Examples with solutions for Vertical Subtraction: 5-digits and above-Borrowing across zeros

Exercise #1

amp;12001amp;amp;  1542amp;776amp; \begin{aligned} &12001 \\ -& \\ &~~1542 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve the problem of subtracting 1542 from 12001, we will perform vertical subtraction, borrowing where necessary:

  • Step 1: Align the numbers by place value:

  •    1200101542 \begin{array}{c} ~~~12001 \\ - \phantom{0} 1542 \\ \hline \end{array}

  • Step 2: Start subtracting from the rightmost digit (ones place):

  • The ones column requires borrowing since 1 < 2. Borrow from the tens.

  • The tens column is 0, so we need to borrow from the hundreds. The hundreds column is also 0, so we move to the thousands. The thousands column has 2, which becomes 1, and the hundreds column becomes 10, and then the tens column becomes 9. The ones column becomes 11.

  • Now subtract: Ones column: 112=911 - 2 = 9

  • Step 3: Move to the tens place: Subtract 94=59 - 4 = 5

  • Step 4: Move to the hundreds place: Subtract 95=49 - 5 = 4 after borrowing.

  • Step 5: Move to the thousands place: Subtract 11=01 - 1 = 0

  • Step 6: Finally, in the ten-thousands: Note that 11 merely moves down as there’s no digit to deduct.

Putting it all together:

   1200101542   10459 \begin{array}{c} ~~~ 12001 \\ - \phantom{0}1542 \\ \hline ~~~10459 \\ \end{array}

Therefore, the final solution to the problem is 10459 10459 .

Answer

10459

Exercise #2

amp;23004amp;amp;11799amp;776amp; \begin{aligned} &amp;23004 \\ -&amp; \\ &amp;11799 \\ &amp;\underline{\phantom{776}} &amp; \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this subtraction problem, we will work through each digit systematically:

  • Units Place:
    4 (from 23004) is less than 9 (from 11799). We need to borrow. We take 1 from the tens place of 23004, changing the tens digit from 0 to 9, and making the units digit 14.
    Perform the subtraction: 149=5 14 - 9 = 5 .
  • Tens Place:
    Initially, we had 0 as the tens digit of 23004, but after borrowing, it became 9. Now, subtract: 99=0 9 - 9 = 0 .
  • Hundreds Place:
    0 is less than 7. We need to borrow. We take 1 from the thousands place (a 3), changing the thousands digit from 3 to 2, and making the hundreds digit 10.
    Perform the subtraction: 107=3 10 - 7 = 3 .
  • Thousands Place:
    2 (after borrowing) and 1.
    Perform the subtraction: 21=1 2 - 1 = 1 .
  • Tens of Thousands Place:
    2 - 1 (since we didn’t need to touch this digit for any borrowing) is simply 21=1 2 - 1 = 1 .

Therefore, merging these stepped results, we find the final answer is 11205 11205 .

Thus, the solution to the subtraction problem is 11205 11205 .

Answer

11205

Exercise #3

amp;70005amp;amp;24126amp;776amp; \begin{aligned} &amp;70005 \\ -&amp; \\ &amp;24126 \\ &amp;\underline{\phantom{776}} &amp; \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Align the two numbers vertically with the minuend (70005) on top and the subtrahend (24126) below it.
  • Step 2: Subtract digit by digit from the rightmost side and borrow as necessary.

Let's break this down:

Step-by-step Solution:

1. Subtract the rightmost digit:
- Subtract 6 from 5. Since 5 is less than 6, we need to borrow from the next digits.

2. Borrowing:
- The immediate next digit is '0', so we continue borrowing to the left. We borrow 1 from the third zero (turning it into a 9), which makes the second zero a 9 and the third zero a 9, and we subtract the borrowed 1 from the 7, turning it into 6.

3. Complete the subtraction:
- For the units column (now 15 and 6), subtract to get: 156=915 - 6 = 9.
- For the tens column (now 9 and 2), subtract to get: 92=79 - 2 = 7.
- For the hundreds column (now 9 and 1), subtract to get: 91=89 - 1 = 8.
- For the thousands column (6 and 4), subtract to get: 64=26 - 4 = 2.
- For the ten-thousands column (no borrowing needed, 6 and 2), subtract to get: 62=46 - 2 = 4.

The final result after all column-based subtractions, including borrowing corrections, is: 45879 \text{45879} .

Therefore, the solution to the problem is 45879 45879 .

Answer

45879

Exercise #4

amp;80004amp;amp;54636amp;776amp; \begin{aligned} &amp;80004 \\ -&amp; \\ &amp;54636 \\ &amp;\underline{\phantom{776}} &amp; \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this subtraction problem, we will perform vertical subtraction, paying close attention to borrowing across zeros:

Step-by-step solution:

  • Write the numbers such that they align vertically, with the larger number on top and the smaller number directly below each corresponding digit:

amp;80004amp;54636amp;77600amp; \begin{aligned} &amp;80004 \\ -&amp;54636 \\ &amp;\overline{\phantom{77600}} &amp; \\ \end{aligned}

  • Start subtracting from the rightmost digit:

  • 1. Units place: 464 - 6. Since 4 is less than 6, borrow 1 from the tens place (next digit).
    2. Tens place: Now, treat it as 10310 - 3, but since you borrowed 1 for the units place, it becomes 93=69 - 3 = 6.
    3. Hundreds place: Borrow from the thousands place since you need a digit to make 060 - 6. It becomes 106=410 - 6 = 4.
    4. Thousands place: Now subtract from what remains after borrowing from it, 949 - 4, which equals 5.
    5. Ten-thousands place: Since you borrowed to the right, 75=27 - 5 = 2 in this position.

  • The subtraction yields the result as follows:

amp;956014amp;054636amp;025368amp; \begin{aligned} &amp;9560 14 \\ -&amp;\phantom{0}54636 \\ &amp;\phantom{0}\underline{25368} &amp; \\ \end{aligned}

Therefore, the solution to the subtraction problem is 25368\mathbf{25368}.

Answer

25368

Exercise #5

amp;90007amp;amp;61358amp;776amp; \begin{aligned} &amp;90007 \\ -&amp; \\ &amp;61358 \\ &amp;\underline{\phantom{776}} &amp; \\ \end{aligned}

Video Solution

Answer

28649