Examples with solutions for Vertical Addition: 4 digits

Exercise #1

amp;1054+amp;amp;  353amp;776amp; \begin{aligned} &1054 \\ +& \\ &~~353 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we will perform the vertical addition of 1054 and 353 as follows:

  • Step 1: Align the numbers:
      1054+ 35377600 \begin{array}{c} ~~ 1054 \\ + \ 353 \\ \underline{\phantom{77600}}\\ \end{array}

  • Step 2: Add the digits in the units place: 4+3=7 4 + 3 = 7 (no carry is needed).

  • Step 3: Add the digits in the tens place: 5+5=10 5 + 5 = 10 . Write down 0 and carry over 1 to the hundreds place.

  • Step 4: Add the digits in the hundreds place, including the carry: 0+3+1=4 0 + 3 + 1 = 4 (from the carry operation).

  • Step 5: Add the digits in the thousands place: 1+0=1 1 + 0 = 1 .

Thus, the solution is 1407 1407 .

Given the choices, the correct answer is choice 4:

1407

Answer

1407

Exercise #2

amp;2789+amp;amp;  456amp;776amp; \begin{aligned} &2789 \\ +& \\ &~~456 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve the addition of 2789+4562789 + 456, we'll proceed with vertical addition:

  • Step 1: Align the numbers by their digits:
    02789+04560000 \begin{array}{c} \phantom{0}2789 \\ +\phantom{0}456 \\ \underline{\phantom{0000}} \\ \end{array}
  • Step 2: Start adding from the rightmost column (ones place):
    9+6=159 + 6 = 15. Write down 55 and carry over 11 to the tens place.
  • Step 3: Add the tens place:
    8+5=138 + 5 = 13, and add the carry over 11, getting 1414. Write down 44 and carry over 11 to the hundreds place.
  • Step 4: Add the hundreds place:
    7+4=117 + 4 = 11, and add the carry over 11, getting 1212. Write down 22 and carry over 11 to the thousands place.
  • Step 5: Add the thousands place:
    Since we only have 22 and a carry of 11, the result is 33.
  • Step 6: Compile the result across all columns:
    3245 3245

Therefore, the solution to the addition problem is 32453245.

Answer

3245

Exercise #3

amp;7831+amp;amp;  673amp;776amp; \begin{aligned} &7831 \\ +& \\ &~~673 \\ &\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 by their place values:
  • amp;7831+amp;amp;  673amp;776amp; \begin{aligned} &7831 \\ +& \\ &~~673 \\ &\underline{\phantom{776}} & \\ \end{aligned}

  • Step 2: Add the digits in each column, starting from the right (units) column.
  • The unit's column: 1+3=41 + 3 = 4. Write 4 under the units column.

  • Step 3: Move to the ten's column.
  • Add: 3+7=103 + 7 = 10. Write 0 under the tens and carry 1 to the hundreds column.

  • Step 4: Move to the hundred's column.
  • Add: 8+6=148 + 6 = 14, and don't forget the carried 1, making it 1515.

    Write 5 under the hundreds and carry 1 to the thousands.

  • Step 5: Move to the thousand's column.
  • Add: 7+1=87 + 1 = 8. Don't forget the carried 1, making it 88.

    Write 8 under the thousands.

    The sum of the numbers is:

    amp;7831+amp;amp;  673amp;776amp;amp;8504 \begin{aligned} &7831 \\ +& \\ &~~673 \\ &\underline{\phantom{776}} & \\ &8504 \\ \end{aligned}

Therefore, the sum of 7831 and 673 is 8504 \mathbf{8504} .

This corresponds to the choice: :

8504

.

Answer

8504

Exercise #4

amp;8974+amp;amp;  264amp;776amp; \begin{aligned} &8974 \\ +& \\ &~~264 \\ &\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 with 8974 on top and 264 below it.
  • Step 2: Add the numbers column by column, starting from the rightmost (units) column.
  • Step 3: Record the sum below the line, carrying over wherever necessary.

Let's perform the addition:

Step 1: Arrange the numbers vertically.

8974+264776 \begin{array}{c} 8974 \\ +264 \\ \underline{\phantom{776}} \\ \end{array}

Step 2: Begin adding from the rightmost column (units):

  • Units digit: 4+4=84 + 4 = 8, so write 8 in the units place.
  • Tens digit: 7+6=137 + 6 = 13, write 3 and carry over 1 to the hundreds column.
  • Hundreds digit: 9+2+1=129 + 2 + 1 = 12, write 2 and carry over 1 to the thousands column.
  • Thousands digit: 8+1=98 + 1 = 9, write 9.

Step 3: Write the final result:

8974+2649238 \begin{array}{c} 8974 \\ +264 \\ \underline{9238} \\ \end{array}

Therefore, the solution to the problem is 9238 9238 .

Answer

9238

Exercise #5

amp;4653+amp;amp;  867amp;776amp; \begin{aligned} &4653 \\ +& \\ &~~867 \\ &\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 4653 and 867 for vertical addition:
  • Step 2: Add each digit column, starting from the right side (units place), and handle any necessary carrying over.

Let's proceed with the addition:

Step 1: Align the numbers as follows:
          4653
+         867

Step 2: Start with the rightmost column (units):

  • Units: 3+7=103 + 7 = 10. Place 0 and carry over 1 to the tens column.
  • Tens: 5+6=115 + 6 = 11, plus the carryover 1 gives us 12. Place 2 and carry over 1 to the hundreds column.
  • Hundreds: 6+8=146 + 8 = 14, plus the carryover 1 gives us 15. Place 5 and carry over 1 to the thousands column.
  • Thousands: 4+0=44 + 0 = 4, plus the carryover 1 gives us 5. Place 5.

Thus, the complete addition yields:
          5520

Therefore, the solution to the problem is 5520 5520 .

Answer

5520

Exercise #6

amp;5421+amp;amp;1657amp;776amp; \begin{aligned} &5421 \\ +& \\ &1657 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve the problem of adding 5421 and 1657 using vertical addition, we will proceed through the following steps:

Step 1: Align the numbers vertically according to their place values:

5421+1657 \begin{aligned} &5421 \\ + &1657 \\ \end{aligned}

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

  • Units place: 1+7=81 + 7 = 8. Write 8 in the units place.
  • Tens place: 2+5=72 + 5 = 7. Write 7 in the tens place.
  • Hundreds place: 4+6=104 + 6 = 10. Write 0 in the hundreds place and carry over 1 to the thousands place.
  • Thousands place: 5+1=65 + 1 = 6, plus the carried over 1 gives 6+1=76 + 1 = 7. Write 7 in the thousands place.

Step 3: Write down the final result underneath the drawn line:

7078 \begin{aligned} &\underline{7078} \end{aligned}

Therefore, the sum of 5421 and 1657 is 7078\textbf{7078}.

Answer

7078

Exercise #7

amp;4652+amp;amp;2161amp;776amp; \begin{aligned} &4652 \\ +& \\ &2161 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we will utilize the vertical addition method as follows:

First, write the numbers one below the other, aligning them by their respective place values:

4652+2161776 \begin{aligned} &4652 \\ +& \\ &2161 \\ &\underline{\phantom{776}} \\ \end{aligned}

Now, let's add the numbers column by column starting from the rightmost side (units place):
1. **Units Column**: 2+1=32 + 1 = 3. Write 3 in the units place.
2. **Tens Column**: 5+6=115 + 6 = 11. Write 1 in the tens place and carry over 1 to the hundreds place.
3. **Hundreds Column**: 6+1+1=86 + 1 + 1 = 8. Write 8 in the hundreds place.
4. **Thousands Column**: 4+2=64 + 2 = 6. Write 6 in the thousands place.

The sum is arranged as follows:

4652+21616813 \begin{aligned} &4652 \\ +& \\ &2161 \\ &\underline{6813} \\ \end{aligned}

Therefore, the result of adding 46524652 and 21612161 is 6813\textbf{6813}.

Checking against the choices provided, the correct answer is Choice 4: 68136813.

Answer

6813

Exercise #8

amp;3289+amp;amp;2835amp;776amp; \begin{aligned} &3289 \\ +& \\ &2835 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this addition problem, we will follow a systematic step-by-step approach:

  • Step 1: Align the numbers vertically so that corresponding place values line up. We have:

3289+2835 \begin{aligned} &3289 \\ + &2835 \\ \end{aligned}

  • Step 2: Start adding from the rightmost digit (units place).
    • Units place: 9+5=149 + 5 = 14. Write 4 and carry over 1 to the tens place.
  • Step 3: Move to the next digit (tens place).
    • Tens place: 8+3=118 + 3 = 11. Add the carry 1: 11+1=1211 + 1 = 12. Write 2 and carry over 1 to the hundreds place.
  • Step 4: Proceed to the hundreds place.
    • Hundreds place: 2+8=102 + 8 = 10. Add the carry 1: 10+1=1110 + 1 = 11. Write 1 and carry over 1 to the thousands place.
  • Step 5: Finally, add the thousands place.
    • Thousands place: 3+2=53 + 2 = 5. Add the carry 1: 5+1=65 + 1 = 6. Write 6.

By compiling these results, the sum is 6124.

Therefore, the solution to the problem is 61246124.

Answer

6124

Exercise #9

amp;6324+amp;amp;2798amp;776amp; \begin{aligned} &6324 \\ +& \\ &2798\\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Set up the numbers for vertical addition:

6324+2798776 \begin{aligned} &6324 \\ +&2798\\ \underline{\phantom{776}} & \\ \end{aligned}

  • Step 2: Add the digits in the units place: 4+8=124 + 8 = 12, write down 22, carry over 11.

13  232 \begin{aligned} &\phantom{1} \\ &\phantom{3} \;232 \\ \end{aligned}

  • Step 3: Add the digits in the tens place: 2+9=112 + 9 = 11 plus carry 11 makes 1212. Write down 22, carry over 11.

13  32 \begin{aligned} &\phantom{1} \\ &\phantom{3} \;32 \\ \end{aligned}

  • Step 4: Add the digits in the hundreds place: 3+7=103 + 7 = 10 plus carry 11 makes 1111. Write down 11, carry over 11.

12  1 \begin{aligned} &\phantom{1} \\ &\phantom{2} \;1 \\ \end{aligned}

  • Step 5: Add the digits in the thousands place: 6+2=86 + 2 = 8 plus carry 11 makes 99. Write down 99.

97122 \begin{aligned} &\phantom{9}7122 \\ \end{aligned}

Therefore, the sum of 63246324 and 27982798 is 9122\mathbf{9122}.

Answer

9122

Exercise #10

amp;7256+amp;amp;1967amp;776amp; \begin{aligned} &7256 \\ +& \\ &1967\\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we will apply vertical addition:

Let's add the numbers 7256 and 1967 by arranging them in a column:

  • First, arrange the numbers by place value:
  • 7256
    +1967
  • Next, add the rightmost column (units place):
    **6 + 7 = 13**. Write down 3 and carry over 1 to the next column (tens place).
  • Proceed to the tens place:
    **5 + 6 = 11**, plus the carry-over 1 gives **12**. Write down 2 and carry over 1.
  • Now, add the hundreds place:
    **2 + 9 = 11**, plus the carry-over 1 gives **12**. Write down 2 and carry over 1.
  • Finally, add the thousands place:
    **7 + 1 = 8**, plus the carry-over 1 gives **9**. Write down 9.

The sum of the numbers is written as:

7256
+1967
9223

Therefore, the correct sum of the numbers 7256 and 1967 is 92239223.

Answer

9223

Exercise #11

amp;1547+amp;amp;7656amp;776amp; \begin{aligned} &1547 \\ +& \\ &7656 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

Let's solve the problem by completing an addition of the numbers vertically.

  • Write the numbers vertically, aligning them by their place values:
    \begin{array}{c@{}c@{}c@{}c@{}c} & 1 & 5 & 4 & 7 \\ + & & 7 & 6 & 5 & 6 \\ \end{array}

  • Add the digits starting from the rightmost (units place):

    • Units Place: 7+6=137 + 6 = 13. Write 3 and carry over 1 to the tens place.

    • Tens Place: 4+5=94 + 5 = 9, plus 1 from the carry-over equals 10. Write 0 and carry over 1 to the hundreds place.

    • Hundreds Place: 5+6=115 + 6 = 11, plus 1 from the carry-over equals 12. Write 2 and carry over 1 to the thousands place.

    • Thousands Place: 1+7=81 + 7 = 8, plus 1 from the carry-over equals 9. Write 9.

  • The final addition gives us:
    9203\begin{array}{c} 9 \quad 2 \quad 0 \quad 3 \\ \end{array}

Thus, the sum of 1547 and 7656 is 9203\boxed{9203}.

Answer

9203

Exercise #12

amp;3267+amp;amp;1662amp;776amp; \begin{aligned} &3267 \\ +& \\ &1662 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve the problem of adding the numbers 3267 and 1662, let's use vertical addition:

Step 1: Align the numbers by their place values, from right to left:

3267+1662 \begin{aligned} &3267 \\ +& \\ &1662 \\ \end{aligned}

Step 2: Begin adding from the units place (rightmost):

  • Units place: 7+2=97 + 2 = 9
  • Tens place: 6+6=126 + 6 = 12. Write 2, carry over 1.
  • Hundreds place: 2+6+12 + 6 + 1 (carried over) =9= 9
  • Thousands place: 3+1=43 + 1 = 4

The final sum by place value is 4929.

Therefore, the sum of 3267 and 1662 is 4929 4929 .

The correct choice is option 4: 4929

Answer

4929

Exercise #13

amp;7351+amp;amp;2499amp;776amp; \begin{aligned} &7351 \\ +& \\ &2499 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve the problem of finding the sum of 7351 and 2499, we will proceed with vertical addition. Here are the steps:

  • Align the numbers with their rightmost digits: 07351+24990000 \begin{array}{c} \phantom{0}7351 \\ +2499 \\ \underline{\phantom{0000}} \end{array}
  • Begin adding from the rightmost column (units):
    - Units column: 1+9=101 + 9 = 10. Write 0, carry over 1.
  • Next, move to the tens column:
    - Tens column: 5+9=145 + 9 = 14, plus the carry of 1 gives 1515. Write 5, carry over 1.
  • Proceed to the hundreds column:
    - Hundreds column: 3+4=73 + 4 = 7, plus the carry of 1 gives 88. Write 8.
  • Finally, add the thousands column:
    - Thousands column: 7+2=97 + 2 = 9. Write 9.

After completing these steps, the final sum is written as:

07351+2499000009850 \begin{array}{c} \phantom{0}7351 \\ +2499 \\ \underline{\phantom{0000}} \\ \phantom{0}9850 \\ \end{array}

Therefore, the solution to the problem is 9850 9850 .

Answer

9850

Exercise #14

amp;8472+amp;amp;5261amp;776amp; \begin{aligned} &8472\\ +& \\ &5261 \\ &\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 by their place values.
  • Step 2: Add the digits starting from the rightmost column.
  • Step 3: Handle any carryovers properly.
  • Step 4: Write down the final result.

Now, let's work through each step:

Step 1: Align the numbers:

84728472
+5261+ 5261
_________\_\_\_\_\_\_\_\_\_

Step 2: Begin adding the digits starting from the rightmost side:

Units column: 2+1=32 + 1 = 3.

Tens column: 7+6=137 + 6 = 13. Write 33 and carry over 11.

Hundreds column: 4+2+1(carry)=74 + 2 + 1 \,(carry) = 7.

Thousands column: 8+5=138 + 5 = 13. Write 33 and carry over 11.

Step 3: Handle the extra thousands place from the carryover: 11.

Thus, the full addition with carryovers corrected is:

84728472
+5261+ 5261
________=_13733\_\_\_\_\_\_\_\_=\_13733

Therefore, the correct solution to the problem is 1373313733.

Answer

13733

Exercise #15

amp;2781+amp;amp;8417amp;776amp; \begin{aligned} &2781 \\ +& \\ &8417 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Set up the numbers for addition in a vertical format, aligning the rightmost digits.
  • Step 2: Add each column starting from the right, keeping track of the carryover.
  • Step 3: Continue the addition for all columns, incorporating any carryover into the next left column.

Now, let's work through the addition process:

Add the units column: 1+7=81 + 7 = 8. No carryover occurs here.

Next, add the tens column: 8+1=98 + 1 = 9. Still, no carryover is involved.

Then, add the hundreds column: 7+4=117 + 4 = 11. Because this is more than 9, we write down 1 and carry over 1 to the next column.

Finally, add the thousands column: 2+8=102 + 8 = 10, plus the 1 carried over gives 11. Thus, we write down 11.

Therefore, the sum of the numbers is 11198 \boxed{11198} .

Answer

11198