Examples with solutions for Vertical Addition: Addition of 2-digit and 1-digit numbers with the regrouping of tens

Exercise #1

amp;74+amp;amp;  6amp;776amp; \begin{aligned} &74 \\ +& \\ &~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Align the numbers 7474 and 66 vertically.
  • Step 2: Begin by adding the digits in the ones place.
  • Step 3: Move to the tens place and include any carryover.

Let's work through each step:


Step 1: Write the numbers vertically, aligning by place value:
amp;74+amp;amp; 6amp;   \begin{aligned} &74 \\ +& \\ &~6 \\ \hline \\ &~~ \\ \end{aligned}

Step 2: Add the ones place. The digit in the ones place of 74 is 4, and for 6 is 6. Add them together:
4+6=104 + 6 = 10.

Since the result is 10, write down 0 in the ones place and carry over 1 to the tens place.

Step 3: Now, move to the tens place. Add the tens digit from 74, which is 7, and add the 1 carried over from the previous step:
7+1=87 + 1 = 8.

This results in:
amp;74+amp;amp; 6amp;80 \begin{aligned} &74 \\ +& \\ &~6 \\ \hline \\ &80 \\ \end{aligned}

Therefore, the solution to the problem is 8080.

Answer

80

Exercise #2

amp;12+amp;amp;  8amp;776amp; \begin{aligned} &12 \\ +& \\ &~~8 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To approach this problem, we'll use vertical addition of the numbers 12 and 8:

  • Step 1: Write the numbers vertically, aligning their place values.
    12+  8  ?\begin{aligned} &12 \\ +& \\ &~~8 \\ \hline &~~? \\ \end{aligned}
  • Step 2: Start adding from the rightmost column (units position).
    Add the units: 2+8=102 + 8 = 10.
    Write down the 0 in the units column and carry over the 1 to the tens column.
  • Step 3: Move to the next column on the left (tens position).
    Add the tens: 1+1=21 + 1 = 2 (including the carryover 1).
    Write down the result in the tens column.
  • Step 4: Combine these results to find the final sum:
    12+  820\begin{aligned} &12 \\ +& \\ &~~8 \\ \hline &20 \\ \end{aligned}

Therefore, the solution to the problem is 2020.

Answer

20

Exercise #3

amp;45+amp;amp;  5amp;776amp; \begin{aligned} &45 \\ +& \\ &~~5 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Add the ones place digits.
  • Step 2: If needed, adjust by carrying over any excess to the tens place.
  • Step 3: Add the tens place digits.

Now, let's work through each step:
Step 1: We start by adding the digits in the ones place: 5+5=105 + 5 = 10. Since 1010 is greater than 99, we write down 00 in the ones place and carry over 11 to the tens place.
Step 2: Then, add the tens place digits. The tens digit of 45 is 4, and we add the carried over 1: 4+1=54 + 1 = 5.
Step 3: Therefore, after adding, the complete sum is 5050.

Thus, the solution to the problem is 50 50 , which corresponds to choice 4.

Answer

50

Exercise #4

amp;23+amp;amp;  7amp;776amp; \begin{aligned} &23 \\ +& \\ &~~7 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Write the numbers in a column, aligning them by the right:

  • 23+7 \begin{array}{c} 23 \\ + 7 \\ \hline \end{array}

  • Step 2: Add the digits in the rightmost column (ones place):

  • The digits are 3 and 7. So, 3+7=103 + 7 = 10. Write 0 in the ones place and carry over 1 to the tens place.

    23+7   0 \begin{array}{c} 23 \\ + 7 \\ \hline ~~~ 0 \end{array}

  • Step 3: Add the digits in the tens place:

  • The digits are 2 and, due to the carry, 1. So, 2+1=32 + 1 = 3. Write 3 in the tens place.

    1  23+7 30 \begin{array}{c} 1~~ \\ 23 \\ + 7~ \\ \hline 30 \end{array}

Therefore, the sum of 23 and 7 is 3030.

Answer

30

Exercise #5

amp;81+amp;amp;  9amp;776amp; \begin{aligned} &81 \\ +& \\ &~~9 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

The problem is to perform vertical addition for the numbers 8181 and 99. Here’s the step-by-step approach:

  • Step 1: Align the numbers vertically by their rightmost digits. The digit 11 from 8181 is aligned with 99.
  • Step 2: Add the digits in the units place: 1+9=101 + 9 = 10. Here, 1010 is a two-digit result, where 00 remains in the units place and 11 is carried to the tens place.
  • Step 3: Add the digits in the tens place, including the carried digit: 8+1=98 + 1 = 9. This accounts for the 11 we carried over from the units place addition.

Since no further carrying is necessary, the result of adding 8181 and 99 is 9090.

Therefore, the solution to the problem is 9090, which corresponds to choice 2.

Answer

90

Exercise #6

amp;67+amp;amp;  3amp;776amp; \begin{aligned} &67 \\ +& \\ &~~3 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Align the numbers vertically according to their place values:
    67+  3776 \begin{aligned} &67 \\ +& \\ &~~3 \\ &\underline{\phantom{776}} \end{aligned}
  • Step 2: Begin adding from the rightmost column (units).
  • Step 3: Add the digits in the units place: 7+3=10 7 + 3 = 10 .
  • Step 4: Since the result is 10, write down the 0 under the units column and carry over the 1 to the tens column.
  • Step 5: Next, add the digits in the tens column: 6+1=7 6 + 1 = 7 .
  • Step 6: Combine the results from the tens and units columns to form the final sum.

Therefore, the solution to the problem is 70 70 .

Answer

70