Vertical Subtraction: Finding the Difference Between 1000 and 872

Q: Why can't I just subtract 2 from 0 in the units place?

You cannot subtract a larger number from a smaller one in standard arithmetic. When you see 0 - 2, you must borrow from the next digit to make it 10 - 2 = 8.

Q: What happens when I need to borrow from multiple zeros?

Work from right to left, borrowing from the first non-zero digit. In 1000, the 1 becomes 0, and each 0 becomes 9, then adjust the final digit to 10 for subtraction.

Q: How do I keep track of all the borrowing changes?

Write down each step! Cross out old digits and write new ones above. For 1000 - 872, you'll see: 0̶9̶9̶1̶0̶ above the original numbers.

Q: Is there an easier way to check my subtraction?

Yes! Addition is the opposite of subtraction. Add your answer to the number you subtracted: 128 + 872. If you get the original number (1000), you're correct!

Q: What if I get confused during the borrowing process?

Take it one column at a time from right to left. Don't rush! Make sure each borrowing step is complete before moving to the next column.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Each time it's considered a borrowing of 2 digits, and then we'll place

00:06 0 is less than 2

00:09 The tens digit is also equal to 0 so we can't borrow from it

00:12 The hundreds digit is also equal to 0 so we can't borrow from it

00:15 We'll borrow a thousand from the thousands for the hundreds

00:19 Which means now instead of 0 we'll have 10, in hundreds!

00:22 And now we'll borrow ten from the hundreds for the tens

00:25 Which will turn the hundreds from 10 to 9

00:29 Which means now instead of 0 we'll have 10, in tens!

00:32 And now we'll borrow ten from the tens for the ones

00:35 Which will turn the tens from 10 to 9

00:39 Which means now instead of 0 we'll have 10, in ones!

00:42 Now we'll subtract ones from ones, and place in ones

00:45 Subtract tens from tens, and place in tens

00:49 Subtract hundreds from hundreds, and place in hundreds

00:56 Place 0 in the missing digits

00:59 Subtract thousands from thousands, and place in thousands

01:02 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

$\begin{aligned} &1000 \\ -& \\ &~~872 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

2

Step-by-step solution

To solve this problem, we will use vertical subtraction with borrowing:

Step 1: Understand the given numbers
We need to perform the subtraction $1000 - 872$ . Let's write them vertically:

1000
-872
_____

Step 2: Begin with the units digit
The units digit for the minuend $1000$ is 0, and the subtrahend $872$ is 2. Because you cannot subtract $2$ from $0$ , we need to borrow from the next digit over.
- The tens digit is also $0$ , so we need to borrow from the hundreds digit, $0$ .
- Continue borrowing to the thousands place:
- The thousands digit $1$ will become $0$ , the hundreds digit becomes $10$ , then $9$ (after lending $1$ to adjust tens place), tens digit becomes $10$ , then $9$ (after lending $1$ to adjust units place), and finally, units digit becomes $10$ .
- Result during subtraction step:
- The number adjusted pre-subtraction is $09910$ .
Step 3: Perform the subtraction
- Now perform each column subtraction:
- Units: $10 - 2 = 8$
- Tens: $9 - 7 = 2$
- Hundreds: $9 - 8 = 1$
- There is no digit left to subtract in the thousands place, following the adjustment.
Conclusion
Bringing the results together from the adjustments and borrowing:
- The result of the subtraction is $128$ .

Therefore, the solution to the problem is $128$ .

3

Final Answer

128

Key Points to Remember

Essential concepts to master this topic

Borrowing Rule: When subtracting from zero, borrow from the next non-zero digit
Technique: Transform 1000 into 0999+1 for easier column subtraction
Check: Add your answer to subtrahend: 128 + 872 = 1000 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to reduce borrowed digits
Don't just add 10 to the units place without reducing the digit you borrowed from = wrong calculation! This creates an imbalanced borrowing system. Always reduce each digit by 1 when you borrow from it, creating a chain of adjustments.

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 can't I just subtract 2 from 0 in the units place?

+

You cannot subtract a larger number from a smaller one in standard arithmetic. When you see 0 - 2, you must borrow from the next digit to make it 10 - 2 = 8.

What happens when I need to borrow from multiple zeros?

+

Work from right to left, borrowing from the first non-zero digit. In 1000, the 1 becomes 0, and each 0 becomes 9, then adjust the final digit to 10 for subtraction.

How do I keep track of all the borrowing changes?

+

Write down each step! Cross out old digits and write new ones above. For 1000 - 872, you'll see: 0̶9̶9̶1̶0̶ above the original numbers.

Is there an easier way to check my subtraction?

+

Yes! Addition is the opposite of subtraction. Add your answer to the number you subtracted: 128 + 872. If you get the original number (1000), you're correct!

What if I get confused during the borrowing process?

+

Take it one column at a time from right to left. Don't rush! Make sure each borrowing step is complete before moving to the next column.

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Vertical Subtraction: Finding the Difference Between 1000 and 872

Subtraction with Multi-Digit Borrowing

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