Examples with solutions for Vertical Addition: Simple addition of 3-digit and 1-digit numbers

Exercise #1

amp;100+amp;amp;    5amp;776amp; \begin{aligned} &100 \\ +& \\ &~~~~5 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we will use vertical addition.

Let's perform the steps:

  • Step 1: Write the numbers 100 and 5 vertically, aligning them by place value. Since 5 is a single-digit number, it will align under the ones place of 100. This gives us:

    100+  5 \begin{aligned} &100 \\ +& \\ &~~5 \\ \end{aligned}

  • Step 2: Add the numbers column by column, starting from the right.

    • Add the ones place: 0+5=50 + 5 = 5
    • Add the tens place: 0+0=00 + 0 = 0
    • Add the hundreds place: 1+0=11 + 0 = 1

    This results in a sum of 105105.

Therefore, the solution to the problem is 105105.

Answer

105

Exercise #2

amp;215+amp;amp;    3amp;776amp; \begin{aligned} &215 \\ +& \\ &~~~~3 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we'll perform vertical addition by following these steps:

  • Step 1: Align the numbers 215 and 3 vertically, ensuring the rightmost digits (the ones place) line up:

215+13776 \begin{array}{r} 215 \\ + \phantom{1}3 \\ \underline{\phantom{776}} \\ \end{array}

  • Step 2: Add the digits in the ones place: 5+3=85 + 3 = 8. Write 8 in the ones place of the sum.
  • Step 3: Move to the tens place. Since there is no digit in the tens place for 3, we add 1+0=11 + 0 = 1. Write 1 in the tens place of the sum.
  • Step 4: For the hundreds place, there is only the digit 2 from 215, so write 2 in the hundreds place of the sum.

The resulting sum is:

1218 \begin{array}{r} \phantom{1}218 \\ \end{array}

Therefore, the solution to the problem is 218 218 .

Answer

218

Exercise #3

amp;957+amp;amp;    3amp;776amp; \begin{aligned} &957 \\ +& \\ &~~~~3 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

We will solve the problem using vertical addition as follows:

  • Step 1: Align the numbers by their place values.
    957+    3 \begin{aligned} &957 \\ + &~~~~3 \\ \end{aligned}
  • Step 2: Add the digits starting from the rightmost side, which is the units column.

First, add the digits in the units place:
7+3=107 + 3 = 10.

Since 10 is composed of 0 in the units place and carry over 1 to the tens place, write 0 in the units place and remember to carry over the 1.

Next, move to the tens place and add up the digits, considering the carryover:
5+0+1=65 + 0 + 1 = 6.

Finally, add the hundreds place, which has no other digits to add:
9 9 (hundreds) \begin{aligned} & 9 \\ &\underline{ }\ \\ & 9 \quad\ (hundreds)\\ \end{aligned}

Summarizing, the addition yields the following:

957+    3776 960 \begin{aligned} \qquad\qquad &957 \\ + &~~~~3 \\ &\underline{\phantom{776}} \\ \quad\ &960 \\ \end{aligned}

Therefore, the result of adding 957 and 3 is 960\mathbf{960}.

The correct answer from the choices given is Choice 4: 960.

Thus, the correct solution to the problem is 960 960 .

Answer

960

Exercise #4

amp;862+amp;amp;    4amp;776amp; \begin{aligned} &862 \\ +& \\ &~~~~4 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve the problem of adding 862862 and 44 vertically, follow these steps:

  • Step 1: Align the numbers as follows:
    862+4776 \begin{array}{c} 862 \\ + 4 \\ \underline{\phantom{776}} \\ \end{array}
  • Step 2: Add the digit in the units’ place:
    2+4=62 + 4 = 6
  • Step 3: Since 66 is less than 1010, place the 66 directly in the units’ place of the result:
  • Step 4: Move to the tens and hundreds places. Since there is no carry, just bring down the 66 from the tens place and the 88 from the hundreds place directly.

Therefore, the sum of 862862 and 44 is 866866.

The correct answer choice is: :

866

Answer

866

Exercise #5

amp;521+amp;amp;    8amp;776amp; \begin{aligned} &521 \\ +& \\ &~~~~8 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we will add the numbers 521 and 8 using vertical addition:

  • Step 1: Write the numbers in vertical form, aligning by the units place:
  • 521+  8529 \begin{array}{c} 521 \\ +~~8 \\ \hline \underline{\phantom{529}} \end{array}

  • Step 2: Add the digits in the units place: 1+8=91 + 8 = 9. Write the result below the line in the units place.
  • Step 3: Add the digits in the tens place: 2+0=22 + 0 = 2. Write the result in the tens place.
  • Step 4: Add the digits in the hundreds place: 5+0=55 + 0 = 5. Write the result in the hundreds place.

Thus, the sum of 521 and 8 is 529529.

Therefore, the solution to the problem is 529\boxed{529}.

Answer

529