Vertical Addition - Examples, Exercises and Solutions

Understanding Vertical Addition

Complete explanation with examples

Vertical Addition

How do we solve vertical addition?
1) Write the numbers vertically one under the other in an organized way.
2) Mark + on the left side and draw a line to separate between the exercise and the results line.
3) Add the ones digit of the first number together with the ones digit of the second number and so on.
If we obtain a two-digit number - write the ones in the result and carry the 11 to the next digit above.

Vertical addition example showing place value alignment of hundreds, tens, and ones with the sum of 397 and 425 equaling 822, emphasizing structured multi-digit addition.

Detailed explanation

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\( \begin{aligned} &81 \\ +& \\ &~~9 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

Examples with solutions for Vertical Addition

Step-by-step solutions included
Exercise #1

amp;81+amp;amp;  8amp;776amp; \begin{aligned} &81 \\ +& \\ &~~8 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

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+81 + 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 89 .

Answer:

89

Video Solution
Exercise #2

amp;90+amp;amp;  9amp;776amp; \begin{aligned} &90 \\ +& \\ &~~9\\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

To solve this addition problem, follow these steps:

  • Step 1: Align the numbers vertically. We have the numbers 9090 and 99.
  • Step 2: Write them down with equal alignment such that their units digits are aligned:

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

  • Step 3: Begin by adding the rightmost column (units column): 0+9=90 + 9 = 9. Write 99 in the units place below the line.
  • Step 4: Move to the left column (tens column). Add: 9+0=99 + 0 = 9.
  • Step 5: Write 99 in the tens place below the line.

This gives us the complete sum:

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

Therefore, the sum of 9090 and 99 is 99\textbf{99}.

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

Answer:

99

Video Solution
Exercise #3

amp;24+amp;amp;  4amp;776amp; \begin{aligned} &24 \\ +& \\ &~~4 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

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:
  • 24+  4 \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 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:

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

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

Answer:

28

Video Solution
Exercise #4

amp;72+amp;amp;  7amp;776amp; \begin{aligned} &72 \\ +& \\ &~~7 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

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:
  • 72+7 \begin{array}{r} 72 \\ + 7 \\ \hline \end{array}

  • Step 2: Add the units column. The units are 2 and 7.
  • Calculation: 2+7=92 + 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 7 + 0 = 7 . The result for the tens column remains 7.

  • Step 4: Combine both results:
  • Therefore, the sum is 7979.

Hence, the final answer is 7979. The correct choice is option 3.

Answer:

79

Video Solution
Exercise #5

amp;44+amp;amp;  4amp;776amp; \begin{aligned} &44 \\ +& \\ &~~4 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

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

  • Step 1: Align the numbers 4444 and 44 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 44 and 44 to get 88.
  • 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 44 from 4444 with the implied 00 from 44 (tens place) to get 44.
  • Step 4: Combine the results. The tens place gives 44 and the units place gives 88, forming the number 4848.

Now, let's work through each step:
Step 1: Vertical alignment:
44+04\begin{array}{c} 44 \\ + 04 \\ \hline \end{array}
Step 2: Units column 4+4=84 + 4 = 8 (no carry over).
Step 3: Tens column 4+0=44 + 0 = 4.
Step 4: Combining the tens and units results: the number is 4848.

Therefore, the sum of 4444 and 44 is 4848. The correct choice from the provided options is choice 33.

Answer:

48

Video Solution

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4 digits 5-digits Addition of 2-digit-and 1-digit numbers with the regrouping of both tens and ones Addition of 2-digit and 1-digit numbers with the regrouping of tens Addition of 2-digit and 2-digit numbers with the regrouping of tens Addition of 2-digit and 2-digit numbers with the regrouping of tens and ones Addition of 3-digit and 1-digit numbers with the regrouping of both tens and ones Addition of 3-digit and 1-digit numbers with the regrouping of tens Addition of 3-digit and 2-digit numbers with regrouping Addition of 3-digit and 2-digit numbers with regrouping beyond 1000 Addition of 3-digit and 2-digit numbers with regrouping beyond 1000 Addition of 3-digit and 2-digit numbers with regrouping within 1000 Addition of 3-digit and 2-digit numbers with some regrouping Addition of 3-digit and 2-digit numbers with some regrouping beyond 1000 Addition of 3-digit and 2-digit numbers with the regrouping of hundreds Addition of 3-digit and 2-digit numbers with the regrouping of tens Addition of 3-digit and 2-digit numbers with the regrouping of thousands Addition of 3-digit numbers with the regrouping of numbers in excess of ten Addition of 3-digit numbers with the regrouping of tens and hundreds Double digit addition beyond 100 Double digit addition within 100 Simple addition of 2-digit and 1-digit numbers Simple addition of 2-digit and 2-digit numbers Simple addition of 3-digit and 1-digit numbers Simple addition of 3-digit and 2-digit numbers Simple addition of 3-digit numbers