Examples with solutions for Vertical Addition: 5-digits

Exercise #1

amp;10256+amp;amp;17435amp;776amp; \begin{aligned} &10256\\ +& \\ &17435 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Start by adding the numbers column by column from right to left.
  • Step 2: Handle any carries appropriately as you move from one column to the next.
  • Step 3: Verify the result by comparing it to the provided answer choices.

Now, let's perform the addition step by step:

Step 1: Add the units column:
6 (from 10,256) + 5 (from 17,435) = 11
Write down 1 and carry over 1 to the tens column.

Step 2: Add the tens column:
5 + 3 = 8, plus the carry over 1, totals 9.
Write down 9.

Step 3: Add the hundreds column:
2 + 4 = 6.
Write down 6.

Step 4: Add the thousands column:
0 + 7 = 7.
Write down 7.

Step 5: Add the ten-thousands column:
1 + 1 = 2.
Write down 2.

Therefore, the sum of 10,256 and 17,435 is 27,691 27,691 .

Answer

27691

Exercise #2

amp;24789+amp;amp;35140amp;776amp; \begin{aligned} &24789\\ +& \\ &35140 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we will perform vertical addition of the given numbers:

24789+35140776 \begin{aligned} &24789\\ +& \\ &35140 \\ &\underline{\phantom{776}}\\ \end{aligned}

We add column by column starting from the rightmost digit (units):

  • Units: 9+0=99 + 0 = 9. Write 9 below the line.
  • Tens: 8+4=128 + 4 = 12. Write 2 below the line and carry over 1 to the next column.
  • Hundreds: 7+1+1(carry)=97 + 1 + 1 (\text{carry}) = 9. Write 9 below the line.
  • Thousands: 4+5=94 + 5 = 9. Write 9 below the line.
  • Ten-thousands: 2+3=52 + 3 = 5. Write 5 below the line.

Putting it all together, the sum is 5992959929.

Therefore, the solution to the problem is 5992959929.

Answer

59929

Exercise #3

amp;35612+amp;amp;44675amp;776amp; \begin{aligned} &35612\\ +& \\ &44675 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we'll use vertical addition, carefully ensuring each digit is correctly placed and carried over if necessary:

  • Write the numbers on top of each other as such:
         35612
    +
         44675

Begin with the rightmost column (ones place):

  • Column 1 (Units): 2+5=72 + 5 = 7. Place 7 below the line.
  • Column 2 (Tens): 1+7=81 + 7 = 8. Place 8 below the line.
  • Column 3 (Hundreds): 6+6=126 + 6 = 12. The sum is greater than 9, so place 2 below the line and carry over 1 to the next column.
  • Column 4 (Thousands): 5+4=95 + 4 = 9, then add the carryover 1 to get 10. Place 0 below the line and carry over 1.
  • Column 5 (Ten-Thousands): 3+4=73 + 4 = 7, then add the carryover 1 to get 8. Place 8 below the line.

The complete addition step-by-step is as follows:

     35612
+
     44675
    _____
     80287

Therefore, the sum of 3561235612 and 4467544675 is 8028780287.

Comparing with the choices given, our result matches choice 2.

Thus, the solution to the problem is 8028780287.

Answer

80287

Exercise #4

amp;46891+amp;amp;27108amp;776amp; \begin{aligned} &46891\\ +& \\ &27108 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this addition problem, follow these steps:

We'll first perform vertical addition with the given numbers:

  • 46891
  • +27108

Align the numbers vertically, ensuring each digit lines up with the same place value:

46891+27108
  \begin{array}{c}
    & 4 & 6 & 8 & 9 & 1 \\
  + & 2 & 7 & 1 & 0 & 8 \\
  \hline
\end{array}

Now, we add each column from right to left:
1. Units place: 1+8=91 + 8 = 9. Write 9.
2. Tens place: 9+0=99 + 0 = 9. Write 9.
3. Hundreds place: 8+1=98 + 1 = 9. Write 9.
4. Thousands place: 6+7=136 + 7 = 13. Write 3 and carry over 1 to the ten-thousands place.
5. Ten-thousands place: 4+2+1 (carry over)=74 + 2 + 1 \text{ (carry over)} = 7. Write 7.

The result is formed as:

73999
  \begin{array}{c}
    & 7 & 3 & 9 & 9 & 9 \\
\end{array}

\)

Thus, the solution to the problem is 73999 73999 .

Answer

73999

Exercise #5

amp;66543+amp;amp;52456amp;776amp; \begin{aligned} &66543\\ +& \\ &52456 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

Let's solve the problem step-by-step:

Step 1: Align the numbers for vertical addition as follows:

\begin{array}{c@{}c@{}c@{}c@{}c@{}c} & 6 & 6 & 5 & 4 & 3 \\ + & 5 & 2 & 4 & 5 & 6 \\ \hline \end{array}

Step 2: Perform the addition from the rightmost digit (units place):

  • Units place: 3+6=93 + 6 = 9
  • Tens place: 4+5=94 + 5 = 9
  • Hundreds place: 5+4=95 + 4 = 9
  • Thousands place: 6+2=86 + 2 = 8
  • Ten-thousands place: 6+5=116 + 5 = 11
  • Write 1 in the ten-thousands place and carry over 1 to the next column.
  • Since there are no more columns left to add the carry over, the final digit in the ten-thousands place is 11.

The final result is:

\begin{array}{c@{}c@{}c@{}c@{}c@{}c} & 1 & 1 & 8 & 9 & 9 & 9 \\ \end{array}

Therefore, the sum of 66543 and 52456 is 118999118999.

Answer

118999

Exercise #6

amp;72354+amp;amp;29563amp;776amp; \begin{aligned} &72354\\ +& \\ &29563 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we will add the two numbers using vertical addition:

  • Step 1: Write the numbers vertically, aligning them by their place values:
    \begin{array}{c@{}c@{}c@{}c@{}c@{}c} & 7 & 2 & 3 & 5 & 4 \\ + & & 2 & 9 & 5 & 6 & 3 \\ \hline \end{array}
  • Step 2: Add the digits in each column starting from the rightmost (units) column:
    • Units place: 4+3=74 + 3 = 7
    • Tens place: 5+6=115 + 6 = 11. Write 1 and carry over 1 to the hundreds place.
    • Hundreds place: 3+5+1=93 + 5 + 1 = 9 (including the carry-over).
    • Thousands place: 2+9=112 + 9 = 11. Write 1 and carry over 1 to the ten-thousands place.
    • Ten-thousands place: 7+2+1=107 + 2 + 1 = 10 (including the carry-over). Write 0 and carry over 1.
  • Step 3: Write down the complete sum:
  • \begin{array}{c@{}c@{}c@{}c@{}c@{}c} & & 1 & 0 & 1 & 9 & 1 & 7 \\ \hline \end{array}

  • Adding all values gives us the final sum.

Therefore, the sum of 72354 and 29563 is 101917 101917 .

Answer

101917

Exercise #7

amp;81541+amp;amp;17759amp;776amp; \begin{aligned} &81541\\ +& \\ &17759 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Arrange the numbers vertically and align by the rightmost digit.
  • Step 2: Add digits starting from the right (units place) and move left.
  • Step 3: Carry over any value over 9 to the next set of digits.

Now, let's work through each step:

Step 1: Arrange the numbers:

+81541++17759 \begin{aligned} &\phantom{+}81541 \\ + &\phantom{+}17759 \\ \end{aligned}

Step 2: Add digits starting from the rightmost digit:

  1. Units place: 1+9=101 + 9 = 10. Write down 0 and carry over 1.
  2. Tens place: 4+5=94 + 5 = 9. Add the carried 1: 9+1=109 + 1 = 10. Write down 0 and carry over 1.
  3. Hundreds place: 5+7=125 + 7 = 12. Add the carried 1: 12+1=1312 + 1 = 13. Write down 3 and carry over 1.
  4. Thousands place: 1+7=81 + 7 = 8. Add the carried 1: 8+1=98 + 1 = 9. Write down 9.
  5. Ten-thousands place: 8+1=98 + 1 = 9. Write down 9.

The addition will look like this:

881541+817759899300 \begin{aligned} &\phantom{8}81541 \\ + &\phantom{8}17759 \\ \hline &\phantom{8}99300 \\ \end{aligned}

Therefore, the addition of these two numbers results in 9930099300.

Answer

99300

Exercise #8

amp;95781+amp;amp;22245amp;776amp; \begin{aligned} &95781\\ +& \\ &22245 \\ &\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 vertically for addition.
  • Step 2: Add each column starting from the rightmost digit (units) and moving to the left.
  • Step 3: Record any carry needed for sums exceeding 9.

Let's execute the vertical addition:
Write the numbers aligning each digit according to its place value:

95781+22245 \begin{array}{c} 95781 \\ +22245 \\ \end{array}

Step-by-step vertical addition:

  • Starting with the units place: 1+5=61 + 5 = 6. Record 6.
  • Tens place: 8+4=128 + 4 = 12. Record 2, carry over 1 to the hundreds place.
  • Hundreds place: 7+2=97 + 2 = 9, add the carry 1 to get 1010. Record 0, carry over 1 to the thousands place.
  • Thousands place: 5+2=75 + 2 = 7, add the carry 1 to get 88. Record 8.
  • Ten-thousands place: 9+2=119 + 2 = 11. Record 1 and carry over 1 to the next place.
  • Since there's no next place, record this final carry in the ten-thousands place: 1.

Therefore, the sum of 95781 and 22245 is:

118026 \boxed{118026}

The correct choice in the multiple-choice options is option 2, which matches our calculated sum.

Therefore, the solution to the problem is 118026.

Answer

118026

Exercise #9

amp;19785+amp;amp;30406amp;776amp; \begin{aligned} &19785\\ +& \\ &30406 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Align the two numbers, 19785 and 30406, for vertical addition.
  • Step 2: Add the numbers column by column, starting from the rightmost digit.
  • Step 3: Carry over any value greater than 9 to the next column on the left.

Now, let's work through each step:

Step 1: Align the numbers:
19785+30406\begin{array}{c} 19785 \\ +30406 \\ \hline \end{array}

Step 2: Add the columns starting from the right:

  • Rightmost column (ones): 5+6=115 + 6 = 11. Write down 11, carry over 11.
  • Tens column: 8+0=88 + 0 = 8, plus the carry over 11 gives 99.
  • Hundreds column: 7+4=117 + 4 = 11. Write down 11, carry over 11.
  • Thousands column: 9+0=99 + 0 = 9, plus the carry over 11 gives 1010. Write down 00, carry over 11.
  • Ten-thousands column: 1+3=41 + 3 = 4, plus the carry over 11 gives 55.
  • Assembling these results, we have the sum of 5019150191.

Therefore, the solution to the problem is 50191\boxed{50191}.

Answer

50191

Exercise #10

amp;78156+amp;amp;19763amp;776amp; \begin{aligned} &78156\\ +& \\ &19763 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we will perform vertical addition of the two numbers:

We have: \begin{array}{c@{}c@{}c@{}c@{}c@{}c} & & & & & \\ & 7 & 8 & 1 & 5 & 6 \\ + & 1 & 9 & 7 & 6 & 3 \\ \hline \end{array}

Let's add the numbers column by column from right to left:

  • Units place: 6+3=96 + 3 = 9. Write 9.
  • Tens place: 5+6=115 + 6 = 11. Write 1 and carry over 1 to the hundreds place.
  • Hundreds place: 1+7+1(carried)=91 + 7 + 1 \, (\text{carried}) = 9. Write 9.
  • Thousands place: 8+9=178 + 9 = 17. Write 7 and carry over 1 to the ten-thousands place.
  • Ten-thousands place: 7+1+1(carried)=97 + 1 + 1 \, (\text{carried}) = 9. Write 9.

Thus, the sum is 97919\boxed{97919}.

The solution to the problem is 9791997919, which matches choice :

97919

.

Answer

97919

Exercise #11

amp;63636+amp;amp;12197amp;776amp; \begin{aligned} &63636\\ +& \\ &12197 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Add the digits in the units place: 6+7=136 + 7 = 13. Write down 33 and carry over 11.
  • Add the digits in the tens place with the carry-over: 3+9+1=133 + 9 + 1 = 13. Write down 33 and carry over 11.
  • Add the digits in the hundreds place with the carry-over: 6+1+1=86 + 1 + 1 = 8. Write down 88.
  • Add the digits in the thousands place: 3+2=53 + 2 = 5. Write down 55.
  • Add the digits in the ten-thousands place: 6+1=76 + 1 = 7. Write down 77.

Carrying out these calculations step-by-step gives us the final sum as:

7583375833

This corresponds to choice 4. Therefore, the solution to the problem is 7583375833.

Answer

75833

Exercise #12

amp;83716+amp;amp;19194amp;776amp; \begin{aligned} &83716\\ +& \\ &19194 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow a systematic vertical addition process:

  • Step 1: Align the numbers vertically by their place values:

83716+19194 \begin{array}{c} 83716 \\ +19194 \end{array}

  • Step 2: Start adding from the rightmost column (units place).
        - Units: 6+4=106 + 4 = 10 — write down 00 and carry 11.
  • Step 3: Move to the tens column.
        - Tens: 1+9=101 + 9 = 10, plus the carry of 11, gives 1111 — write down 11 and carry 11.
  • Step 4: Move to the hundreds column.
        - Hundreds: 7+1=87 + 1 = 8, plus the carry of 11, gives 99 — write down 99.
  • Step 5: Move to the thousands column.
        - Thousands: 3+9=123 + 9 = 12 — write down 22 and carry 11.
  • Step 6: Move to the ten-thousands column.
        - Ten-thousands: 8+1=98 + 1 = 9, plus the carry of 11, gives 1010 — write down 00 and carry 11, adding it as a new leading digit.

Thus, the resulting sum of 83716+1919483716 + 19194 is 102910102910.

Answer

102910

Exercise #13

amp;15637+amp;amp;29181amp;776amp; \begin{aligned} &15637\\ +& \\ &29181 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we need to perform vertical addition on the two numbers 15637 15637 and 29181 29181 . Follow these steps:

  • Step 1: Align the numbers vertically, ensuring the rightmost digits (units place) align.
  • Step 2: Start adding from the rightmost digits (units place):
    • Add 7 (from 15637) + 1 (from 29181) = 8. Write 8 in the units place.
    • Move to the next column: add 3 + 8 = 11. Write 1 in the tens place and carry over 1 to the hundreds place.
    • Now add the hundreds place: 6 + 1 (carry-over) + 1 = 8. Write 8 in the hundreds place.
    • Next, add the thousands place: 5 + 9 = 14. Write 4 in the thousands place and carry over 1 to the ten-thousands place.
    • Finally, add the ten-thousands place: 1 + 1 (carry-over) + 2 = 4. Write 4 in the ten-thousands place.
  • After carrying over appropriately and adding each digit, the result is 44818.

Therefore, the sum of 15637 15637 and 29181 29181 is 44818 44818 .

Answer

44818

Exercise #14

amp;24679+amp;amp;35813amp;776amp; \begin{aligned} &24679\\ +& \\ &35813 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Align the numbers 24679 and 35813 by their place values. Write the numbers one above the other, ensuring digits align from right (units) to left (ten-thousands).
  • Step 2: Add each column starting from the rightmost side:
    • Add the units: 9+3=129 + 3 = 12. Write 2 in the units place and carry over 1 to the tens.
    • Add the tens: 7+1=87 + 1 = 8 plus carry 1 gives 9. Write 9 in the tens place.
    • Add the hundreds: 6+8=146 + 8 = 14. Write 4 in the hundreds place and carry over 1 to the thousands.
    • Add the thousands: 4+5=94 + 5 = 9 plus carry 1 gives 10. Write 0 in the thousands place and carry over 1 to the ten-thousands.
    • Add the ten-thousands: 2+3=52 + 3 = 5 plus carry 1 gives 6. Write 6 in the ten-thousands place.

Therefore, the sum of 24679 and 35813 is 60492 60492 .

Answer

60492

Exercise #15

amp;36715+amp;amp;45192amp;776amp; \begin{aligned} &36715\\ +& \\ &45192 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve the problem effectively, we will follow a systematic approach:

  • Step 1: Write the two numbers one above the other, aligning by columns according to their place value.
  • Step 2: Begin adding from the rightmost column (the units place), moving leftward. Remember to carry over any tens to the next place value.
  • Step 3: Continue to add column by column, including any carries from the previous column.

Let's work through these steps with the given numbers:

+36715+45192 \begin{aligned} &\phantom{+}36715 \\ + &45192 \\ \hline \end{aligned}

Units Column (far right):
5 (from 36715) + 2 (from 45192) = 7

Tens Column:
1 (from 36715) + 9 (from 45192) = 10
Write down 0, and carry over 1.

Hundreds Column:
7 (from 36715) + 1 (carry) + 1 (from 45192) = 9

Thousands Column:
6 (from 36715) + 5 (from 45192) = 11
Write down 1, and carry over 1.

Tens of Thousands Column:
3 (from 36715) + 4 (from 45192) + 1 (carry) = 8

Thus, the sum is:

+36715+4519281907 \begin{aligned} &\phantom{+}36715 \\ + &45192 \\ \hline &81907 \\ \end{aligned}

Therefore, the solution to the problem is 81907 81907 .

Answer

81907