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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\( \begin{aligned} &178 \\ -& \\ &125 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

Examples with solutions for Vertical Subtraction

Step-by-step solutions included
Exercise #1

amp;157amp;amp;    4amp;776amp; \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.
    157 4776 \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 #2

amp;478amp;amp;    2amp;776amp; \begin{aligned} &478 \\ -& \\ &~~~~2 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

Let's solve the subtraction problem by following these steps:

First, align the numbers vertically:

478    2776 \begin{aligned} &478 \\ -& \\ &~~~~2 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Starting with the rightmost digits:

  • In the units place, subtract 22 from 88: 82=68 - 2 = 6.
  • Since there are no other digits from the subtrahend, bring down the remaining digits as they are.

This results in:

476 \begin{aligned} &476 \\ \end{aligned}

Therefore, the solution to the problem is 476476.

Answer:

476

Video Solution
Exercise #3

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

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:
    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):
    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: 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 .

Answer:

102

Video Solution
Exercise #4

amp;37amp;amp;25amp;776amp; \begin{aligned} &37 \\ -& \\ &25 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

Let's solve the subtraction problem 372537 - 25 using vertical subtraction:

  • Step 1: Align the numbers vertically:

           37    25 \begin{array}{c} \ \ \ \ \ \ \ 37 \\ - \ \ \ \ 25 \\ \hline \end{array}

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

    75=27 - 5 = 2

    Write 22 under the line in the units place.

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

    32=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
Exercise #5

amp;578amp;amp;    6amp;776amp; \begin{aligned} &578 \\ -& \\ &~~~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

Let's solve this subtraction problem step-by-step:

  • Step 1: Align the numbers vertically by place value, ensuring units are aligned under units.
  • Step 2: Start subtraction from the rightmost column (units column). Here, subtract 6 from 8 in the units place: 86=28 - 6 = 2.
  • Step 3: Since we have dealt with the units place, move one step to the left to the tens place. Here, subtract 0 (since nothing is being subtracted from this place after borrowing) from 7 in the tens place: 70=77 - 0 = 7.
  • Step 4: Finally, move to the hundreds place. Subtract 0 from 5 (again, no borrowing affects this place): 50=55 - 0 = 5.

After completing the steps, the subtraction gives us the result.

Therefore, the solution to the problem is 572572.

Answer:

572

Video Solution

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