Examples with solutions for Vertical Subtraction: Triple digit addition with regrouping

Exercise #1

amp;285amp;amp;196amp;776amp; \begin{aligned} &285 \\ -& \\ &196 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve the problem of subtracting 196 from 285 using vertical subtraction, follow these steps:

  • Step 1: Write the numbers vertically, aligning them by place value:
    0285196076 \begin{array}{c} \phantom{0}285 \\ -196 \\ \underline{\phantom{076}} \\ \end{array}
  • Step 2: Start with the units column (rightmost digits). Subtract 6 from 5. Since 5 is smaller than 6, we need to carry from the tens column:
    - Take 1 from 8 (in the tens column) to make it 7. - Add 10 to the 5 in the units column, making it 15. - Now, 156=915 - 6 = 9.
  • Step 3: Move to the tens column. Subtract 9 from 7. Since 7 is smaller than 9, we need to carry from the hundreds column:
    - Take 1 from 2 (in the hundreds column) to make it 1. - Add 10 to the 7 in the tens column, making it 17. - Now, 179=817 - 9 = 8.
  • Step 4: Finish with the hundreds column. Subtract 1 from 1 (after carrying):
    - 11=01 - 1 = 0.
  • Step 5: Combine the results to get the final answer:
    - The result of the subtraction is 089, or simply 89.

Therefore, the result of subtracting 196 from 285 is 89 89 .

Answer

89

Exercise #2

amp;314amp;amp;126amp;776amp; \begin{aligned} &314 \\ -& \\ &126 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

We'll align the numbers by their place values:
     314314
-  126

Start with the rightmost column (the units place):

  • Units Place: 464 - 6 requires borrowing because 4 is less than 6. Borrow 1 from the tens column in 314, turning it into 10, leaving 0 in the tens place. Now, 146=814 - 6 = 8.

  • Tens Place: After borrowing, 020 - 2 also requires borrowing from the hundreds column. Borrow 1 from the hundreds column, leaving 22 in the hundreds place. Now, 102=810 - 2 = 8.

  • Hundreds Place: Subtract as normal, 21=12 - 1 = 1.

When we put it all together, the result is:

  • Hundreds: 11

  • Tens: 88

  • Units: 88

Therefore, 314126=188314 - 126 = 188.

The solution to the problem is 188188, which matches choice 44.

Answer

188

Exercise #3

amp;453amp;amp;269amp;776amp; \begin{aligned} &453 \\ -& \\ &269\\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Subtract the units place.
  • Step 2: Subtract the tens place after borrowing if necessary.
  • Step 3: Subtract the hundreds place.

Now, let's work through each step:

Step 1: Units Place
We have 33 (from 453) and 99 (from 269). Since 33 is less than 99, we need to borrow 1 from the tens column:

  • Borrow 1 from the tens column (making it 434 \rightarrow 3), change units to 1313.
  • Subtract: 139=413 - 9 = 4.

Step 2: Tens Place
After borrowing, we have 33 in the tens place (originally 55, but 11 was borrowed) and 66 in the tens place of 269. Since 33 is less than 66, we need to borrow 1 from the hundreds column:

  • Borrow 1 from the hundreds column (making it 434 \rightarrow 3), change tens to 1313.
  • Subtract: 136=713 - 6 = 7.

Step 3: Hundreds Place
After borrowing, we have 33 in the hundreds place and 22 in the hundreds place of 269:

  • Subtract: 32=13 - 2 = 1.

Therefore, the solution to the problem is 184 184 .

Answer

184

Exercise #4

amp;542amp;amp;356amp;776amp; \begin{aligned} &542 \\ -& \\ &356\\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To begin solving the subtraction 542356 542 - 356 , we will break it down step by step:

  • Step 1: Subtract the units digit
    - The units digits are 2 (from 542) and 6 (from 356).
    - Since 2 is smaller than 6, we need to borrow 1 ten from the tens place, changing it from 40 to 30 (of the minuend).
    - The borrowed 10 changes the 2 to 12: 126=6 12 - 6 = 6 .
  • Step 2: Subtract the tens digit
    - Now the tens digit is 3 (originally 4 but reduced to 3 due to borrowing) minus 5.
    - We need to borrow 1 hundred (from 5 hundreds), which changes it to 4 hundreds, making the tens digit 13.
    - Calculate 135=8 13 - 5 = 8 .
  • Step 3: Subtract the hundreds digit
    - The hundreds digit is 4 (from the previous borrow) minus 3 from the subtrahend.
    - Calculate 43=1 4 - 3 = 1 .

Thus, combining all these, we obtain the result of the subtraction: 186 186 .

Therefore, the solution to the problem is 186 186 .

Answer

186

Exercise #5

amp;664amp;amp;275amp;776amp; \begin{aligned} &664 \\ -& \\ &275\\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we will perform a detailed step-by-step subtraction:

  • Step 1: Write the numbers in column format, aligning them by place value:

664275    \begin{array}{c} 664 \\ -275 ~~~\\ \hline \end{array}

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

  • Subtract the units: 454 - 5. Since 4 is smaller than 5, we need to borrow from the tens place.

    - Borrow 1 from the tens (making it 5), the 4 becomes 14: (145=9).(14 - 5 = 9).

  • Step 3: Move to the tens place:

  • Since we borrowed 1, we have the tens as 5 now, perform: 575 - 7. Again, 5 is smaller than 7, so borrow from the hundreds place.

    - Borrow 1 from the hundreds (making it 5), the 5 becomes 15: (157=8).(15 - 7 = 8).

  • Step 4: Now, proceed to the hundreds place:

  • After borrowing, the hundreds place is 5 (originally 6, minus 1 borrowed), perform: 525 - 2.

    - No need to borrow here, simply calculate: (52=3).(5 - 2 = 3).

  • Step 5: Compile the final result from top to bottom:

  • 389389

Therefore, the answer to the subtraction 664275664 - 275 is 389\mathbf{389}.

Answer

389

Exercise #6

amp;756amp;amp;667amp;776amp; \begin{aligned} &756 \\ -& \\ &667 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Write down the numbers aligning them by their place values:

7566670 \begin{aligned} & 756 \\ - & 667 \\ \hline \phantom{0} \end{aligned}

  • Step 2: Subtract the units digit:

The units digit of 756 is 6, and the units digit of 667 is 7. Since 6 < 7, we need to regroup. We borrow 1 from the tens column, turning the 5 into a 4, and make the 6 into 16. Now 167=9 16 - 7 = 9 .

  • Step 3: Subtract the tens digit:

After regrouping, the tens digit of 756 became 4, and we subtract the tens digit of 667, which is 6. Again, since 4 < 6, we need to regroup from the hundreds column. Borrowing 1, we turn the 7 into a 6, and the 4 into 14. Now 146=8 14 - 6 = 8 .

  • Step 4: Subtract the hundreds digit:

The hundreds digit of 756 after regrouping is now 6, and for 667, it is 6 as well. So, 66=0 6 - 6 = 0 .

After completing the subtraction, we have:

756667089 \begin{aligned} & 756 \\ - & 667 \\ \hline & 089 \end{aligned}

Therefore, the solution to the subtraction problem is 89 \boldsymbol{89} .

Answer

89

Exercise #7

amp;867amp;amp;578amp;776amp; \begin{aligned} &amp;867 \\ -&amp; \\ &amp;578 \\ &amp;\underline{\phantom{776}} &amp; \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Subtract the units digit: 77 (in 867) - 88 (in 578) requires borrowing. Borrow 1 ten from the tens place of 867, making the units place 1717 and the tens place 55.
  • Step 2: Now, 178=917 - 8 = 9. The digit in the units place of the answer is 9.
  • Step 3: Subtract the tens digit: With the new tens digit, 575 - 7 also requires borrowing. Borrow 1 from the hundreds place, making the tens place 1515 and the hundreds place 77.
  • Step 4: Now, 157=815 - 7 = 8. The digit in the tens place of the answer is 8.
  • Step 5: Subtract the hundreds digit: 75=27 - 5 = 2. The digit in the hundreds place of the answer is 2.

Therefore, the final answer after subtraction is 289 289 .

Answer

289

Exercise #8

amp;936amp;amp;768amp;776amp; \begin{aligned} &amp;936 \\ -&amp; \\ &amp;768 \\ &amp;\underline{\phantom{776}} &amp; \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this subtraction problem, we'll perform vertical subtraction, which involves subtracting each corresponding pair of digits from right to left.

  • Step 1: Arrange the numbers vertically.
    • Write 936 (the minuend) on top.
    • Write 768 (the subtrahend) below it, aligning the digits by place value.
  • Step 2: Subtract the ones place.
    Subtract 8 from 6. Since 8 is larger than 6, we need to borrow 1 from the tens place:
    • Decrease the digit in the tens place (from 3 to 2).
    • Increase the ones digit by 10 (making it 16).
    • 16 - 8 = 8, write 8 below the line.
  • Step 3: Subtract the tens place.
    Now subtract 6 from the adjusted tens digit (2):
    • Since 6 is larger than 2, borrow 1 from the hundreds place (from 9 to 8).
    • Increase the tens digit by 10 (making it 12).
    • 12 - 6 = 6, write 6 below the line.
  • Step 4: Subtract the hundreds place.
    Subtract 7 from the adjusted hundreds digit (8):
    • 8 - 7 = 1, write 1 below the line.

Thus, the result of the subtraction 936768936 - 768 is 168.

Answer

168

Exercise #9

amp;478amp;amp;289amp;776amp; \begin{aligned} &amp;478 \\ -&amp; \\ &amp;289\\ &amp;\underline{\phantom{776}} &amp; \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve the problem of subtracting 289 from 478, we perform the following steps:

  • Setup: Write the numbers in column form, aligning by place value:
    478289\begin{aligned} & 478 \\ - & 289 \\ \end{aligned}
  • Subtract Ones: Start from the rightmost column (ones place):
    898 - 9. Since 8 is smaller than 9, borrow 1 from the tens place (7), making it 6 and converting the 8 to 18.
    Now, perform 189=918 - 9 = 9.
  • Subtract Tens: Move to the tens column, now having 66 from borrowing from the previous step:
    686 - 8. Again, since 6 is less than 8, borrow 1 from the hundreds place (4), making it 3 and converting the 6 to 16.
    Now, perform 168=816 - 8 = 8.
  • Subtract Hundreds: Finally, subtract the hundreds column:
    32=13 - 2 = 1.
  • Assemble the result: The completed subtraction gives us 189189.

Therefore, the solution to the problem is 189189, which corresponds to choice 2.

Answer

189

Exercise #10

amp;843amp;amp;157amp;776amp; \begin{aligned} &amp;843 \\ -&amp; \\ &amp;157\\ &amp;\underline{\phantom{776}} &amp; \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve the subtraction problem 843157 843 - 157 , follow these steps:

  • Align the numbers vertically:

       843
      - 157
      ------
      
  • Start subtracting from the rightmost column (units):

    • Units place: 373 - 7. Since 3 is less than 7, we need to borrow. Borrow 1 from the tens place, turning the 4 into a 3, and making the 3 in the units place a 13.

    • After borrowing, subtract: 137=613 - 7 = 6.

  • Move to the tens column:

    • After borrowing, we have 353 - 5. Borrow 1 from the hundreds place, turning the 8 into a 7, and making the tens 3 into 13.

    • Subtract: 135=813 - 5 = 8.

  • Finally, subtract the hundreds column: 71=67 - 1 = 6.

 843
- 157
-----
  686

Therefore, the final result of the subtraction 843157 843 - 157 is 686 686 .

Answer

686

Exercise #11

amp;686amp;amp;499amp;776amp; \begin{aligned} &amp;686 \\ -&amp; \\ &amp;499\\ &amp;\underline{\phantom{776}} &amp; \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow the vertical subtraction method:

  • First, subtract the ones place: 696 - 9. Since 66 is less than 99, we need to borrow from the tens place.
  • Turn 88 in the tens place of 686686 into 77, and the ones place becomes 1616.
  • Now subtract the ones place: 169=716 - 9 = 7.
  • Then subtract the tens place: 797 - 9. Again, we need to borrow.
  • Turn 66 in the hundreds place of 686686 into 55, and the tens place becomes 1717.
  • Subtract the tens: 179=817 - 9 = 8.
  • Finally, subtract the hundreds place: 54=15 - 4 = 1.

Therefore, the result of the subtraction 686499686 - 499 is 187187.

Answer

187

Exercise #12

amp;372amp;amp;185amp;776amp; \begin{aligned} &amp;372 \\ -&amp; \\ &amp;185 \\ &amp;\underline{\phantom{776}} &amp; \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Set up the numbers for vertical subtraction

  • Step 2: Perform subtraction starting from the rightmost column

  • Step 3: Apply regrouping (borrowing) if necessary

Let's work through each step:

Step 1: Set up the numbers as follows:
amp;3amp;7amp;2amp;1amp;8amp;5amp;amp; \begin{array}{c} &amp; 3 &amp; 7 &amp; 2 \\ - &amp; 1 &amp; 8 &amp; 5 \\ \hline &amp; &amp; \\ \end{array}

Step 2: Start with the units column: 252 - 5. Since 2 is less than 5, we need to regroup:

Step 3: Borrow 1 from the tens column, turning 7 into 6 and 2 into 12. Now subtract the units: 125=712 - 5 = 7.

Next, move to the tens column. After borrowing, we have 66 in the tens column, subtract 88 (from the subtrahend):

Since 686 - 8 is not possible without borrowing, we need to regroup.

Borrow 1 from the hundreds column, turning 33 into 22 and 66 into 1616. Now subtract the tens: 168=816 - 8 = 8.

Lastly, move to the hundreds column. After borrowing, it's 21=12 - 1 = 1. Place this value in the hundreds place.

The final subtraction setup and answer is:
amp;2amp;16amp;12amp;1amp;8amp;5amp;1amp;8amp;7 \begin{array}{c} &amp;2 &amp; 16 &amp; 12 \\ - &amp; 1 &amp; 8 &amp; 5 \\ \hline &amp;1 &amp; 8 &amp; 7 \\ \end{array}

Therefore, the solution to the problem is 187187.

Answer

187