Solve Vertical Subtraction: 3167 minus 2245

Multi-Digit Subtraction with Borrowing

31672245776 \begin{aligned} &3167 \\ -& \\ &2245 \\ &\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 Subtract ones from ones, and place in ones
00:09 Subtract tens from tens, and place in tens
00:13 1 is less than 2
00:19 Therefore we'll borrow 1 from thousands, and add this amount to hundreds
00:24 This means now instead of 1 we'll have 11
00:28 Subtract the hundreds from hundreds plus the hundred
00:32 Place in hundreds
00:36 Subtract thousands from thousands, and place in thousands
00:39 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

31672245776 \begin{aligned} &3167 \\ -& \\ &2245 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve the problem of subtracting 22452245 from 31673167, we'll perform vertical subtraction using step-by-step borrowing:

Let's set up the subtraction:

  • Write the numbers vertically aligning them by place value:

31672245 \begin{array}{c} & 3 & 1 & 6 & 7 \\ - & 2 & 2 & 4 & 5 \\ \hline \\ \end{array}

We start subtracting from the rightmost column (units):

  • Units: 75=27 - 5 = 2

  • Tens: We need to subtract 44 from 66: 64=26 - 4 = 2

  • Hundreds: 1<21 < 2, so borrow 11 from the thousands place:

    • The number becomes 22 in thousands place and hundreds place becomes 1111.

    • Subtract 22 from 1111: 112=911 - 2 = 9.

  • Thousands: 22=02 - 2 = 0

The calculation results in:

922 \begin{array}{c} & & & & 9 & 2 & 2 \\ \hline \end{array}

Thus, the final result of the subtraction is 922922.

Therefore, the solution to the problem is 922 922 .

3

Final Answer

922

Key Points to Remember

Essential concepts to master this topic
  • Rule: Always align place values vertically for accurate subtraction
  • Technique: Borrow from thousands: 3167 becomes 2 and 11 in hundreds column
  • Check: Add your answer to subtrahend: 922 + 2245 = 3167 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to reduce borrowed digit
    Don't borrow 1 from thousands (making hundreds 11) but forget to reduce thousands from 3 to 2 = wrong answer 1922! This leaves the borrowed amount uncounted. Always reduce the digit you borrowed from AND increase the target 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

When do I need to borrow in subtraction?

+

You need to borrow when the top digit is smaller than the bottom digit in any column. Like when 1 < 2 in the hundreds place, so you borrow from the thousands.

What happens to the digit I borrow from?

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Always reduce it by 1! If you borrow from the thousands place (3), it becomes 2. The borrowed amount goes to make the hundreds place bigger.

How do I know if I borrowed correctly?

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Check that you can subtract in every column without negative results. If 1 becomes 11 in hundreds, then 11 - 2 = 9 works perfectly!

Can I check my subtraction answer?

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Yes! Use addition to check: 922 + 2245 should equal your original number 3167. This proves your subtraction is correct.

What if I need to borrow from zero?

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When borrowing from 0, you need to keep going left until you find a non-zero digit to borrow from. The 0 becomes 10, then you can borrow from it.

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