- Properties of Real Numbers
- Home
- Identifying Like Terms
- Combining like terms: Whole number coefficients
- Introduction to properties of addition
- Multiplying a constant and a linear monomial
- Distributive property: Whole Number coefficients
- Factoring a linear binomial
- Identifying parts in an algebraic expression
- Identifying equivalent algebraic expressions
- Introduction to properties of multiplication

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# 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

**Commutative property of addition**

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*

**Associative property of addition**

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:**

So, the answer is 21

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:**

So, the answer is 10

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:**

So, the answer is 8