Addition

Addition is one of the four basic arithmetic operations in mathematics namely addition, subtraction, multiplication and division. This operator is used to add two or more numbers or things together. This plays a vital role in our daily existence while dealing with different types of transactions. Also, addition is the basic operation which is introduced to the students at their primary level. In this article, you are going to learn the meaning of addition, properties, addition on number line, different addition techniques and formulas.

Addition image 1

Meaning of Addition

Addition is the term used to describe adding two or more numbers together. The addition is denoted using the plus sign ‘+‘ such as the addition of 3 and 3 can be written as 3 + 3. Also, the plus sign (+) can be used as many times as required, such as 3 + 3 + 3 + 3.

For lists of large numbers, it usually is more comfortable to write the list of numbers in a column and execute the calculation at the bottom. In this case, the addition of the list of numbers is termed as the sum and is represented using the symbol ∑.

Addition Properties

Addition of two or more numbers possesses some important properties. The list of properties of addition given below will help in predicting the sign of the result obtained in the addition process.

  • Addition of two whole numbers is again a whole number.
  • Addition of two natural numbers will result in the natural number again.
  • Addition of two integers will be an integer; addition of two positive integers will be a positive integer, addition of two negative integers will be a negative number and the addition of one positive and one negative integer will be an integer with sign same as the sign of the largest number.
  • Addition of two rational numbers will be a rational number again. Also, the property related to positive and negative signs will be the same as for integers.
  • Addition of any number with 0 gives the number itself.

Addition on Number Line

The basic method of adding integers involves the representation of numbers on the number line and then adding them by counting the numbers. This can be understood clearly with the help of the below given example:

Example: Perform -3 + 5 on the number line.

Solution:

Given, -3 + 5

That means, five points to be added to -3.

This can be done using number line as shown below:

Addition on number line

Since, the operation is addition, we need to move towards the right of -3. Step towards the right of -3 to 5 units (as shown with red arrow curves). The final unitary addition ends at 2.

Therefore, -3 + 5 = -3 + 1 + 1 + 1 + 1 +1 = 2

Addition with regrouping

As explained above, addition of single digit numbers can be done easily on the number line. Now, the question comes in the minds of how to add two or more digits numbers? This can be done using regrouping of digits of the same place value together. In maths, regrouping can be defined as the process of creating groups of tens, hundreds, or thousands when carrying out some operations like addition and subtraction with two or more digit numbers.

Let’s have a look at the example given below:

Example: Add two numbers 57 and 46.

Solution:

57 + 46

addition with regrouping

When we add the digits of numbers from the bottom of the ones column to the one on top, we get 7 + 6, which is equal to 13.

As we know, a maximum of 9 can be written in the ones column so we can’t put the whole eleven there. We can write the digit representing the ones (i.e. 3) in the ones column, and the other digit (i.e. digit 1 from 13) gets regrouped to the tens column digits.

Now, we can complete this by adding the numbers in the tens column: 5 + 4.

Do not forget to add the regrouped ten as well, i.e. 5 + 4 + 1.

This equals 10 so write it in the tens column, as a total of 103.

A similar approach can be used to add three or more digit numbers.

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