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
00:05 Let's solve the problem step by step.
00:09 Start by subtracting each pair of digits.
00:13 Four is less than six, so we need to borrow.
00:17 To do this, borrow from the larger digits.
00:22 Both tens and hundreds are zero, so borrow from thousands.
00:27 Change eight in ten thousands to seven.
00:31 Now, we have ten in the thousands place.
00:35 Borrow again from thousands to hundreds.
00:39 Keep borrowing until you reach the ones.
00:47 Borrow from tens to ones. Turn four into fourteen.
00:56 Subtract ones from ones. Write the result in the ones place.
01:01 Subtract tens from tens. Write in the tens place.
01:06 Subtract hundreds from hundreds. Mark in the hundreds.
01:11 Subtract thousands from thousands. Write in thousands.
01:16 Subtract ten thousands from ten thousands. Write it.
01:21 And that's how we solve this 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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