Vertical Addition - Examples, Exercises and Solutions

To solve this problem, we will follow these steps:

• Step 1: Align the numbers vertically by place value. We have:
  $\begin{array}{c} 12 \\ + \\ \phantom{0}2 \\ \hline \end{array}$

• Step 2: Start from the rightmost digits in the units column. Add $2$ (from the bottom number) to $2$ (from the top number).
  $\phantom{x}2 + 2 = 4$

• Step 3: Now, move to the next column. We have $1$ in the tens column only from the top number, so it's $1 + 0 = 1$.

• Step 4: Combine the sums from each column starting from the left to form the final answer: $14$.

Therefore, the solution to the problem is $14$, which corresponds to choice 4.

To solve this problem, we'll add the numbers 24 and 4 using vertical addition:

• Step 1: Align the numbers vertically with the units and tens digits properly aligned:
$\begin{aligned} &24 \\ +& \\ &~~4 \\ \end{aligned}$

• Step 2: Add from the rightmost column (units position):
  The units digits are 4 and 4. Their sum is $4 + 4 = 8$.
• Step 3: Move to the next column (tens position):
  In this case, the tens digit of the first number is 2, and there is no tens digit in the number 4. Since there is no carry, we simply bring down the 2.

The sum of the numbers is 28, which is represented as:

$\begin{aligned} &28 \end{aligned}$

Therefore, the correct answer is 28, which corresponds to choice .

To solve this problem, we will follow these steps:

• Step 1: Align the numbers vertically with the units digits under each other: $31$ and $6$.
• Step 2: Add the units digits: $1 + 6 = 7$. There is no carryover in this simple addition.
• Step 3: The tens digit from the number 31, which is $3$, remains unchanged as there is no carry that affects this place value.
• Step 4: Write down the result of the addition, which is $37$.

Therefore, the sum of $31$ and $6$ is $37$.

The correct answer is choice 1: $37$.

To solve this problem, we'll perform vertical addition of the numbers 40 and 3:

• Step 1: Write the numbers vertically, aligning by place value:
  $\begin{array}{c} 40 \\ + 3 \\ \hline \end{array}$
• Step 2: Start adding from the rightmost column (units place).
  Units column: 0 + 3 = 3, write this number directly below the line.
  $\begin{array}{c} 40 \\ + 3 \\ \hline 43 \\ \end{array}$
• Step 3: Move to the next column (tens place):
  In the tens place: 4 + 0 = 4, write this number below the line in the tens place.

As a final result, the sum of 40 and 3 is 43.

Therefore, the solution to the problem is $43$, which matches choice number 4 in the provided options.

To solve this problem, we will use vertical addition:

• Step 1: Write down the numbers as they are presented, ensuring digits are aligned:
• $\begin{array}{c} 57\\ + 2 \\ \hline \\ \end{array}$
• Step 2: Add the units column first, which contains 7 and 2:

$7 + 2 = 9$

• Step 3: Since there is no other digit in the tens column from the number 2, bring down the 5 as it is.
• Thus, the tens column remains the same: $5$.
• Step 4: Write down the final answer below the line:
• $\begin{array}{c} 57\\ + 2 \\ \hline 59 \\ \end{array}$

Therefore, the sum of 57 and 2 is $59$, which corresponds to the correct choice 1.

To solve this problem, we'll perform vertical addition of the numbers 65 and 4:

• Step 1: Align the numbers vertically with the digits correctly placed (units under units, tens under tens).
• Step 2: Start with the rightmost digits (the units place). Add the units: $5 + 4 = 9$.
• Step 3: No carrying is necessary as the sum is less than 10.
• Step 4: Move to the tens place. Since we're adding a single-digit number, only the left number (6 in the tens place) remains as it is.

Combining these, the result of $65 + 4$ is $69$.

Thus, the correct answer is $69$.

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

• Step 1: Align the numbers such that the units are directly under each other:

$\begin{array}{r} 72 \\ + 7 \\ \hline \end{array}$

• Step 2: Add the units column. The units are 2 and 7.

Calculation: $2 + 7 = 9$. The result for the units column is 9.

• Step 3: Add the tens column. The tens are 7 with no carry from the previous step.

Calculation: $7 + 0 = 7$. The result for the tens column remains 7.

• Step 4: Combine both results:

Therefore, the sum is $79$.

Hence, the final answer is $79$. The correct choice is option 3.

To solve the given vertical addition problem, follow these steps:

• Step 1: Align the numbers by place value: 81 has a tens digit (8) and a ones digit (1). The number 8 is placed under the ones digit.
• Step 2: Start with the ones column: Add the digits $1 + 8$. The sum of 1 and 8 is 9.
• Step 3: Since the sum in the ones column is less than 10, there is no need to carry over a number to the tens column.
• Step 4: Move to the tens column: There is no additional number under the 8, so it remains as 8.
• Step 5: Combine these results to get the final sum: The tens digit is 8 and the ones digit is 9, resulting in the number 89.

Therefore, the solution to the problem is $89$.

To solve this addition problem, follow these steps:

• Step 1: Align the numbers vertically. We have the numbers $90$ and $9$.
• Step 2: Write them down with equal alignment such that their units digits are aligned:

$\begin{aligned} &90 \\ + &~9\\ \end{aligned}$

• Step 3: Begin by adding the rightmost column (units column): $0 + 9 = 9$. Write $9$ in the units place below the line.
• Step 4: Move to the left column (tens column). Add: $9 + 0 = 9$.
• Step 5: Write $9$ in the tens place below the line.

This gives us the complete sum:

$\begin{aligned} &90 \\ + &9 \\ \underline{~~~~} \\ &99 \\ \end{aligned}$

Therefore, the sum of $90$ and $9$ is $\textbf{99}$.

Referring to the multiple-choice answers provided, the correct choice is \textbf{choice 4: 99}.

We will perform vertical addition to find the sum of $92$ and $5$.

• Step 1: Align the numbers by place value:

$\begin{array}{c} 92 \\ +\,\,\,5 \\ \underline{\phantom{776}} \end{array}$

• Step 2: Add the rightmost column (units):

$2 + 5 = 7$. Write down $7$ under the units column.

• Step 3: Add the leftmost column (tens):

The tens digit of $92$ is $9$. As there are no tens in $5$, simply bring down $9$.

• Step 4: Combine:

Thus, writing the results from both columns, we have $97$.

Therefore, the sum of $92$ and $5$ is $97$.

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

• Step 1: Align the numbers $44$ and $4$ such that digits of the same place value (units) are below one another.
• Step 2: Add the digits in the units column. This means summing $4$ and $4$ to get $8$.
• Step 3: Check for carry over, if any, and add digits in the next column (tens column). In this case, there's no carry over needed, so just add the digit $4$ from $44$ with the implied $0$ from $4$ (tens place) to get $4$.
• Step 4: Combine the results. The tens place gives $4$ and the units place gives $8$, forming the number $48$.

Now, let's work through each step:
Step 1: Vertical alignment:
$\begin{array}{c} 44 \\ + 04 \\ \hline \end{array}$
Step 2: Units column $4 + 4 = 8$ (no carry over).
Step 3: Tens column $4 + 0 = 4$.
Step 4: Combining the tens and units results: the number is $48$.

Therefore, the sum of $44$ and $4$ is $48$. The correct choice from the provided options is choice $3$.

To solve this problem, we need to perform vertical addition of the numbers $83$ and $6$.

Let's work through the problem step-by-step:

• Write the numbers vertically, aligning them by place value:
       83
  +      6
  

  ---

• First, add the digits in the ones place:
      3 (from 83) + 6 = 9
• Next, add the digits in the tens place (given no carry was needed):
      8 (from 83) + 0 (implicit from 6) = 8
• Combine the results of those sums, which gives us the final result as:

$89$.

Therefore, the solution to the problem is $89$, which corresponds to the choice: :

89

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

• Step 1: Align the numbers $74$ and $6$ 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:
$\begin{aligned} &74 \\ +& \\ &~6 \\ \hline \\ &~~ \\ \end{aligned}$

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

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:
$7 + 1 = 8$.

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

Therefore, the solution to the problem is $80$.

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.
  $\begin{aligned} &12 \\ +& \\ &~~8 \\ \hline &~~? \\ \end{aligned}$
• Step 2: Start adding from the rightmost column (units position).
  Add the units: $2 + 8 = 10$.
  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: $1 + 1 = 2$ (including the carryover 1).
  Write down the result in the tens column.
• Step 4: Combine these results to find the final sum:
  $\begin{aligned} &12 \\ +& \\ &~~8 \\ \hline &20 \\ \end{aligned}$

Therefore, the solution to the problem is $20$.

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: $5 + 5 = 10$. Since $10$ is greater than $9$, we write down $0$ in the ones place and carry over $1$ 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: $4 + 1 = 5$.
Step 3: Therefore, after adding, the complete sum is $50$.

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