Solve the Subtraction Problem: 186 minus 29 Using Column Method

Column Subtraction with Borrowing

186  29776 \begin{aligned} &186 \\ -& \\ &~~29 \\ &\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
00:06 6 is less than 9
00:09 So we borrow 1 from the tens column and add this amount to the ones
00:14 Which means now instead of 6 we will have 16
00:17 Subtract the ones from the ones plus the ten
00:21 Place in the ones column
00:28 Subtract tens from tens, and place in tens column
00:32 Place 0 in the borrowed digits
00:35 Subtract hundreds from hundreds, and place in hundreds column
00:38 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

186  29776 \begin{aligned} &186 \\ -& \\ &~~29 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem of subtracting 29 from 186 using vertical subtraction, we will follow these steps:

  • Step 1: Set up the subtraction problem by writing 186 above 29, aligning them based on place value (units, tens, hundreds).
  • Step 2: Begin subtracting from the rightmost column (units).
  • Step 3: If the top digit in a column is smaller than the bottom digit, regroup from the next left column.
  • Step 4: Write the result beneath the line for each column.

Let's work through the subtraction problem:
186
- 29
--------

Step 1: Start with the units column: 696 - 9. Because 6 is less than 9, we need to regroup.

Step 2: Look at the tens column. From the tens column represented as 8, we borrow 1 ten (equivalent to 10 units), converting 8 tens to 7, and adding 10 to the units column, making it 16.

Step 3: Now subtract in the units column: 169=716 - 9 = 7.

Step 4: Move to the tens column. After borrowing, we have 7 tens minus 2 tens: 72=57 - 2 = 5.

Step 5: Finally, subtract the hundreds column: 10=11 - 0 = 1, as no borrowing was needed here.

Combine these results from each column to obtain the final answer: 157.

Therefore, the solution to the problem is 157157, which matches choice 3 from the provided options.

3

Final Answer

157

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Place digits by position value before starting subtraction
  • Borrowing: When top digit < bottom digit, borrow 1 from left column
  • Verification: Add your answer to the subtracted number: 157 + 29 = 186 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to reduce the borrowed-from digit
    Don't borrow 1 ten from 8 but keep writing 8 in your work = wrong answer like 167! When you borrow 1 ten, the 8 becomes 7 and must be written as 7. Always reduce the digit you borrowed from by 1.

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 6 - 9 in the ones place?

+

You cannot subtract a larger number from a smaller one in basic subtraction! When the top digit is smaller, you must borrow from the next column to make it larger.

What does borrowing actually mean?

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Borrowing means taking 1 group of 10 from the left column and adding it to the current column. So 6 ones becomes 16 ones, but 8 tens becomes 7 tens.

How do I know when to borrow?

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Borrow whenever the top digit is smaller than the bottom digit in any column. Compare each column from right to left before subtracting.

What if I need to borrow from a zero?

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When borrowing from 0, you must keep borrowing left until you find a non-zero digit. For example: 302 - 156 requires borrowing from the hundreds place first.

Can I check my answer?

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Always check by adding! Your answer plus the number you subtracted should equal the original number: 157+29=186 157 + 29 = 186

Why do we line up the numbers by place value?

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Lining up by place value ensures you subtract ones from ones, tens from tens, and hundreds from hundreds. Misalignment leads to completely wrong answers!

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