Examples with solutions for Vertical Addition: Addition of 3-digit and 2-digit numbers with regrouping beyond 1000

Exercise #1

amp;569+amp;amp;437amp;776amp; \begin{aligned} &569 \\ +& \\ &437 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we will perform vertical addition as follows:

  • First, align the numbers:
            569
    +      437
           ----

  • Add the units' digit (rightmost column):
       9 (from 569) + 7 (from 437) = 16
    Write the 6 in the units place of the result and carry over the 1.

  • Add the tens' digit:
       6 (from 569) + 3 (from 437) + 1 (carry) = 10
    Write the 0 and carry over the 1.

  • Add the hundreds' digit:
       5 (from 569) + 4 (from 437) + 1 (carry) = 10
    Write the entire number since this is the leftmost position.

Hence, the final sum is:
       1006

Therefore, the solution to the problem is 1006 1006 .

Answer

1006

Exercise #2

amp;743+amp;amp;259amp;776amp; \begin{aligned} &743 \\ +& \\ &259 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we'll engage in vertical addition for the given numbers 743743 and 259259:

  • Step 1: Align the numbers by their place value (units, tens, and hundreds).
  • Step 2: Add each column starting from the right, taking care to carry over if needed.

Let's perform the addition:
Starting from the rightmost column (units):

  • Add 33 (from 743743) and 99 (from 259259): 3+9=123 + 9 = 12.
    Place 22 in the units place and carry over 11 to the tens column.
  • Move to the tens column:
    Add 44 (from 743743), 55 (from 259259), and the carryover 11: 4+5+1=104 + 5 + 1 = 10.
    Place 00 in the tens place and carry over 11 to the hundreds column.
  • Finally, add the hundreds column:
    Add 77 (from 743743), 22 (from 259259), and the carryover 11: 7+2+1=107 + 2 + 1 = 10.
    Place 00 in the hundreds place and 11 in the thousands place.

The final result of adding 743+259743 + 259 is 10021002.

Comparing this with the answer choices, the correct choice is (1): 10021002.

Therefore, the solution to the problem is 10021002.

Answer

1002

Exercise #3

amp;689+amp;amp;317amp;776amp; \begin{aligned} &689 \\ +& \\ &317 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we will perform vertical addition starting from the rightmost digit:

  • Step 1: Add the units digits.
    9+7=169 + 7 = 16. Write down 66 and carry over 11 to the tens place.
  • Step 2: Add the tens digits.
    8+1=98 + 1 = 9, now add the carry 11, so 9+1=109 + 1 = 10. Write down 00 and carry over 11 to the hundreds place.
  • Step 3: Add the hundreds digits.
    6+3=96 + 3 = 9, now add the carry 11, so 9+1=109 + 1 = 10. Write down 00 in the hundreds place and write down 11 in the thousands place (since it's the final column, the carry becomes a leading digit).

Therefore, the sum of 689689 and 317317 is 1006\mathbf{1006}.

Answer

1006

Exercise #4

amp;548+amp;amp;459amp;776amp; \begin{aligned} &548 \\ +& \\ &459 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Add the units digits of both numbers.
  • Step 2: Handle any regrouping if necessary and add the tens digits.
  • Step 3: Handle any regrouping if necessary and add the hundreds digits.

Now, let's work through each step:

Step 1: Add the units digits of both numbers:
8+9=17 8 + 9 = 17 . Here, 7 is placed in the units place, and 1 is carried over to the tens column.

Step 2: Add the tens digits along with the carry-over:
4+5+1=10 4 + 5 + 1 = 10 . Here, 0 is placed in the tens place, and 1 is carried over to the hundreds column.

Step 3: Add the hundreds digits along with the carry-over:
5+4+1=10 5 + 4 + 1 = 10 . Here, 0 is placed in the hundreds place, and 1 is carried over to the thousands column.

The final sum is 10071007, where 1 is now the digit in the thousands place.

Therefore, the solution to the problem is 1007 1007 .

Answer

1007

Exercise #5

amp;826+amp;amp;178amp;776amp; \begin{aligned} &826 \\ +& \\ &178 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem of adding 826826 and 178178 using vertical addition, we proceed as follows:

  • First, we align the numbers vertically, ensuring that digits are in their respective places:

amp;8amp;2amp;6+amp;1amp;7amp;8 \begin{array}{c} & 8 & 2 & 6 \\ + & 1 & 7 & 8 \\ \hline \end{array}

  • Step 1: Add the units (rightmost) column: 6+8=146 + 8 = 14. Place the 44 in the units column of the result and carry over the 11 to the tens column.

  • Step 2: Add the tens column: 2+7=92 + 7 = 9 and add the carried over 11: 9+1=109 + 1 = 10. Place 00 in the tens column of the result and carry over the 11 to the hundreds column.

  • Step 3: Add the hundreds column: 8+1=98 + 1 = 9 and add the carried over 11: 9+1=109 + 1 = 10. Write down the entire sum, 1010, in the hundreds and beyond place.

The resulting sum is 10041004.

Thus, the solution to the problem is 10041004.

Answer

1004