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Addition with Larger Numbers
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Introduction

In this lesson, you will learn about the steps of addition. The pattern used to do addition is the same no matter how many digits are in the numbers, or how many numbers are being added together.

This video illustrates the lesson material below. Watching the video is optional.

Steps for Addition


  1. Stack the numbers according to place value.
  2. Add the numbers by column, starting on the right.
  3. Carry numbers to the left place value, as needed.
  4. Repeat steps 1–3 for each remaining column.

Example 1
\(6437+5639\)

First, stack the numbers according to place value. It doesn’t matter which number goes on top, only that the numbers are lined up by place value and aligned to the right.

6437 + 5639 with the first digits in each figure noted as in the thousands place, the second in the hundreds, the third in the tens, and the fourth in the ones place.

Figure 1

Second, add the numbers by column. Always start on the right side of the equation, which means the numbers in the ones column. In the ones place is \(7+9\), which equals 16. This means there are 16 ones, or 1 ten and 6 ones. Carry the 1 ten to the tens column and place the 6 ones as part of the answer, right below the line in the ones column.

6437 + 5639 with the first step completed of adding the ones column: a 6 in the answer spot and a 1 carried above the tens column

Figure 2

Next, add the tens column: \(1+3+3=7\). Notice that this answer, 7, is only one digit, which means it can be placed to the left of the 6 in the answer.

6437 + 5639 with the first two steps completed of adding the ones and tens columns: 76 in the answer spot and a 1 carried above the tens column

Figure 3

Next, add the hundreds place: \(4+6=10\). This translates to 0 hundreds and 1 thousand. The 1 thousand needs to be carried over to the thousands place, while the 0 can be placed to the left of the 7 in the answer.

6437 + 5639 with the first three steps completed of adding the ones, tens, and hundreds columns: 076 in the answer spot, a 1 carried above the tens column, and a 1 carried above the thousands column

Figure 4

Lastly, add the thousands: \(1+6+5=12\). This means there are 2 thousands and 1 ten thousand. Since there is nothing in the 10 thousands column, simply write the number 12 into the answer, to the left of the 0.
The complete answer is \(6437+5639=12076\).

6437 + 5639 completed with 12076 in the answer spot, a 1 carried above the tens column, and a 1 carried above the thousands column

Figure 5

Example 2
\(54+4369+912\)

Notice the first step has already been completed by stacking the numbers according to their place value.

54 + 4369 + 912 with a blank answer spot

Figure 6

Do steps two and three, beginning by adding the ones column: \(4+9+2=15\). Drop the 5 below the equation in the one's column. Carry the 1 over to the tens place, to be added in the proper column.

54 + 4369 + 912 with the first step completed of adding the ones column: 5 in the answer spot and a 1 carried above the tens column

Figure 7

Now add the tens column: \(1+5+6+1=13\). Drop the 3 below the equation, placing it in the ten’s column, to the left of the 5. The 1 will be carried over to the hundred's column.

54 + 4369 + 912 with the first two steps completed of adding the ones and tens columns: 35 in the answer spot, a 1 carried above the tens column, and a 1 carried above the hundreds column

Figure 8

Add the hundreds column: \(1+3+9=13\). Drop the 3, to the left of the other numbers in the answer and carry the 1 over to the thousands place.

54 + 4369 + 912 with the first three steps completed of adding the ones, tens, and hundreds columns: 335 in the answer spot, a 1 carried above the tens column, a 1 carried above the hundreds column, and a 1 carried above the thousands column

Figure 9

Finally, add the thousands column: \(1+4=5\). Drop the 5 to the left of the numbers in the answer, completing the solution: \(54+4369+912=5335\).

54 + 4369 + 912 completed with 5335 in the answer spot, a 1 carried above the tens column, a 1 carried above the hundreds column, and a 1 carried above the thousands column

Figure 10

Things to Remember


  • The steps for addition:
    1. Stack by place value
    2. Add by column, starting on the right
    3. Carry over numbers, as needed
    4. Repeat for each column, left to right

Practice Problems

Evaluate the following expressions:
  1. \(62 + 33 = ?\) (
    Solution
    x
    Solution: 95
    Details:
    One way to solve this problem is to think in terms of place values.

    There are:
    6 tens or 60
    3 tens or 30
    2 ones or 2
    3 ones or 3

    The following bars represent 6 tens. Each bar has 10 squares for a total of 60 squares.

    This image displays six bars. Each bar is made from ten identical squares stacked on top of each other.

    The following bars represent 3 tens. Each bar has 10 squares for a total of 30 squares.

    This image displays three bars. Each bar has ten identical squares stacked on top of each other.

    Now, add 6 tens plus 3 tens or \(60 + 30\).

    This image displays six bars on the left and three bars on the right with an addition sign in between them. Each bar is made of ten identical squares stacked on top of each other.

    Now, there are 9 tens, for a total of 90 squares.

    This image displays nine bars. Each bar is made of ten identical squares stacked on top of each other.

    Then you can add the ones: \(2 + 3 = 5\) or 5 ones.

    This image has two identical squares on the left and three identical squares on the right, with an addition sign between the two groups.

    The answer is 9 tens and 5 ones, which is 95.

    This image displays nine bars. Each bar is made of ten identical squares stacked on top of each other. There are also five individual squares to the right of those nine bars.
    )
  2. \(525 + 25 = ?\) (
    Solution
    x
    Solution: 550
    Details:
    Using place values, the problem \(525 + 25\) is shown below.

    An equation: 525 plus 25. The numbers are aligned in columns by place value: hundreds to the left, tens in the middle, and ones to the right. For the number 525, the first 5 is in the hundreds column. The 2 is in the tens column. The other 5 is in the ones column. For the number 25, the 2 is in the tens column and the 5 is in the ones column.

    Start by adding the numbers in the ones column: \(5 + 5 = 10\). The first answer is 10. Put the 0 in the ones column and carry the 1 into the tens column.

    This is the same as the previous image except it displays an orange 0 in the ones column of the solution box. There is also an orange 1 (carried) at the top of the tens column.

    Continue by adding the numbers in the tens columns: \(1 + 2 + 2 = 5\). Put the 5 in the tens column.

    This is the same as the previous image except there is also an orange 5 at the bottom of the tens column in the solution box.

    Finally, add the hundreds column. In this column, there is a 5 and nothing else. Hence the answer here is 5.

    This is the same as the previous image except there is an orange 5 at the bottom of the hundreds column in the solution box.

    The answer is: \(525 + 25 = 550\).
    )
  3. \(19 + 52 + 61 = ?\) (
    Video Solution
    x
    Solution: 132
    Details:


    (Addition with Larger Numbers #3 (01:23 mins) | Transcript)
    )
  4. \(637 + 400 = ?\) (
    Solution
    x
    Solution:
    1037
    )
  5. \(710 + 231 = ?\) (
    Solution
    x
    Solution:
    941
    )
  6. \(968 + 875 + 682 = ?\) (
    Video Solution
    x
    Solution: 2525
    Details:

    (Addition with Larger Numbers #6 (01:48 mins) | Transcript)
     | Transcript)

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