Solve Vertical Subtraction: 76 minus 8 Step-by-Step

Vertical Subtraction with Borrowing

76  8776 \begin{aligned} &76 \\ -& \\ &~~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 borrowing 2 digits, and then we'll place
00:06 6 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 6 we will have 16
00:18 We subtract the ones from the ones plus the ten
00:21 We place in the ones
00:24 We place 0 in the borrowed digits
00:27 We subtract tens from tens, and place in the tens
00:30 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

76  8776 \begin{aligned} &76 \\ -& \\ &~~8 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Arrange the numbers in a column, aligning them by place value. The number 76 is our minuend, and 8 is our subtrahend.

  • Step 2: We start the subtraction from the rightmost column, the units place.

  • Step 3: Subtract 8 from 6 in the units column. Since 8 is greater than 6, we need to borrow from the tens column.

Let's break down the subtraction:

Since 8 cannot be subtracted directly from 6, we borrow 10 from the tens place.
This makes the 6 into 16 (i.e., 6+10=166 + 10 = 16), and the 7 in the tens place becomes 6.

Now subtract in the units column:
168=816 - 8 = 8

Next, move to the tens column. After borrowing to help the units column:
66 remains as it is. There is nothing to subtract in the tens column (conceptually subtracting zero), so 66 stays as 66.

As a result, the difference is:
6868

Therefore, the solution to the subtraction 76876 - 8 is 6868.

3

Final Answer

68

Key Points to Remember

Essential concepts to master this topic
  • Borrowing Rule: When minuend digit is smaller, borrow 10 from left column
  • Technique: Change 6 to 16, reduce 7 to 6: 168=816 - 8 = 8
  • Check: Add result to subtrahend: 68+8=7668 + 8 = 76 matches original ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting smaller from larger digit regardless of position
    Don't subtract 6 from 8 to get 2 in the units place! This ignores place value and gives 62 instead of 68. Always borrow from the left column when the top digit is smaller than the bottom digit.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &15 \\ -& \\ &~~4 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

Why can't I just subtract 6 from 8 to get 2?

+

Because in subtraction, you must subtract the bottom number from the top number, not the other way around. When the top digit is smaller, you need to borrow from the left column first.

What happens to the 7 when I borrow from it?

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When you borrow 10 from the 7, it becomes 6. Think of it as trading one ten for ten ones. The 7 tens becomes 6 tens, and you add those 10 ones to the 6 in the units place.

How do I know when I need to borrow?

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You need to borrow whenever the top digit is smaller than the bottom digit in any column. In this problem, 6 is smaller than 8, so borrowing is necessary.

Can I check my answer without using addition?

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Yes! You can think logically: 76876 - 8 should be close to 7610=6676 - 10 = 66, but 2 more. So 66+2=6866 + 2 = 68 makes sense!

What if there's nothing in the tens column to subtract?

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When there's no digit to subtract in the tens column (like here), you simply bring down the remaining digit after borrowing. The 6 stays as 6 in our final answer.

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