Examples with solutions for Vertical Addition: Double digit addition within 100

Exercise #1

amp;12+amp;amp;88amp;776amp; \begin{aligned} &12 \\ +& \\ &88 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow a step-by-step vertical addition method:

  • Step 1: Arrange the numbers vertically: 12+88 \begin{aligned} &12 \\ + & \\ &88 \\ \end{aligned} Make sure the digits of the numbers are aligned correctly: units under units and tens under tens.
  • Step 2: Start by adding the numbers in the units place (rightmost column): 2+8=102 + 8 = 10
  • Since 1010 is a two-digit number, write down 00 in the units place under this column and carry over 11 to the tens column (left). Carrying over is essential when the sum of any column exceeds 9.

  • Step 3: Next, add the numbers in the tens place, don't forget adding the carry from the previous addition: 1+1+8=101 + 1 + 8 = 10
  • As before, 1010 is a two-digit number. Write down 00 in the tens place and carry over 11 (although in this case, it gets added to a zero since this is the leftmost column, resulting in a new column).

    Thus, the complete addition looks like this: 12+88100 \begin{aligned} &12 \\ + & \\ &88 \\ & \underline{100} \end{aligned}

Therefore, the correct solution to the problem is 100100, which corresponds to the answer choice provided.

Answer

100

Exercise #2

amp;26+amp;amp;74amp;776amp; \begin{aligned} &26 \\ +& \\ &74 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we'll use vertical addition as follows:

Step 1: Arrange the numbers vertically with the place values aligned.

  2626
+ 7474
776\underline{\phantom{776}} 

Step 2: Add the numbers starting from the ones column:
- Add the ones place: 6+4=106 + 4 = 10. Write down 00 and carry over 11 to the tens column.

  2626
+ 7474
776\underline{\phantom{776}} 
  0000

Step 3: Move to the tens column: Add 2+7=92 + 7 = 9, then add the carried over 11 to get 1010.
- Write down 1010.

     2626
  + 7474
  6707\underline{\phantom{6707}}
  100100

Therefore, the sum of 2626 and 7474 is 100100.

The correct answer amongst the choices provided is :

100

.

Therefore, the solution to the problem is 100 100 .

Answer

100

Exercise #3

amp;48+amp;amp;52amp;776amp; \begin{aligned} &48 \\ +& \\ &52 \\ &\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 by their place value.
  • Step 2: Add the digits in the units column.
  • Step 3: Manage any carryover if necessary.
  • Step 4: Add the digits in the tens column along with any carryover.

Now, let's work through each step:

Step 1: Align the numbers.

48
+52
___

Step 2: Add the digits in the units column:
8 (from 48) + 2 (from 52) = 10.
This gives us 0 in the units place and we carry over 1 to the tens place.

Step 3: Add the digits in the tens column, including the carried over 1:

4 (from 48) + 5 (from 52) + 1 (carryover) = 10.

Thus, the digit 0 goes to the tens place, and 1 will be placed in the hundreds place.

Therefore, the full solution looks like this:

48
+52
___
100

Therefore, the solution to the problem is 100100.

Answer

100

Exercise #4

amp;56+amp;amp;44amp;776amp; \begin{aligned} &56 \\ +& \\ &44 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Write the numbers vertically, ensuring the digits are aligned by place value:
  • 56+44776 \begin{array}{c} 56 \\ + 44 \\ \underline{\phantom{776}} \\ \end{array}

  • Step 2: Add the units digits (rightmost column). The units digit of 56 is 6, and for 44, it is 4.
  • Sum: 6+4=106 + 4 = 10.

  • Step 3: Write down the 0 from the sum (10) in the units place and carry over the 1 to the tens place.
  • Step 4: Add the tens digits (next column to the left). The tens digit of 56 is 5, and for 44, it is 4. Add these along with the carried-over 1.
  • Sum: 5+4+1=105 + 4 + 1 = 10.

  • Step 5: Write down the full result (100) below the line.

Therefore, the sum of 56 and 44 is 100\textbf{100}.

This corresponds to answer choice 1.

Answer

100

Exercise #5

amp;35+amp;amp;65amp;776amp; \begin{aligned} &35 \\ +& \\ &65 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Answer

100

Exercise #6

amp;67+amp;amp;33amp;776amp; \begin{aligned} &67 \\ +& \\ &33 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Answer

100