Examples with solutions for Vertical Addition: Simple addition of 2-digit and 1-digit numbers

Exercise #1

amp;12+amp;amp;  2amp;776amp; \begin{aligned} &12 \\ +& \\ &~~2 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

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

Exercise #2

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

Video Solution

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

Exercise #3

amp;31+amp;amp;  6amp;776amp; \begin{aligned} &31 \\ +& \\ &~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

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

Exercise #4

amp;40+amp;amp;  3amp;776amp; \begin{aligned} &40 \\ +& \\ &~~3 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

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

Exercise #5

amp;57+amp;amp;  2amp;776amp; \begin{aligned} &57\\ +& \\ &~~2 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we will use vertical addition:

  • Step 1: Write down the numbers as they are presented, ensuring digits are aligned:
  • 57+2\begin{array}{c} 57\\ + 2 \\ \hline \\ \end{array}
  • Step 2: Add the units column first, which contains 7 and 2:
  • 7+2=97 + 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: 55.
  • Step 4: Write down the final answer below the line:
  • 57+259\begin{array}{c} 57\\ + 2 \\ \hline 59 \\ \end{array}

Therefore, the sum of 57 and 2 is 5959, which corresponds to the correct choice 1.

Answer

59

Exercise #6

amp;65+amp;amp;  4amp;776amp; \begin{aligned} &65 \\ +& \\ &~~4 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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=95 + 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+465 + 4 is 6969.

Thus, the correct answer is 6969.

Answer

69

Exercise #7

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

Video Solution

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

Exercise #8

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

Video Solution

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

Exercise #9

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

Video Solution

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

Exercise #10

amp;92+amp;amp;  5amp;776amp; \begin{aligned} &92 \\ +& \\ &~~5\\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

We will perform vertical addition to find the sum of 9292 and 55.

  • Step 1: Align the numbers by place value:

92+5776\begin{array}{c} 92 \\ +\,\,\,5 \\ \underline{\phantom{776}} \end{array}

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

2+5=72 + 5 = 7. Write down 77 under the units column.

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

The tens digit of 9292 is 99. As there are no tens in 55, simply bring down 99.

  • Step 4: Combine:

Thus, writing the results from both columns, we have 9797.

Therefore, the sum of 9292 and 55 is 9797.

Answer

97

Exercise #11

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

Exercise #12

amp;83+amp;amp;  6amp;776amp; \begin{aligned} &83 \\ +& \\ &~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we need to perform vertical addition of the numbers 8383 and 66.

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 89 .

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

89

.

Answer

89