Solve 406 minus 78: Vertical Subtraction Practice Problem

Q: Why can't I just subtract 8 from 6 in the units place?

You can't subtract a larger number from a smaller one in basic subtraction! When 6 - 8 isn't possible, you need to borrow from the next column to make it 16 - 8 = 8.

Q: What do I do when the tens place is zero?

When you need to borrow but the tens place is 0, go to the hundreds place first! Borrow 1 from hundreds (4 becomes 3), making tens into 10. Then borrow from that 10 for the units.

Q: How do I know if I borrowed correctly?

After borrowing, check that your top number got smaller in one place and bigger in another. For 406: hundreds went from 4→3, tens from 0→9, units from 6→16.

Q: Is there an easier way than borrowing?

For mental math, you could think 406 - 78 = 406 - 80 + 2 = 326 + 2 = 328. But learning the standard algorithm helps with larger, more complex problems!

Q: How can I check my subtraction answer?

Use addition to check subtraction: $ 328 + 78 $ should equal 406. If it does, your subtraction is correct!

Vertical Subtraction with Regrouping

$\begin{aligned} &406 \\ -& \\ &~~78 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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, we'll subtract two digits at a time.

00:10 Notice that 6 is less than 8.

00:13 The tens digit is zero, so we can't borrow from it.

00:17 We'll borrow a hundred from the hundreds column for the tens.

00:21 Now, instead of zero, we have ten in the tens place.

00:25 We'll borrow ten from the tens column for the ones.

00:30 Now, the tens become nine instead of ten.

00:34 Instead of six, we now have sixteen in the ones place.

00:38 Subtract ones from ones. Place the answer in the ones column.

00:43 Subtract tens from tens. Place the result in the tens column.

00:49 Place zero in any missing digits.

00:52 Subtract hundreds from hundreds. Place the answer in the hundreds column.

00:57 And that's how we solve the problem. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &406 \\ -& \\ &~~78 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this subtraction problem $406 - 78$ , we use the vertical subtraction method, aligning the numbers by their place values:

Step-by-step process:

Align the numbers columnwise:
406
- 78
- - - - -
Subtract each column, starting from the right:
- Units place: $6 - 8$ cannot be done directly, so we need to borrow.
- Look to the tens column (0), but it is not possible to borrow directly from zero. Instead, we move to the hundreds column.
- From the hundreds, the 4 becomes a 3 (after borrowing), and the tens place (0) becomes 10. Borrow from 10 in tens, so it becomes 9 while units becomes 16.
Perform the subtraction with borrowing adjusted:
- Units place: $16 - 8 = 8$
- Tens place: $9 - 7 = 2$
- Hundreds place: $3 - 0 = 3$

The result of subtracting 78 from 406 is $\mathbf{328}$ .

The correct answer, matching our calculation, is option 3: 328.

Final Answer

328

Key Points to Remember

Essential concepts to master this topic

Rule: Always align numbers by place value when subtracting vertically
Technique: Borrow from hundreds to tens: 406 becomes 3-10-16
Check: Add your answer to the smaller number: 328 + 78 = 406 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to borrow through zero in the tens place
Don't try to borrow directly from zero in the tens place = impossible borrowing! You can't take from nothing. Always borrow from the hundreds first to make the tens place 10, then borrow from that 10 to the units.

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 8 from 6 in the units place?

You can't subtract a larger number from a smaller one in basic subtraction! When 6 - 8 isn't possible, you need to borrow from the next column to make it 16 - 8 = 8.

What do I do when the tens place is zero?

When you need to borrow but the tens place is 0, go to the hundreds place first! Borrow 1 from hundreds (4 becomes 3), making tens into 10. Then borrow from that 10 for the units.

How do I know if I borrowed correctly?

After borrowing, check that your top number got smaller in one place and bigger in another. For 406: hundreds went from 4→3, tens from 0→9, units from 6→16.

Is there an easier way than borrowing?

For mental math, you could think 406 - 78 = 406 - 80 + 2 = 326 + 2 = 328. But learning the standard algorithm helps with larger, more complex problems!

What if my answer doesn't match any of the choices?

Double-check your borrowing steps! The most common error is incorrect borrowing through zero. Make sure you borrowed from hundreds to tens first, then tens to units.

How can I check my subtraction answer?

Use addition to check subtraction: $328 + 78$ should equal 406. If it does, your subtraction is correct!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Arithmetic Operations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime