Solve Vertical Subtraction: 576 minus 8

Subtraction with Regrouping from Tens Place

576    8776 \begin{aligned} &576 \\ -& \\ &~~~~8 \\ &\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 6 is less than 8
00:09 Therefore we borrow ten from the tens column for the ones place
00:12 Which will turn the tens from 7 to 6
00:15 And now instead of 6 we'll have 16 in the ones place!
00:19 Subtract ones from ones, and place in ones
00:24 Place 0 in the missing digits
00:27 Subtract tens from tens, and place in tens
00:30 Place 0 in the missing digits
00:33 Subtract hundreds from hundreds, and place in hundreds
00:36 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

576    8776 \begin{aligned} &576 \\ -& \\ &~~~~8 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we will perform subtraction using the vertical method:

  • Step 1: Set up the subtraction problem:
    Write the minuend, 576, above the subtrahend, 8, aligning the digits by place value:

576   8776 \begin{aligned} &576 \\ -& \\ &~~~8 \\ &\underline{\phantom{776}} \end{aligned}

  • Step 2: Start with the ones column:
    Since we have 6 in the ones column of 576, we don't need to regroup:

The subtraction becomes 68 6 - 8 , which is impossible as we cannot subtract a larger number from a smaller number without regrouping.

  • Step 3: Move to the tens column.
    Since we have 7 tens in 576, we can regroup one ten to the ones column:
  • Change the 7 in the tens place to 6 and turn the 6 in the ones place into 16.
  • Now subtract 16 ones - 8 ones = 8 ones.

The subtraction in the ones column now reads 16 - 8 = 8.

  • Step 4: Subtract the tens column:
    After regrouping, the tens column subtraction becomes 6 (in tens from 576) - 0 (in tens from 8):

60=6 6 - 0 = 6

  • Step 5: Subtract the hundreds column:
    The hundreds remain unchanged as the subtrahend does not have hundreds:

50=5 5 - 0 = 5

The subtraction is complete: 5768=568 576 - 8 = 568 .

Therefore, the solution to the problem is 568 568 .

3

Final Answer

568

Key Points to Remember

Essential concepts to master this topic
  • Regrouping Rule: When ones digit is smaller, borrow from tens place
  • Technique: Change 7 tens to 6 tens, making 6 ones into 16 ones
  • Check: Add your answer to subtrahend: 568 + 8 = 576 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting smaller from larger in wrong order
    Don't subtract 6 - 8 = -2 or flip it to 8 - 6 = 2! This ignores place value and gives wrong answers. Always regroup first: borrow 1 ten to make 16 - 8 = 8 in the ones place.

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

Why can't I just subtract 8 from 6 in the ones place?

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You cannot subtract a larger number from a smaller number without regrouping! When you see 6 - 8, you need to borrow from the tens place first.

How do I know when to regroup?

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Look at each column from right to left. If the top digit is smaller than the bottom digit, you need to regroup by borrowing from the next column to the left.

What happens to the tens place when I borrow?

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When you borrow 1 ten, it becomes 10 ones. So the tens digit decreases by 1, and the ones digit increases by 10. In this problem: 7 tens became 6 tens, and 6 ones became 16 ones.

Can I check my answer without adding?

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Yes! You can also count up from 8 to 576. Start at 8, then count: 8 + 2 = 10, then 10 + 566 = 576. This confirms the difference is 568.

What if there's a zero in the tens place?

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If the tens place has 0, you need to keep borrowing from the hundreds place first! Change the hundreds digit, make the tens place 10, then borrow from there.

Why do we line up the numbers on the right?

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Place value alignment is crucial! The ones digits must line up in the ones column, tens in tens column, etc. This ensures you're subtracting the right values.

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