Solve Vertical Subtraction: 867 minus 42 Step-by-Step

Q: Why do I start subtracting from the right side?

We start from the units place (rightmost column) because that's how place value works! Just like counting, we work from smallest to largest place values: ones, then tens, then hundreds.

Q: What if the top number is smaller than the bottom number in a column?

That's when you need to borrow from the next column! In this problem, we didn't need to borrow because 7 > 2 and 6 > 4, making it straightforward.

Q: How do I know I aligned the numbers correctly?

Make sure the ones digits line up, tens digits line up, and hundreds digits line up. In $ 867 - 42 $, the 2 should be under the 7, and the 4 should be under the 6.

Q: Why is there no number above the 8 in the hundreds place?

Because 42 is a two-digit number with no hundreds! Think of it as 042 if it helps - there's a zero in the hundreds place, so 8 - 0 = 8.

Q: How can I check if my answer is right?

Use addition to check subtraction! Add your answer to the number you subtracted: $ 825 + 42 $. If you get the original number (867), you're correct!

Vertical Subtraction with Two-Digit Numbers

$\begin{aligned} &867\\ -& \\ &~~42 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem together.

00:07 First, subtract the digits in the ones place. Write down the result.

00:12 Next, subtract the digits in the tens place. Write down the result.

00:16 If any digits are missing, place a zero.

00:20 Now, move on to the hundreds place and subtract those digits. Write down the result.

00:25 And there you have it! You've solved the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &867\\ -& \\ &~~42 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we will perform vertical subtraction as follows:

Step 1: Write the numbers vertically and align digits by place value:
$867$
$-~~42$
Step 2: Start subtracting from the units place:
$7 - 2 = 5$
Step 3: Move to the tens place:
$6 - 4 = 2$
Step 4: Finally, subtract the hundreds place:
$8 - 0 = 8$ (nothing was borrowed here)

Putting it all together, the result of $867 - 42$ is $825$ .

Therefore, the solution to the problem is $825$ .

Final Answer

825

Key Points to Remember

Essential concepts to master this topic

Alignment: Place digits in columns by place value position
Technique: Start from units place: 7 - 2 = 5
Check: Add the answer to subtrahend: 825 + 42 = 867 ✓

Common Mistakes

Avoid these frequent errors

Misaligning digits by place value
Don't line up 42 under the wrong digits like 86 instead of aligning 2 under 7 and 4 under 6 = wrong calculation! This makes you subtract from wrong place values. Always align digits carefully by ones, tens, hundreds columns.

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 subtracting from the right side?

We start from the units place (rightmost column) because that's how place value works! Just like counting, we work from smallest to largest place values: ones, then tens, then hundreds.

What if the top number is smaller than the bottom number in a column?

That's when you need to borrow from the next column! In this problem, we didn't need to borrow because 7 > 2 and 6 > 4, making it straightforward.

How do I know I aligned the numbers correctly?

Make sure the ones digits line up, tens digits line up, and hundreds digits line up. In $867 - 42$ , the 2 should be under the 7, and the 4 should be under the 6.

Why is there no number above the 8 in the hundreds place?

Because 42 is a two-digit number with no hundreds! Think of it as 042 if it helps - there's a zero in the hundreds place, so 8 - 0 = 8.

How can I check if my answer is right?

Use addition to check subtraction! Add your answer to the number you subtracted: $825 + 42$ . If you get the original number (867), you're correct!

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