Vertical Subtraction - Examples, Exercises and Solutions

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

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\( \begin{aligned} &37 \\ -& \\ &25 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

Examples with solutions for Vertical Subtraction

Step-by-step solutions included
Exercise #1

amp;15amp;amp;  4amp;776amp; \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 5:54=1 5 - 4 = 1 .
  • Step 3: Move to the tens column. There is no subtraction to perform here since it's only 101 - 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 15415 - 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 #2

amp;27amp;amp;  3amp;776amp; \begin{aligned} &27 \\ -& \\ &~~3 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

To solve this problem, we'll perform vertical subtraction:

  • Step 1: Write down the numbers vertically with the larger number (the minuend) on top:

27  3776\begin{aligned} &27 \\ -& \\ &~~3 \\ &\underline{\phantom{776}} &\\ \end{aligned}

  • Step 2: Subtract the digits in the ones place: 77 (from 2727) minus 33 (from 33) equals 44.
  • Step 3: Subtract the digits in the tens place: 22 (from 2727) minus 00 (no tens in 33) equals 22.

Therefore, the difference is 2424.

The solution to the problem is 2424, which corresponds to choice 2.

Answer:

24

Video Solution
Exercise #3

amp;39amp;amp;  6amp;776amp; \begin{aligned} &39 \\ -& \\ &~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

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

  • Step 1: Write the numbers vertically, with each digit aligned in their respective place value.

  • Step 2: Begin subtracting starting from the rightmost column.

  • Step 3: Move to the left, repeating the process for each subsequent column until finished.

Now, let's work through each step:
Step 1: Arrange the numbers vertically, aligning according to the decimal place.
 39
-   6
-----
Step 2: Start subtracting from the right. Subtract the ones place: 96=39 - 6 = 3.
 39
-   6
-----
    3
Step 3: Since there is no need to borrow, move to the tens place:
The tens place comprises '3' from '39', as there is no corresponding digit above '6' to subtract from: 30=33 - 0 = 3.
  39
-   6
-----
   33

Therefore, the solution to the problem is 33 33 .

Answer:

33

Video Solution
Exercise #4

amp;48amp;amp;  7amp;776amp; \begin{aligned} &48 \\ -& \\ &~~7 \\ &\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 place value.

  • Step 2: Subtract the units place.

  • Step 3: Subtract the tens place if necessary.

Now, let's work through each step:
Step 1: Write the numbers 48 and 7 in columns where the digits (ones place) are aligned: 48 7\begin{array}{c} 48 \\ -~7 \\ \end{array} Step 2: Subtract the units (8 - 7 = 1) and write the result in the units position.
Step 3: The tens place after subtraction is unchanged because there is no borrowing needed, so the 4 from 48 stays as 4.
Thus, we have: 48 7  41 \begin{array}{c} 48 \\ -~7 ~~\\ \underline{41} \end{array}

Therefore, the solution to the problem is 41.

Answer:

41

Video Solution
Exercise #5

amp;56amp;amp;  5amp;776amp; \begin{aligned} &56 \\ -& \\ &~~5 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

To solve this problem, let's use a methodical approach as follows:

  • Step 1: Write the numbers in a vertical format, aligning the digits by place value.
  • Step 2: Subtract the ones digit: 66 (from 5656) minus 55 equals 11.
  • Step 3: Bring down the tens digit since we are not subtracting anything from it: 55.

In detail:

  1. Align the numbers vertically, with the larger number on top:
    564005 \begin{array}{r} 56 \\ - \phantom{400}5 \\ \hline \end{array}
  2. Subtract the digits in the ones column. The ones digit in 5656 is 66 and the ones digit in 55 is 55. Subtract 55 from 66 to get 11.
  3. Since there are no numbers to subtract from the tens column of the first number, write down the 55 from 5656.

The result of the vertical subtraction is thus:
56400551 \begin{array}{r} 56 \\ - \phantom{400}5 \\ \hline 51 \\ \end{array}

Therefore, the solution to this problem is 51 51 .

Answer:

51

Video Solution

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