Solve 782 Minus 6: Vertical Subtraction Problem

Vertical Subtraction with Borrowing

782    6776 \begin{aligned} &782 \\ -& \\ &~~~~6 \\ &\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 2 is less than
00:09 Therefore we'll subtract 1 from the tens place, and add this amount to the ones
00:14 Which means now instead of 2 we'll have 12
00:20 We'll subtract the ones from the ones plus the ten
00:23 We'll place in the ones
00:26 We'll place 0 in the borrowed digits
00:30 Subtract tens from tens, and place in tens
00:33 Subtract hundreds from hundreds, and place in hundreds
00:37 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

782    6776 \begin{aligned} &782 \\ -& \\ &~~~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Identify the digits involved in subtraction, starting with the units place.

  • Step 2: Apply the subtraction rules column by column, performing borrowing if necessary.

  • Step 3: Write down the result of each step and obtain the final answer.

Let's work through these steps:

Step 1: We are subtracting 6 from 782. Write the number 782 above the number 6, aligning them to the right:
782 6 \begin{array}{c} 782 \\ - \phantom{\ }6 \\ \hline \end{array}

Step 2: Begin the subtraction with the units digit (rightmost digits).

The units digit of 782 is 2, and we need to subtract 6 from it. Since 2 is smaller than 6, we must borrow from the tens place.

Borrow 1 from the tens digit (8), making it 7, and convert it to ten units. Now, add the borrowed 10 to the 2, making it 12 in the units place.

Now subtract 6 from 12, which gives us 6.

Step 3: Move to the tens place where we have adjusted the previous digit, 8 (now 7), which doesn’t involve subtraction as the only subtraction required was in the units place.

The hundreds digit remains unchanged as no borrowing affected it.

Therefore, we write this subtraction out as follows:

782 60776 \begin{array}{c} 782 \\ - \phantom{\ }6 \\ \hline \phantom{0}776 \\ \end{array}

Therefore, the solution to the problem is 776 776 .

3

Final Answer

776

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Place digits in correct columns with smaller number underneath
  • Borrowing: When 2 < 6, borrow 10 from tens place: 12 - 6 = 6
  • Check: Add your answer to the subtracted number: 776 + 6 = 782 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting smaller from larger regardless of position
    Don't subtract 2 - 6 = 4 by switching to 6 - 2 = 4! This ignores place value and gives wrong answers like 784. Always borrow from the next 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

What does borrowing mean in subtraction?

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Borrowing means taking 10 from the next column to the left. When you can't subtract (like 2 - 6), you borrow 1 from the tens place, making it 12 - 6 = 6 in the ones place.

Why can't I just subtract 6 - 2 = 4 instead?

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Because that changes the place value! In 782 - 6, you're subtracting 6 ones from 2 ones, not the other way around. Always subtract the bottom number from the top number in each column.

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. Like here: 2 < 6, so you must borrow from the tens place.

What happens to the digit I borrowed from?

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The digit you borrowed from decreases by 1. In this problem, the 8 in the tens place became 7 after we borrowed 1 (which equals 10 ones) for the units place.

How can I check if my subtraction is correct?

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Add your answer to the number you subtracted! If you get the original number, you're right. Here: 776+6=782 776 + 6 = 782

Do I always write the bigger number on top?

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Yes! In vertical subtraction, the larger number (minuend) goes on top, and the smaller number (subtrahend) goes underneath, aligned by place value.

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