answer to the subtracted number: 289 + 578 = 867 ✓

Common Mistakes

Avoid these frequent errors

Subtracting smaller from larger regardless of position
Don't subtract 7 - 8 as 8 - 7 = 1! This ignores place value and gives completely wrong answers like 389. Always borrow from the left column 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

Why do I need to borrow when doing 867 - 578?

You need to borrow because 7 is smaller than 8 in the ones place, and 6 is smaller than 7 in the tens place. Borrowing lets you make these digits big enough to subtract!

What happens to the number I borrow from?

When you borrow 1 ten from the tens place, that digit gets reduced by 1. So the 6 in 867 becomes 5 after you borrow 1 ten for the ones place.

How do I remember which direction to borrow?

Always borrow from the left! Think of it like borrowing money from a friend - you take from the bigger amount (left column) to help the smaller amount (current column).

What if I need to borrow from zero?

If the column to the left has 0, you need to keep borrowing left until you find a non-zero digit. Then work your way back right, turning each 0 into 9.

How can I check if my subtraction is correct?

Use addition to check! Add your answer to the number you subtracted: $289 + 578 = 867$ . If you get the original top number, you're right!

Why is my answer different when I don't borrow?

Without borrowing, you're not following place value rules! You might get 389 instead of 289, which is completely wrong. Borrowing is required when the top digit is smaller.

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