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 - a 00 that cannot be borrowed from becomes 99 until we reach a digit that is not 00 from which we can borrow 11.
Note! If there is a third 00 right after, it will become 88, if there is a fourth 00 right after, it will become 77, and so on.

Detailed explanation

Practice Vertical Subtraction

Test your knowledge with 33 quizzes

\( \begin{aligned} &478 \\ -& \\ &~~~~2 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

Examples with solutions for Vertical Subtraction

Step-by-step solutions included
Exercise #1

amp;97βˆ’amp;amp;63amp;776β€Ύamp; \begin{aligned} &97 \\ -& \\ &63 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Align the numbers vertically by their place values.

  • Step 2: Subtract the digits in the ones place.

  • Step 3: Subtract the digits in the tens place, borrowing if needed.

Now, let's work through each step together:

Step 1: Align 97 and 63 vertically:

00Β 907βˆ’0603 \begin{array}{c} \phantom{00\ }9\phantom{0}7 \\ -\phantom{0}6\phantom{0}3 \\ \hline \end{array}

Step 2: Start with the ones place:

The digits are 7 and 3.

Subtract 3 from 7: 7βˆ’3=47 - 3 = 4.

Step 3: Move to the tens place:

The digits are 9 and 6.

Subtract 6 from 9: 9βˆ’6=39 - 6 = 3.

Write the results in their respective place values:

00Β 907βˆ’060300Β 304 \begin{array}{c} \phantom{00\ }9\phantom{0}7 \\ -\phantom{0}6\phantom{0}3 \\ \hline \phantom{00\ }3\phantom{0}4 \\ \end{array}

Therefore, the solution to the problem is 34.

Answer:

34

Video Solution
Exercise #2

amp;99βˆ’amp;amp;Β Β 9amp;776β€Ύamp; \begin{aligned} &99 \\ -& \\ &~~9 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

To solve this problem, let's perform vertical subtraction:

  • Step 1: Align the numbers 99 and 9 for subtraction.
  • Step 2: Subtract starting from the rightmost digits: the ones place.
  • Step 3: 9βˆ’9=0 9 - 9 = 0 in the ones place.
  • Step 4: Move to the tens place: 9βˆ’0=9 9 - 0 = 9 . (Since we did not borrow any value from the tens place, the 9 remains.)

Thus, the result of the subtraction is 90 90 .

Therefore, the solution to the mathematical problem is 90 90 , which corresponds to choice 2.

Answer:

90

Video Solution
Exercise #3

amp;105βˆ’amp;amp;Β Β Β Β 3amp;776β€Ύamp; \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:
    1amp;0amp;5 \begin{array}{c} 1 & 0 & 5 \\ \end{array}

  • Place 3 beneath 105 such that it aligns with the rightmost digit (units place):
    βˆ’amp;amp;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 #4

amp;157βˆ’amp;amp;Β Β Β Β 4amp;776β€Ύamp; \begin{aligned} &157 \\ -& \\ &~~~~4 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

Let's solve the basic vertical subtraction problem where we subtract 4 from 157 step by step:

  • Step 1: Write the numbers in a vertical format, ensuring to align them by place values.
    157βˆ’Β 4776β€Ύ \begin{array}{c} 157 \\ -\ 4 \\ \underline{\phantom{776}} \\ \end{array}

  • Step 2: Perform subtraction starting from the rightmost digit (the ones place).
    - Subtract 4 from 7 in the ones column, resulting in 3.

  • Step 3: Since the number being subtracted, 4, has no digit in the tens and hundreds places, bring down the remaining digits from 157. These are 5 in the tens place and 1 in the hundreds place.

Thus, the result of subtracting 4 from 157 is 153153.

Among the options provided, choice 2 is the correct answer, which states 153.

Therefore, the solution to the problem is 153 153 .

Answer:

153

Video Solution
Exercise #5

amp;15βˆ’amp;amp;Β Β 4amp;776β€Ύamp; \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

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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