Properties of Addition

Properties of Addition

Concept

The addition is a process of adding two or more items together. In math, addition is the method of calculating the total of two or more numbers to know the sum of the numbers. It is a primary arithmetic operation.

Rules

While performing addition we use the basic properties listed below:

Commutative Property: The commutative property of addition says that the order in which we add the addends does not change the sum.
The sum of two or more addends will be the same irrespective of the order of the addends. For example, 5 + 3 = 3 + 5 = 8

Associative Property: The associative property of addition is a rule that states that while adding three or more numbers, we can group them in any combination, the sum that we get remains the same irrespective of the manner in which they are grouped. In this case, grouping refers to the placement of brackets.
The sum of three or more addends will be the same irrespective of the grouping or order of the addends. For example, (6 + 4) + 5 = 6 + (4 + 5)

Additive Identity Property: If we add 0 to any number, the sum remains the actual number. The addition of the whole number 0 to any other number does not change the value of the sum. For example, 0 + 8 = 8.

Example

Which property of addition does this equation show?
14.12 + (9.5 + 7.3) = (14.12 + 9.5) + 7.3

Solution

Associative property
When adding 3 numbers, grouping does not change the sum.

Practice Properties of Addition

Practice Problem 1

Identify the equation that shows the commutative property of addition.
 Properties of Addition- Practice Problem 1

Practice Problem 2

Identify the equation that shows the associative property of addition.
 Properties of Addition- Practice Problem 2

Practice Problem 3

Identify the equation that shows the identity property of addition.
 Properties of Addition- Practice Problem 3

Practice Problem 4

A factory manufactures plastic products. It produced 18,606 pieces in June, 35,417 pieces in July and 14,877 pieces in August. How many total number of pieces did it produce in all?
 Properties of Addition- Practice Problem 4