Solve 13579 - 9756: Multi-digit Subtraction Practice

Multi-digit Subtraction with Borrowing

13579  9756776 \begin{aligned} &13579 \\ -& \\ &~~9756 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve a math problem together.
00:11 We'll consider each pair of digits at a time.
00:15 First, subtract the ones place, and write the result in ones.
00:20 Next, subtract the tens place, and record it in tens.
00:25 Notice that 5 is less than 7.
00:28 So, let's borrow from thousands to help the hundreds.
00:34 Now, we have 15 instead of 5 in hundreds.
00:39 Subtract in the hundreds place, and write it down.
00:49 Here, 2 is less than 9.
00:53 Let's borrow from hundred thousands to help the thousands.
00:59 Now, it's 12 instead of 2 in thousands.
01:03 Subtract in the thousands place, and write it down.
01:09 Fill in missing digits with 0.
01:12 Subtract the ten thousands place, and record it.
01:18 And that's how we solve this problem, great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

13579  9756776 \begin{aligned} &13579 \\ -& \\ &~~9756 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve the subtraction problem 135799756 13579 - 9756 , we will use the vertical subtraction method. Here are the steps:

Step 1: Align the numbers by their place values:

213579009756 \begin{array}{c} \phantom{-2}13579 \\ -\phantom{00}9756 \\ \hline \end{array}

Step 2: Start from the rightmost column:

  • Units place: 96=3 9 - 6 = 3

Step 3: Move to the tens place:

  • Tens place: 75=2 7 - 5 = 2

Step 4: Hundreds place:

  • Hundreds place: 57 5 - 7 , since 5 is less than 7, we need to borrow 1 from the thousands place, making it 157=8 15 - 7 = 8 .

Step 5: Thousands place (after borrowing):

  • Thousands place: Originally 3 3 , after borrowing it becomes 2 2 , so 29 2 - 9 , we again need to borrow from ten-thousands place, thus 129=3 12 - 9 = 3 .

Final step: Ten-thousands place (after all adjustments):

  • Ten-thousands place: Originally 1 1 , after borrowing it became 0 0 , so concludes with 00=0 0 - 0 = 0 .

Therefore, by combining all steps, the result is:

135790975693823 \begin{array}{c} \phantom{-}13579 \\ -\phantom{0}9756 \\ \hline \phantom{-9}3823 \\ \end{array}

Hence, the solution to the subtraction problem is 3823 \boxed{3823} .

3

Final Answer

3823

Key Points to Remember

Essential concepts to master this topic
  • Rule: Always align numbers by place value before subtracting
  • Technique: When top digit is smaller, borrow 1 from next column: 5 becomes 15
  • Check: Add your answer to the number you subtracted: 3823 + 9756 = 13579 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to reduce the borrowed-from digit
    Don't just add 10 to make 15 - 7 = 8 without changing the 3 to 2! This creates extra value and gives wrong answers. Always reduce the digit you borrow from by 1 after adding 10 to the current column.

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 I start from the rightmost column?

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Starting from the ones place (rightmost) follows the same pattern you learned with smaller numbers. This way, any borrowing moves logically from right to left, just like counting!

What happens when I need to borrow from zero?

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You can't borrow from 0 directly! First, you need to borrow from the next column over, turning that 0 into 10, then borrow 1 from that 10 for your current column.

How do I know when to borrow?

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Borrow whenever the top digit is smaller than the bottom digit in any column. For example, in 5 - 7, since 5 < 7, you need to borrow to make it 15 - 7.

Can I check my answer without adding?

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Yes! You can also estimate: 1357914000 13579 \approx 14000 and 975610000 9756 \approx 10000 , so the answer should be around 1400010000=4000 14000 - 10000 = 4000 . Since 3823 is close to 4000, it makes sense!

What if I make a mistake while borrowing?

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Don't panic! Erase your work and start that column over. It's better to be careful with borrowing than to rush and get the wrong answer.

Why is my answer different from 4823?

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Check your borrowing in the thousands place! Remember: after borrowing 1 from the ten-thousands place (1), it becomes 0, and the thousands place (3) becomes 13, so 139=4 13 - 9 = 4 ... wait, that would give 4823, but we need to account for the hundreds borrowing too!

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