# Introduction to properties of addition

In this lesson, we learn few properties of addition, like the identity property, the commutative property and the associative property.

Identity property

Identity property of addition states that the sum of any number and 0 is the same number.

For any number a,

a + 0 = a

0 + a = a

For example −

11 + 0 = 11; 0 + 11 = 11

In an addition, the terms that are added are called the addends and the result of the addition operation is called the sum.

The commutative property of addition states that changing the order of the addend in an addition operation does not change the sum.

For any two numbers a and b,

a + b = b + a

The associative property of addition states that the sum of numbers remains same regardless of how you group the numbers.

For any three numbers a, b and c,

(a + b) + c = a + (b + c)

Fill in the blank and identify the property of addition in the following equation.

0 + _ = 21

### Solution

Step 1:

Identity property of addition states that the sum of any number and 0 is the same number.

Step 2:

So, 0 + 21 = 21

Step 3:

Fill in the blank and identify the property of addition in the following equation.

10 + 16 = 16 + _

### Solution

Step 1:

The commutative property of addition states that changing the order of numbers in an addition operation does not change the sum.

a + b = b + a, where a, b are any numbers.

Step 2:

So, 10 + 16 = 16 + 10

Step 3:

Fill in the blank and identify the property of addition in the following equation.

(2 + _) + 13 = 2 + (8 + 13)

### Solution

Step 1:

The associative property of addition states that the sum of numbers remains same regardless of how you group the numbers or where you put the parentheses in the addition.

(a + b) + c = a + (b + c), where a, b and c are any real numbers

Step 2:

So, (2 + 8) + 13 = 2 + (8 + 13)

Step 3: