Solve the Subtraction: 70005 minus 24126

Multi-Digit Subtraction with Borrowing

7000524126776 \begin{aligned} &70005 \\ -& \\ &24126 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve this math problem together.
00:09 We'll borrow digits step by step, so follow along.
00:13 Five is smaller than six. Let's borrow from the bigger digits.
00:19 We'll borrow since the tens and hundreds digits are both zero.
00:23 Let's change the ten thousands digit from seven to six.
00:27 Now, we have ten in the thousands place instead of zero.
00:32 Next, we'll borrow from the thousands for the hundreds digit.
00:36 Keep going with this method until we reach the ones place.
00:40 Finally, from tens to ones, making fifteen instead of five in the ones!
00:48 Now, subtract ones from ones and write the result.
00:54 Subtract tens from tens and put down the answer.
00:59 Subtract hundreds from hundreds. Write the answer here.
01:04 Move on to subtract thousands from thousands and jot it down.
01:08 Finally, subtract ten thousands from ten thousands and place it.
01:13 Great job! 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

7000524126776 \begin{aligned} &70005 \\ -& \\ &24126 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Align the two numbers vertically with the minuend (70005) on top and the subtrahend (24126) below it.
  • Step 2: Subtract digit by digit from the rightmost side and borrow as necessary.

Let's break this down:

Step-by-step Solution:

1. Subtract the rightmost digit:
- Subtract 6 from 5. Since 5 is less than 6, we need to borrow from the next digits.

2. Borrowing:
- The immediate next digit is '0', so we continue borrowing to the left. We borrow 1 from the third zero (turning it into a 9), which makes the second zero a 9 and the third zero a 9, and we subtract the borrowed 1 from the 7, turning it into 6.

3. Complete the subtraction:
- For the units column (now 15 and 6), subtract to get: 156=915 - 6 = 9.
- For the tens column (now 9 and 2), subtract to get: 92=79 - 2 = 7.
- For the hundreds column (now 9 and 1), subtract to get: 91=89 - 1 = 8.
- For the thousands column (6 and 4), subtract to get: 64=26 - 4 = 2.
- For the ten-thousands column (no borrowing needed, 6 and 2), subtract to get: 62=46 - 2 = 4.

The final result after all column-based subtractions, including borrowing corrections, is: 45879 \text{45879} .

Therefore, the solution to the problem is 45879 45879 .

3

Final Answer

45879

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers vertically with place values properly aligned
  • Borrowing: When 5 < 6, borrow from left: 15 - 6 = 9
  • Check: Add result to subtrahend: 45879 + 24126 = 70005 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to adjust borrowed digits
    Don't borrow 1 and forget to reduce the lending digit = wrong calculations throughout! When you borrow 1 from a digit, that digit becomes 1 less. Always reduce every digit you borrow from and continue the pattern across zeros.

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 need to borrow from zero?

+

When borrowing from zero, you need to keep going left until you find a non-zero digit! Each zero becomes 9, and the non-zero digit decreases by 1.

Why does borrowing work?

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Borrowing works because 10 ones = 1 ten! When you borrow 1 from the tens place, you're actually borrowing 10 ones, so 5 becomes 15.

How can I check if my subtraction is correct?

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Add your answer to the number you subtracted (subtrahend). If you get the original number (minuend), your answer is right!

  • Example: 45879+24126=70005 45879 + 24126 = 70005

What if I make a mistake while borrowing?

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Start over! Borrowing mistakes spread through the whole problem. It's faster to restart than to find and fix each error.

Do I always start subtracting from the right?

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Yes! Always start from the ones place (rightmost column) and work left. This ensures borrowing works correctly through all place values.

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