Solve Vertical Subtraction: 10154 minus 8154

Vertical Subtraction with Borrowing Across Thousands

10154  8154776 \begin{aligned} &10154 \\ -& \\ &~~8154 \\ &\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 deficit of 2 digits, and then we place
00:06 Now we subtract ones from ones, and place in ones
00:09 Subtract tens from tens, and place in tens
00:12 Subtract hundreds from hundreds, and place in hundreds
00:18 0 is less than 8
00:23 We borrow hundred thousand from hundreds thousands for the thousands
00:29 In other words, now instead of 0 we'll have 10, in thousands!
00:35 Subtract thousands from thousands, and place in thousands
00:39 Place 0 in the missing digits
00:42 Subtract tens of thousands from tens of thousands, and place
00:45 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

10154  8154776 \begin{aligned} &10154 \\ -& \\ &~~8154 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve the subtraction problem 10,1548,15410,154 - 8,154, follow these steps:

  1. Write down the numbers with their digits aligned according to place value:

      10154 8154 \begin{array}{c} ~~10154 \\ \underline{-~8154} \\ \end{array}

  2. Subtract each pair of digits starting from the right (units place):

    1. Units place: 44=04 - 4 = 0

    2. Tens place: 55=05 - 5 = 0

    3. Hundreds place: 11=01 - 1 = 0

    4. Thousands place: 080 - 8 – since 00 is less than 88, we need to borrow.

  3. Borrows and adjusts:

    1. Borrow from the ten-thousands place. Convert 10,00010,000 to 9,0009,000, and increase thousands by 1010: 101=910 - 1 = 9 (because of borrowed 1 from ten-thousands).

  4. Perform the borrowing adjustment and subtraction:

    1. Thousands place after borrowing: 108=210 - 8 = 2

    2. Ten-thousands place (after borrowing): 11=01 - 1 = 0

After performing these operations, the final result is:

2,0002,000

Therefore, the difference when 8,1548,154 is subtracted from 10,15410,154 is: 2,0002,000

3

Final Answer

2000

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Line up digits by place value before subtracting
  • Borrowing: When 0 - 8 in thousands, borrow 1 from ten-thousands
  • Check: Add your answer to the smaller number: 2000 + 8154 = 10154 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to borrow when subtracting from zero
    Don't try to subtract 8 from 0 in the thousands place = impossible! This creates negative digits or wrong answers. Always borrow from the next higher place value 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 do I do when I see 0 minus a bigger number?

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You need to borrow from the next place value! In this problem, borrow 1 from the ten-thousands place (making it 0) and add 10 to the thousands place (making it 10). Now you can subtract: 10 - 8 = 2.

Why does borrowing work this way?

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Borrowing is like trading money! One ten-thousand is worth 10 thousands, just like one dollar is worth 10 dimes. When you borrow 1 from ten-thousands, you get 10 extra thousands to work with.

How can I check if my subtraction is correct?

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Use addition to check! Add your answer (2000) to the number you subtracted (8154). If you get the original number (10154), your answer is right!

What if both numbers have the same digits in some places?

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That makes it easier! When digits are the same (like 4-4, 5-5, 1-1), the result is always 0. Focus your attention on the places where digits are different.

Do I always start subtracting from the right?

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Yes, always start from the rightmost column (ones place) and work left! This ensures you handle any borrowing correctly as you move through each place value.

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