Solve Vertical Subtraction: 105 minus 3

Vertical Subtraction with Three-Digit Numbers

105    3776 \begin{aligned} &105 \\ -& \\ &~~~~3 \\ &\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 subtracting 2 digits, and then we write
00:06 We'll start by subtracting ones from ones, and write in the ones place
00:09 Write 0 in the missing digits
00:12 Subtract tens from tens, and write in the tens place
00:15 Subtract hundreds from hundreds, and write in the hundreds place
00:18 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

105    3776 \begin{aligned} &105 \\ -& \\ &~~~~3 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

Let's solve the subtraction problem 1053 105 - 3 :

Align the numbers vertically to ensure each digit is in the correct place value position:

  • Write 105 as:
    105 \begin{array}{c} 1 & 0 & 5 \\ \end{array}

  • Place 3 beneath 105 such that it aligns with the rightmost digit (units place):
    3 \begin{array}{c} - & & 3 \\ \end{array}

  • Subtract each column starting from the rightmost side (units digit) to the left:

Step-by-step subtraction:

  • Units column: 53=2 5 - 3 = 2

  • Tens column: There is nothing to subtract with 0, so it remains 0 0 .

  • Hundreds column: Similarly, there is nothing to subtract, so it remains 1 1 .

Combine the results of these steps to find the answer:

The result of the subtraction 1053=102 105 - 3 = 102 .

Therefore, the correct answer is 102 102 .

3

Final Answer

102

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Place digits in correct columns by place value positions
  • Technique: Start subtracting from rightmost column: 5 - 3 = 2
  • Check: Add your answer to subtrahend: 102 + 3 = 105 ✓

Common Mistakes

Avoid these frequent errors
  • Misaligning digits in wrong place value columns
    Don't place 3 under the tens or hundreds column = wrong alignment and incorrect answer! This puts digits in wrong place values, leading to errors like 75 or 72. Always align the rightmost digit of the smaller number with the units column of the larger number.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &97 \\ -& \\ &63 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)\( \)

FAQ

Everything you need to know about this question

Why do I need to align the numbers vertically?

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Vertical alignment ensures each digit is in its correct place value position. When you align properly, you subtract units from units, tens from tens, and hundreds from hundreds!

What if there's nothing to subtract in a column?

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When there's no digit to subtract (like in the tens and hundreds columns here), the original digit stays the same. Think of it as subtracting zero from that digit.

Do I always start from the right side?

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Yes! Always start subtracting from the rightmost column (units place) and work your way left. This follows the proper place value order and prevents errors.

How can I check if my subtraction is correct?

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Add your answer to the number you subtracted. If you get the original number, you're correct! For example: 102+3=105 102 + 3 = 105

What if I need to borrow in subtraction?

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In this problem, you don't need to borrow since 53 5 \geq 3 . But when the top digit is smaller than the bottom digit, you borrow from the next column to the left.

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