Vertical Addition Practice Problems - Step by Step Solutions

Master vertical addition with guided practice problems. Learn column addition, carrying digits, and multi-digit number alignment with detailed step-by-step solutions.

📚Master Vertical Addition with Interactive Practice
  • Align multi-digit numbers correctly using place value columns
  • Practice carrying digits when sums exceed 9 in any column
  • Solve complex addition problems like 4356 + 213 step-by-step
  • Master the vertical format with proper + signs and result lines
  • Build confidence with hundreds, tens, and ones digit addition
  • Apply vertical addition rules to real-world math scenarios

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 digits together, then move to the tens digits, then the hundreds digits, and so on.
If we obtain a two-digit number - write the ones digit in the result and carry the 11 above the next digit.

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

Practice Vertical Addition

Test your knowledge with 38 quizzes

\( \begin{aligned} &23 \\ + \\ &~~7 \\ & \underline{\phantom{776}} \end{aligned} \)

Examples with solutions for Vertical Addition

Step-by-step solutions included
Exercise #1

90+  9776‾ \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 #2

12+  2776‾ \begin{aligned} &12 \\ +& \\ &~~2 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Align the numbers vertically by place value. We have:
    12+02 \begin{array}{c} 12 \\ + \\ \phantom{0}2 \\ \hline \end{array}

  • Step 2: Start from the rightmost digits in the units column. Add 22 (from the bottom number) to 22 (from the top number).
    x2+2=4\phantom{x}2 + 2 = 4

  • Step 3: Now, move to the next column. We have 11 in the tens column only from the top number, so it's 1+0=11 + 0 = 1.

  • Step 4: Combine the sums from each column starting from the left to form the final answer: 1414.

Therefore, the solution to the problem is 1414, which corresponds to choice 4.

Answer:

14

Video Solution
Exercise #3

31+  6776‾ \begin{aligned} &31 \\ +& \\ &~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Align the numbers vertically with the units digits under each other: 3131 and 66.
  • Step 2: Add the units digits: 1+6=71 + 6 = 7. There is no carryover in this simple addition.
  • Step 3: The tens digit from the number 31, which is 33, remains unchanged as there is no carry that affects this place value.
  • Step 4: Write down the result of the addition, which is 3737.

Therefore, the sum of 3131 and 66 is 3737.

The correct answer is choice 1: 3737.

Answer:

37

Video Solution
Exercise #4

40+  3776‾ \begin{aligned} &40 \\ +& \\ &~~3 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Step-by-Step Solution

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:
    40+3 \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.
    40+343 \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 43 , which matches choice number 4 in the provided options.

Answer:

43

Video Solution
Exercise #5

44+  4776‾ \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

Frequently Asked Questions

What is vertical addition and why is it important?

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Vertical addition is a method of adding numbers by writing them in columns with digits aligned by place value (ones under ones, tens under tens, etc.). It's essential for solving complex multi-digit addition problems that would be difficult to calculate mentally, such as 4356 + 213 or 2734 + 9763.

How do you align numbers properly in vertical addition?

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To align numbers correctly: 1) Write the ones digit under the ones digit, 2) Place tens under tens, hundreds under hundreds, and so on, 3) Add the + sign on the left side, 4) Draw a horizontal line below the numbers to separate the problem from the answer area.

What does carrying mean in vertical addition?

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Carrying occurs when adding digits in a column results in a two-digit number (like 7 + 7 = 14). You write the ones digit (4) in the result and carry the tens digit (1) to the top of the next column to the left, where it gets added with the other digits in that column.

What order should I follow when solving vertical addition problems?

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Always solve vertical addition from right to left: 1) Start with the ones column, 2) Move to the tens column, 3) Continue to hundreds, then thousands, 4) Remember to add any carried digits from the previous column, 5) Only write two-digit results when there are no more columns to carry to.

How do I handle carrying in the final column of vertical addition?

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When you reach the leftmost column and get a two-digit sum, you can write the entire two-digit number in the result since there's no next column to carry to. For example, if adding thousands digits gives you 12, write both digits (12) in the final answer.

What are common mistakes students make in vertical addition?

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Common mistakes include: • Misaligning digits (not matching place values), • Forgetting to carry digits when sums exceed 9, • Adding carried digits incorrectly, • Writing two-digit sums in single columns instead of carrying, • Starting from the left instead of the right side.

Can vertical addition be used for any size numbers?

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Yes, vertical addition works for any size numbers, from simple two-digit problems to complex multi-digit calculations. The method remains the same regardless of whether you're adding hundreds, thousands, or even larger numbers - just ensure proper place value alignment.

How can I check if my vertical addition answer is correct?

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You can verify your answer by: 1) Adding the numbers in reverse order, 2) Using estimation to see if your answer is reasonable, 3) Adding horizontally if the numbers are small enough, 4) Double-checking that you carried all digits correctly and aligned place values properly.

More Vertical Addition Questions

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Practice by Question Type

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