Solve Vertical Subtraction: 274 minus 86 Step-by-Step

Vertical Subtraction with Borrowing Steps

274  86776 \begin{aligned} &274 \\ -& \\ &~~86 \\ &\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 math problem step by step.
00:07 We begin by looking at borrowing two digits.
00:11 The number 4 is less than 6.
00:15 So, we need to borrow. We subtract 1 from the tens place and add it to the ones.
00:21 Now, instead of 4, we have 14.
00:28 Subtract the ones from 14, and place the result in the ones column.
00:33 Notice that 6 is less than 8.
00:37 We need to borrow again, subtract 1 from the hundreds, and add it to the tens.
00:43 Now, we have 16 instead of 6.
00:46 Subtract the tens from 16, and place the result in the tens column.
00:54 Then place a zero in any missing digits.
00:57 Lastly, subtract the hundreds and place the answer in the hundreds column.
01:02 And there you have it, the problem is solved!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

274  86776 \begin{aligned} &274 \\ -& \\ &~~86 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this subtraction problem, we will follow these steps:

  • Step 1: Line up the numbers vertically to align the digits by place value.

  • Step 2: Start from the units column, note 464 - 6 requires borrowing from the tens place.

    • Since 4 is smaller than 6, we borrow 1 from the next higher place value. The tens digit (7) becomes 6, and the units digit becomes 1414.

  • Step 3: Subtract in the units column: 146=814 - 6 = 8.

  • Step 4: Move to the tens column, subtract 686 - 8. Since we borrowed from the hundreds place, it simplifies to 168=816 - 8 = 8.

  • Step 5: The hundreds digit in the minuend is 22, reduced by 1 due to previous borrowing, makes the effective hundreds 11.

  • Step 6: Finally, in the hundreds column, subtract 10=11 - 0 = 1.

Let's summarize the steps calculations as follows:

274 862188 \begin{aligned} 274& \\ - \ 86& \\ \overline{\phantom{2}188} \\ \end{aligned}

Upon completion, the final result is 188188.

3

Final Answer

188

Key Points to Remember

Essential concepts to master this topic
  • Place Value Alignment: Line up digits by ones, tens, and hundreds columns
  • Borrowing Technique: When 4 < 6, borrow 1 from tens: 14 - 6 = 8
  • Check: Add your answer to subtrahend: 188 + 86 = 274 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to adjust borrowed digits
    Don't borrow from 7 in tens place but forget to reduce it to 6 = wrong final answer! This leaves you with extra value that doesn't exist. Always reduce the borrowed digit by 1 after borrowing.

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 from 4 in the ones place?

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You can't subtract a larger number from a smaller number and get a positive result! When 4 < 6, you must borrow 10 from the tens place to make it 14 - 6 = 8.

What happens to the tens digit after I borrow?

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The tens digit decreases by 1 after borrowing. In this problem, 7 becomes 6 after lending 10 to the ones place. Don't forget this step!

How do I know when to borrow from the hundreds place?

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You borrow from hundreds when the tens subtraction becomes impossible. Here, after borrowing, we have 6 - 8, so we borrow from hundreds: 168=816 - 8 = 8.

Can I check my subtraction answer?

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Yes! Add your answer to the number you subtracted: 188+86188 + 86. If you get the original number (274), your answer is correct!

What if I need to borrow from zero?

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When borrowing from 0, you must first borrow from the next higher place value. For example, if you have 300 - 86, you'd turn it into 2-9-10 before proceeding.

Is there an easier way than borrowing?

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While borrowing is the standard method for vertical subtraction, you could also break apart numbers: 27486=274806=1946=188274 - 86 = 274 - 80 - 6 = 194 - 6 = 188.

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