Addition Table

Addition is an arithmetic operation that is used to find the sum of numbers taken together. The addition table helps us to add numbers by forming a specific pattern and where the numbers are arranged in rows and columns. The addition table helps us to quickly get the result of the summation of two numbers without actually adding them.

Addition operation is defined as the summing of two or more quantities. An addition table is an arrangement of numbers in a tabular format where the same set of numbers are written in the first row and the first column. The addition table helps us to quickly arrive at the result of the addition of two numbers just by observing the pattern. The arithmetic operation used to create the addition table is addition represented as (+). The numbers that are being added to fill the addition chart are known as addends. To fill a particular row of an addition table, we will follow the logic of adding numbers keeping one of the addends constant and changing the other addend to fill in all the entries of that corresponding row such as 1 + 1 = 2, 1 + 2 = 3, 1 + 3 = 4 and so on. The addition table is also known as the addition chart. We will be looking into the addition chart and its working in the next section.

The addition chart follows the addition operation wherein we obtain numbers in the table by adding a number from the topmost horizontal row with a number from the left-most column to fill in all the corresponding row values. Let's look into the addition chart 1 - 10 as shown below.

Description of Addition Table Chart 1 - 10

To fill a particular row of an addition table, we choose the first addend from the set of numbers written in the left-most column and keep changing the second addend vertically written in the top-most row. Each time we change a row, the corresponding addend value also changes and this process continues for all the 10 rows starting from 1 to 10. We will take a few examples to understand the addition chart.

• To fill in the first row, we will take the first addend as the first element of the numbers written in the left most column that is 1 and keep changing the second addend horizontally as per the numbers written in the top most row which is described as follows, 1 + 1 = 2, 1 + 2 = 3, 1 + 3 = 4, 1 + 4 = 5, 1 + 5 = 6, 1 + 6 = 7, 1 + 7 = 8, 1 + 8 = 9, 1 + 9 = 10, and 1 + 10 = 11. Therefore, the entries of the first row will be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
• Similarly, to fill in the second row we will take the first addend as the second element of left most column that is 2 and keep changing the second addend horizontally as follows, 2 + 1 = 3, 2 + 2 = 4, 2 + 3 = 5, 2 + 4 = 6, 2 + 5 = 7, 2 + 6 = 8, 2 + 7 = 9, 2 + 8 = 10, 2 + 9 = 11, and 2 + 10 = 12. Therefore, the entries of the second row will be 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
• Now, to read the addition table chart we will find the result of 7 + 8 by observation. We go down the row which has the number 7 and across the column which has the number 8, this corresponding entry in the addition table shows the result 15. But we know that addition follows commutative property. Hence, 7 + 8 = 8 + 7. Hence, we can reverse the row and column to be observed. We can go down the row having the number 8 and across the column that has 7. The corresponding value at the intersection point will still give us 15. Hence, we conclude that the rows and columns are interchangeable for the addends while reading an addition table.
• To read the value of 5 + 5, we go down the row that has the number 5 and across the column that also has the number 5, the intersection of these shows the entry as 10 as shown in the addition chart.

Thus, we see that we can easily calculate the sum of two numbers by just observing the intersection of corresponding rows and columns of the two addends. Below the individual addition tables are shown for all the numbers 1 - 10 based on which the rows of the addition table chart are filled.

Related Articles

Check the following articles related to the addition table.

• Subtraction Table
• Subtraction
• Arithmetic Operations

What is Addition Table?

An addition table is a tabular representation of numbers arranged in rows and columns that helps us to calculate the sum of two numbers just by observation without performing the actual calculation.

How does an Addition Table Work?

The addition table works by the arrangement of the same set of numbers in the topmost row and the leftmost column. Each time a particular addend is fixed in the row and the other addend is varied throughout the columns to perform the addition and write the result. For example, to fill in the second row, we keep the number 2 fixed and keep changing the second addend such as 2 + 1 = 3, 2 + 2 = 4 , 2 + 3 = 5 and so on. For reading the results, the intersection of the two addends is seen down the row and across the column to determine the result. For example, to calculate 9 + 3 we go down the row till number 9 and across the column till number 3. The intersection point of these will give the result in the table as 12.

How to Write Addition Table?

To write an addition table we always choose a particular row to be filled one at a time. To fill the n^th row, we fix one of the addends as n and vary the other addend accordingly. For example, let's say in an addition table 1 - 10 we have to fill the sixth-row entries. To do this, we fix one of the addends as 6 and vary the other addend as 1, 2, 3... 10. The calculation goes as follows, 6 + 1, 6 + 2, 6 + 3, ..., 6 + 10 and therefore the entries of sixth row will go in this pattern 7, 8, 9,...,16.

How to Read Addition Table?

To read the addition table, we look into the addends given and observe them down the row and across the column to find their intersection point in the table. For example, to calculate 4 + 8, we go down the row till 4 and across the column till number 8. The result will be the intersection point in the addition table that will give us 12. Since addition is commutative, the complete process can be reversed by taking 8 down the row and 4 across the column. This will still give us the same result.

How do you Complete an Addition Table?

An addition table is completed by first placing the same set of numbers on the topmost row and the left-most column and the entries are made by fixing the addend according to the row being filled and the other addend is changed each time to get the values. To fill row 5 (excluding the topmost row) we will fix one of the addends as 5 and keep changing the other addend as follows, 5 + 1, 5 + 2, 5 + 3, and so on... Thus, the row 5 entries will be 6, 7, 8...

What is an Addition Chart?

An addition chart is a representation of the set of numbers arranged in a specific fashion such that it helps us to apply a pattern to get the result by just observation without performing the actual calculation. It is also known as the addition table.