Solve Vertical Subtraction: 354 minus 6 Step-by-Step

Vertical Subtraction with Regrouping

354    6776 \begin{aligned} &354 \\ -& \\ &~~~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Each time consider borrowing 2 digits, and then we'll place
00:06 4 is less than 6
00:09 Therefore we'll subtract 1 from the tens and add this amount to the ones
00:14 So now instead of 4 we'll have 14
00:18 Subtract the ones from the ones plus ten
00:22 Place in the ones
00:25 Place 0 in the borrowed digits
00:29 Subtract tens from tens, and place in tens
00:33 Subtract hundreds from hundreds, and place in hundreds
00:36 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

354    6776 \begin{aligned} &354 \\ -& \\ &~~~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem of subtracting 6 from 354, we'll follow these steps:

  • Step 1: Set up the problem with the two numbers aligned by their place values.
  • Step 2: Start subtracting from the rightmost digits (units).
  • Step 3: Subtract each column, handling any necessary regrouping (borrowing).

Now, let's solve it:

Step 1: Write the numbers with the larger number on top:

35406 \begin{array}{c} 354 \\ -\phantom{0}6 \\ \hline \end{array}

Step 2: Subtract the numbers starting with the units place:

  • Units: 464 - 6 can't be performed as 4 is less than 6; we'll need to borrow from the tens column.
  • To borrow, reduce the tens digit (5) by 1 (making it 4), and add 10 to the units digit (4) making it 14.
  • Subtract 146=814 - 6 = 8.
  • Tens: Now, since we borrowed 1 from the tens, we have 4 left. Thus, 40=44 - 0 = 4.
  • Hundreds: The hundreds digit: 30=33 - 0 = 3.

So the subtraction yields:

35406348 \begin{array}{c} 354 \\ -\phantom{0}6 \\ \hline 348 \\ \end{array}

Therefore, the solution to the problem is 348 348 .

3

Final Answer

348

Key Points to Remember

Essential concepts to master this topic
  • Rule: Align numbers by place value when subtracting vertically
  • Technique: Borrow from tens: 4 becomes 14, subtract 14 - 6 = 8
  • Check: Add your answer to subtrahend: 348 + 6 = 354 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to reduce the borrowed-from digit
    Don't just add 10 to the units digit without reducing the tens digit = wrong answer like 358! When you borrow 1 from the tens place, you must reduce that digit by 1. Always remember: borrow 1 from tens (5 becomes 4), add 10 to units (4 becomes 14).

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 need to borrow when 4 is smaller than 6?

+

You can't subtract a larger number from a smaller number in the same place value! Borrowing lets you 'take' 10 from the next column, making 4 become 14, so you can subtract 14 - 6 = 8.

What happens to the tens digit when I borrow?

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When you borrow 1 from the tens place, that digit decreases by 1. So 5 becomes 4. Think of it as 'lending' 10 to the units column - you have to give up 1 ten to make it happen!

How do I know if I borrowed correctly?

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Check your work by adding: 348 + 6 should equal 354. If it does, you borrowed correctly. If not, double-check that you reduced the borrowed-from digit.

Can I subtract from left to right instead?

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No! Always subtract from right to left (units, then tens, then hundreds). This ensures you handle any borrowing correctly before moving to the next column.

What if there's a zero in the number I'm borrowing from?

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You'll need to borrow from the next column over first! For example, if you have 304 - 6, you'd borrow from the hundreds to make the tens 10, then borrow from that 10 to help the units.

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