Subtract 314 minus 126: Vertical Format Solution

Vertical Subtraction with Multi-Column Borrowing

314126776 \begin{aligned} &314 \\ -& \\ &126 \\ &\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 we consider borrowing 2 digits, and then we place
00:05 4 is less than 6
00:09 Therefore we subtract 1 from the tens and add this amount to the ones
00:13 So now instead of 4 we will have 14
00:19 Subtract the ones from the ones plus ten
00:25 Place in ones
00:29 0 is less than 2
00:33 Therefore we subtract 1 from the hundreds and add this amount to the tens
00:38 So now instead of 0 we will have 10
00:42 Subtract the tens from the tens plus ten
00:47 Place in tens
00:50 Subtract hundreds from hundreds, and place in hundreds
00:53 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

314126776 \begin{aligned} &314 \\ -& \\ &126 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

We'll align the numbers by their place values:
314314
126- 126

Start with the rightmost column (the units place):

  • Units Place: 464 - 6 requires borrowing because 4 is less than 6. Borrow 1 from the tens column in 314, turning it into 10, leaving 0 in the tens place. Now, 146=814 - 6 = 8.

  • Tens Place: After borrowing, 020 - 2 also requires borrowing from the hundreds column. Borrow 1 from the hundreds column, leaving 22 in the hundreds place. Now, 102=810 - 2 = 8.

  • Hundreds Place: Subtract as normal, 21=12 - 1 = 1.

When we put it all together, the result is:

  • Hundreds: 11

  • Tens: 88

  • Units: 88

Therefore, 314126=188314 - 126 = 188.

The solution to the problem is 188188, which matches choice 44.

3

Final Answer

188

Key Points to Remember

Essential concepts to master this topic
  • Borrowing Rule: When top digit is smaller, borrow from the left column
  • Technique: 46 4 - 6 becomes 146=8 14 - 6 = 8 after borrowing from tens
  • Check: Add your answer to the subtrahend: 188+126=314 188 + 126 = 314

Common Mistakes

Avoid these frequent errors
  • Forgetting to adjust borrowed-from digits
    Don't subtract from original digits after borrowing = wrong answer like 288 instead of 188! When you borrow 1 from a column, that digit decreases by 1. Always reduce the borrowed-from digit before continuing your subtraction.

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 does borrowing actually mean?

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Borrowing means taking 10 from the next column to the left. When you borrow 1 from the tens place, you're actually taking 10 ones to help with subtraction in the units place.

What if I need to borrow from zero?

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You'll need to borrow from the next column over! The zero becomes 10, then you borrow 1 from that to help the original column. It's like a chain reaction moving left.

How can I check if my subtraction is correct?

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Use addition to check: Add your answer to the number you subtracted. If you get the original number, you're right! 188+126=314 188 + 126 = 314

Why do we line up numbers by place value?

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Place value alignment ensures you're subtracting units from units, tens from tens, etc. Misaligned numbers lead to completely wrong answers!

Do I always start from the rightmost column?

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Yes, always start from the right (units place)! This way, any borrowing you need flows naturally from right to left, just like how we count.

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