Subtract 54,636 from 80,004: Vertical Format Solution

Multi-Digit Subtraction with Borrowing Across Zeros

8000454636776 \begin{aligned} &80004 \\ -& \\ &54636 \\ &\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 subtract 2 digits, and then we place
00:06 4 is less than 6
00:09 We want to borrow from the larger digits
00:12 Both tens and hundreds equal 0 so we'll borrow from the thousands
00:15 What will change the ten thousands from 8 to 7
00:20 And now we'll have 10 instead of 0, in thousands!
00:23 And we'll borrow from thousands to hundreds
00:26 We'll continue with the same method until we reach the ones
00:42 We'll borrow from tens to ones, and we'll have 14 instead of 4 in ones!
00:51 Subtract ones from ones, and place in ones
00:56 Subtract tens from tens, and place in tens
00:59 Subtract hundreds from hundreds, and place in hundreds
01:06 Subtract thousands from thousands, and place in thousands
01:11 Subtract ten thousands from ten thousands, and place
01:15 And that's the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

8000454636776 \begin{aligned} &80004 \\ -& \\ &54636 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this subtraction problem, we will perform vertical subtraction, paying close attention to borrowing across zeros:

Step-by-step solution:

  • Write the numbers such that they align vertically, with the larger number on top and the smaller number directly below each corresponding digit:

800045463677600 \begin{aligned} &80004 \\ -&54636 \\ &\overline{\phantom{77600}} & \\ \end{aligned}

  • Start subtracting from the rightmost digit:

  • 1. Units place: 464 - 6. Since 4 is less than 6, borrow 1 from the tens place (next digit).
    2. Tens place: Now, treat it as 10310 - 3, but since you borrowed 1 for the units place, it becomes 93=69 - 3 = 6.
    3. Hundreds place: Borrow from the thousands place since you need a digit to make 060 - 6. It becomes 106=410 - 6 = 4.
    4. Thousands place: Now subtract from what remains after borrowing from it, 949 - 4, which equals 5.
    5. Ten-thousands place: Since you borrowed to the right, 75=27 - 5 = 2 in this position.

  • The subtraction yields the result as follows:

956014054636025368 \begin{aligned} &9560 14 \\ -&\phantom{0}54636 \\ &\phantom{0}\underline{25368} & \\ \end{aligned}

Therefore, the solution to the subtraction problem is 25368\mathbf{25368}.

3

Final Answer

25368

Key Points to Remember

Essential concepts to master this topic
  • Rule: When borrowing across zeros, convert each zero to 9 and continue
  • Technique: Change 80004 to 79,9,9,10,4 when borrowing from left to right
  • Check: Add your answer to the subtracted number: 25368 + 54636 = 80004 ✓

Common Mistakes

Avoid these frequent errors
  • Not borrowing properly across multiple zeros
    Don't just borrow from the first non-zero digit without converting zeros = wrong calculations! This creates impossible situations like trying to subtract 6 from 0. Always convert each zero to 9 as you borrow from left to right, making a chain of borrowing.

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

Why do zeros become 9 when I borrow?

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When you borrow 1 from a zero, that zero becomes 10, but since you're lending 1 to the next column, it becomes 10 - 1 = 9. Think of it like borrowing money - you get 10 but owe 1!

How do I know where to start borrowing?

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Start from the rightmost column where you can't subtract (like 4 - 6). Then work your way left, borrowing from each digit until you reach a non-zero number.

What if I have multiple zeros in a row?

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Don't worry! Just keep converting each zero to 9 as you move left. For example, in 80004, all the zeros become 9s: 7-9-9-9-14 after borrowing.

Can I check my work without adding?

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Yes! You can also estimate: 80,000 - 55,000 ≈ 25,000. Since 25368 is close to 25,000, your answer makes sense!

What happens if I forget to borrow?

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You'll get negative numbers or impossible subtractions like 4 - 6. If you see this happening, stop and borrow before continuing with that column.

Is there an easier way to handle zeros?

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Some students find it helpful to rewrite the number first. Change 80004 to 79994 + 10, but the borrowing method is more reliable for complex problems.

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