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

Exercise #1

amp;15+amp;amp;56amp;776amp; \begin{aligned} &15 \\ +& \\ &56 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we will perform vertical addition on the numbers 15 and 56.

Let's break down the steps:

  • Step 1: Write the numbers vertically aligning the digits.
    015+56776 \begin{array}{c} \phantom{0}15 \\ +56 \\ \underline{\phantom{776}} \end{array}
  • Step 2: Add the digits in the ones place. The ones digits are 5 and 6.
    5+6=11 5 + 6 = 11 .
    Write down 1 in the ones place and carry over 1 to the tens place.
  • Step 3: Add the digits in the tens place, including the carried over 1. The tens digits are 1 and 5.
    1+5+1=7 1 + 5 + 1 = 7 .
    Write down 7 in the tens place.

The complete addition is:

015+5671 \begin{array}{c} \phantom{0}15 \\ +56 \\ \underline{71} \end{array}

Thus, the solution to the problem is 71 \boxed{71} .

Answer

71

Exercise #2

amp;23+amp;amp;59amp;776amp; \begin{aligned} &23 \\ +& \\ &59 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we'll use vertical addition and work through each step:

Consider the numbers:

23+59776 \begin{aligned} &23 \\ +& \\ &59 \\ &\underline{\phantom{776}} \end{aligned}


Step 1: Align the numbers by their place values.
Step 2: Add the units place: 3+9=123 + 9 = 12. Here, 1212 has two digits. We place 22 in the units column and carry over 11 to the tens column.
Step 3: Add the tens place along with the carry: 2+5+1=82 + 5 + 1 = 8. Place 88 in the tens column.

The final sum will be as follows:

23+5977682 \begin{aligned} &23 \\ +& \\ &59 \\ &\underline{\phantom{776}} \\ &82 \end{aligned}

Through these steps, we find that the sum of the numbers 2323 and 5959 is 8282.

Therefore, the solution to the problem is 8282.

Answer

82

Exercise #3

amp;37+amp;amp;46amp;776amp; \begin{aligned} &37 \\ +& \\ &46 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To accurately sum the numbers 37 and 46 using vertical addition, follow these steps:

Step 1: Add the Units Column
Start by adding the digits in the units place: 7+6=13 7 + 6 = 13 . Since 13 is greater than 9, we write down the 3 in the units place of the result and carry over 1 to the tens column.

Step 2: Add the Tens Column
Next, add the digits in the tens column, along with any carried over value. Here we have 3+4=7 3 + 4 = 7 , plus the carry over of 1, giving 7+1=87 + 1 = 8.

Final Result:
Combine the tens and units results. The sum is 8383.

Therefore, the solution to the problem is 83 \boxed{83} .

Answer

83

Exercise #4

amp;47+amp;amp;25amp;776amp; \begin{aligned} &47 \\ +& \\ &25 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this vertical addition problem, we follow these steps:

  • Step 1: Write the numbers one below the other, aligning columns by place value.
  • Step 2: Begin with the ones column. Add 77 (from 4747) to 55 (from 2525).
  • Step 3: Calculate the sum in the ones column: 7+5=127 + 5 = 12.
  • Step 4: Since 1212 is greater than 99, we write 22 in the ones place and carry over 11 to the tens column.
  • Step 5: Add the tens column: 44 from 4747, 22 from 2525, and the carried over 11.
  • Step 6: Calculate the tens sum: 4+2+1=74 + 2 + 1 = 7.

Therefore, the final sum is 7272.

By checking the provided choices, the correct choice is: 7272.

Answer

72

Exercise #5

amp;52+amp;amp;39amp;776amp; \begin{aligned} &52 \\ +& \\ &39 \\ &\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 52 and 39 for vertical addition.
  • Step 2: Add the ones place digits: 2 + 9.
  • Step 3: Handle any carry if needed and proceed to the tens place: 5 + 3.

Let's work through each step:

Step 1: Write the numbers in vertical alignment:

52+39 \begin{array}{c} 52 \\ +39 \\\hline \end{array}

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

2+9=11 2 + 9 = 11 . Since this is more than 9, write 1 in the ones place and carry over 1 to the tens place.

Step 3: Add the digits in the tens place:

Including the carried over 1 from the ones addition, add 5+3+1=9 5 + 3 + 1 = 9 .

Write 9 in the tens place.

Therefore, the sum of 52+39 52 + 39 is 91 91 .

Thus, the correct solution to the problem is 91.

Answer

91

Exercise #6

amp;65+amp;amp;18amp;776amp; \begin{aligned} &65 \\ +& \\ &18 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

Let's solve the problem of adding two numbers, 65 and 18, step-by-step using vertical addition:

  • Step 1: Write the numbers vertically, aligning the tens and ones digits as follows:

+65+1876 \begin{array}{c} \phantom{+}65 \\ +18 \\ \underline{\phantom{76}} \\ \end{array}

  • Step 2: Add the digits in the ones column. These digits are 5 and 8.

5+8=13 5 + 8 = 13

  • Since the sum is 13, we place the 3 in the ones column and carry over the 1 to the tens column.
  • Step 3: Move to the tens column. Add the digits in this column: 6 (from 65) and 1 (from 18), plus the 1 we carried over from the ones column.

6+1+1=8 6 + 1 + 1 = 8

  • Step 4: Write 8 in the tens place.

+65+187683 \begin{array}{c} \phantom{+}65 \\ +18 \\ \underline{\phantom{76}} \\ 83 \\ \end{array}

Therefore, the sum of 65 and 18 is 83\mathbf{83}.

Answer

83

Exercise #7

amp;73+amp;amp;18amp;776amp; \begin{aligned} &73\\ +& \\ &18 \\ &\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 by place value, ensuring the units and tens are in the correct columns.
  • Step 2: Add the digits in the units column (3 and 8).
  • Step 3: Address any carryover from the units addition, which affects the tens column calculation.
  • Step 4: Add the digits in the tens column (7 and 1), including any carry.

Now, let's work through each step:

Step 1: The problem provides the vertical alignment:
73+18\begin{array}{c} 73 \\ +18 \\ \end{array}
We confirm that the units and tens digits are properly aligned.

Step 2: Add the units digits (3 and 8):
3+8=113 + 8 = 11
Place the 1 in the units position and carry over 1 to the tens position.

Step 3: Add the tens digits along with the carryover:
7+1+1=97 + 1 + 1 = 9
Write the 9 in the tens position for the sum.

The resulting sum of the numbers vertically added is:
91\begin{array}{cc} & 91 \\ \end{array}
Therefore, the solution to the problem is 91 91 .

Answer

91