Vertical Subtraction Practice Problems & Worksheets

Master vertical subtraction with borrowing through step-by-step practice problems. Learn the three essential rules and solve multi-digit subtraction exercises.

πŸ“šPractice Vertical Subtraction Problems
  • Apply the correct alignment rule: ones under ones, tens under tens
  • Master borrowing from the next digit when upper digit is smaller
  • Handle complex borrowing with zeros using the special transformation rule
  • Solve multi-digit subtraction problems step-by-step with confidence
  • Practice borrowing across multiple place values in challenging exercises
  • Build fluency with vertical subtraction through varied problem types

Understanding Vertical Subtraction

Complete explanation with examples

Vertical Subtraction

In order to solve vertical subtraction, we follow these rules:
First rule - write the problem in the correct order!
Ones digits under ones digits, tens digits under tens digits, and so on.
Second rule - when the upper digit is smaller than the lower digit - we borrow 11 from the next digit.
Third rule - when you need to borrow from a 00, you cannot borrow directly from it. Instead, keep moving left through any consecutive zeros until you find a non-zero digit. Borrow 11 from that digit, turning all the zeros you passed through into 99s, and the original 00 (where you needed to borrow) becomes 1010.

Detailed explanation

Practice Vertical Subtraction

Test your knowledge with 33 quizzes

\( \begin{aligned} &25 \\ -& \\ &24 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)\( \)

Examples with solutions for Vertical Subtraction

Step-by-step solutions included
Exercise #1

105βˆ’Β Β Β Β 3776β€Ύ \begin{aligned} &105 \\ -& \\ &~~~~3 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

Let's solve the subtraction problem 105βˆ’3 105 - 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):
    βˆ’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: 5βˆ’3=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 105βˆ’3=102 105 - 3 = 102 .

Therefore, the correct answer is 102 102 .

Answer:

102

Video Solution
Exercise #2

89βˆ’Β Β 9776β€Ύ \begin{aligned} &89 \\ -& \\ &~~9 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

To find the result of subtracting 9 from 89, we will look at it digit by digit:

  • Step 1: Subtract the units digits:
    9 - 9 = 0.
  • Step 2: Subtract the tens digits:
    8 - 0 = 8.

The subtraction does not require any borrowing since both digits are smaller than or equal to the digits we are subtracting from.

Thus, the result of the subtraction 89βˆ’989 - 9 is 8080.

Considering the given multiple-choice options, the correct choice is option 4: 8080.

Answer:

80

Video Solution
Exercise #3

248βˆ’135776β€Ύ \begin{aligned} &248 \\ -& \\ &135 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

To solve this subtraction problem, we will use the vertical subtraction method as follows:

Step 1: Align the numbers vertically.
We write 248 over 135, ensuring that corresponding digits are aligned correctly, particularly the units, tens, and hundreds places.

\begin{array}{c} 248 \\ - 135 \\ \hline \end{array}

Step 2: Subtract column by column from right to left.

  • Units column: 8βˆ’5=38 - 5 = 3. Write 3 under the units column.

  • Tens column: 4βˆ’3=14 - 3 = 1. Write 1 under the tens column.

  • Hundreds column: 2βˆ’1=12 - 1 = 1. Write 1 under the hundreds column.

The subtraction does not require any borrowing as each digit in the minuend is greater than or equal to the corresponding digit in the subtrahend.

Step 3: Combine the results.
From left to right, the result is 113.

Therefore, the solution to the subtraction problem is 113113, which corresponds to choice 4.

Answer:

113

Video Solution
Exercise #4

15βˆ’Β Β 4776β€Ύ \begin{aligned} &15 \\ -& \\ &~~4 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

To solve this problem, we'll perform simple vertical subtraction for the numbers given, 15 and 4:

Step-by-step solution:

  • Step 1: Write the numbers in a column, aligning the digits according to place value.
  • Step 2: Start subtracting from the rightmost column (the ones column).
    In the ones column, subtract 4 from 5:5βˆ’4=1 5 - 4 = 1 .
  • Step 3: Move to the tens column. There is no subtraction to perform here since it's only 1βˆ’01 - 0, which leaves the digit as is.

Thus, there is no borrowing needed because the digits in the minuend are sufficient to carry out the subtraction.

The result of the subtraction 15βˆ’415 - 4 is 1111.

Therefore, the solution to the problem is 11 11 .

The correct multiple-choice answer is option 1: 11 11 .

Answer:

11

Video Solution
Exercise #5

37βˆ’25776β€Ύ \begin{aligned} &37 \\ -& \\ &25 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

Let's solve the subtraction problem 37βˆ’2537 - 25 using vertical subtraction:

  • Step 1: Align the numbers vertically:

    Β Β Β Β Β Β Β 37βˆ’Β Β Β Β 25 \begin{array}{c} \ \ \ \ \ \ \ 37 \\ - \ \ \ \ 25 \\ \hline \end{array}

  • Step 2: Start with the rightmost column (units place):

    7βˆ’5=27 - 5 = 2

    Write 22 under the line in the units place.

  • Step 3: Move to the left column (tens place):

    3βˆ’2=13 - 2 = 1

    Write 11 under the line in the tens place. This gives us 1212 as the result.

Therefore, the solution to the problem is 1212.

Answer:

12

Video Solution

Frequently Asked Questions

What is the first rule of vertical subtraction?

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The first rule is proper alignment: write ones digits under ones digits, tens under tens, hundreds under hundreds, and so on. Always place the first number in the problem at the top of your vertical setup.

When do I need to borrow in vertical subtraction?

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You need to borrow when the upper digit is smaller than the lower digit you're subtracting from. For example, in 45 - 29, you can't subtract 9 from 5, so you borrow 1 from the tens place.

How do I borrow from a zero in vertical subtraction?

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When borrowing from a zero, the zero becomes 9 and you continue borrowing from the next non-zero digit to the left. For example, in 500 - 365, the first 0 becomes 10, the second 0 becomes 9, and the 5 becomes 4.

What happens when there are multiple zeros in vertical subtraction?

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With multiple consecutive zeros, each zero (except the rightmost one you're borrowing for) becomes 9 until you reach a non-zero digit. The pattern continues: third zero becomes 8, fourth becomes 7, and so on.

How do I check my vertical subtraction answer?

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Add your answer to the bottom number (subtrahend). If correct, this sum should equal the top number (minuend). For example, if 87 - 54 = 33, then 33 + 54 should equal 87.

What are common mistakes in vertical subtraction with borrowing?

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Common mistakes include: 1) Forgetting to reduce the digit you borrowed from, 2) Misaligning place values, 3) Not continuing the borrowing process through multiple zeros, and 4) Subtracting the smaller number from the larger regardless of position.

Why is vertical subtraction better than horizontal subtraction?

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Vertical subtraction organizes complex multi-digit problems clearly by place value, making borrowing easier to track. It reduces errors in alignment and provides a systematic approach for solving problems like 5700 - 3786.

How do I solve vertical subtraction problems with 4 or more digits?

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Follow the same three rules regardless of digit count: proper alignment, borrowing when needed, and handling zeros correctly. Work from right to left (ones to thousands), borrowing across place values as necessary.

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