# Addition of Natural Numbers

**a + b = c **

The terms of the addition, **a and**** b,** are called** addends **and the result, **c is the sum**.

### Properties of the Addition of Natural Numbers

1. **Closure**:

The sum of** two natural numbers** is also a ** natural number**.

**a + b **

**2. Associative**:

The way in which the addends are grouped does not change the result.

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

(2+3) + 5 = 2 + (3+5)

5 + 5 = 2 + 8

10 = 10

**3. Commutative**:

The order of the addends does not change the addition.

**a + b = b + a **

2 + 5 = 5 + 2

7 = 7

**4. Additive identity**:

**The 0 is the identity element** of the addition because every number added with it gives the same number.

**a + 0 = a **

3 + 0 = 3

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