# Multiplication of Natural Numbers

To multiply two natural numbers, add one factor to itself many times as indicated by the other factor.

### a · b = c

The terms a and b are calle factors and the result, c, is the product.

### Properties of the Product of Natural Numbers

1. Closure:

The result of multiplying two natural numbers is another natural number.

a · b

2. Associative:

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

(a · b) · c = a · (b · c)

(2 · 3) · 5 = 2 · (3 · 5)

6 · 5 = 2 · 15

30 = 30

3. Commutative:

The order of the factors does not change the product.

a · b = b · a

2 · 5 = 5 · 2

10 = 10

4. Multiplicative Identity:

The 1 is the neutral element of the multiplication because any number multiplied by it gives the same number.

a · 1 = a

3 · 1 = 3

5. Distributive:

The multiplication of a natural number and a sum is equal to the sum of the multiplication of the natural number for each of the addends.

a · (b + c) = a · b + a · c

2 · (3 + 5) = 2 · 3 + 2 · 5

2 · 8 = 6 + 10

16 = 16

Removing a common factor:

It is the reverse of the distributive property.

a · b + a · c = a · (b + c)

2 · 3 + 2 · 5 = 2 · (3 + 5)

6 + 10 = 2 · 8

16 = 16

Multiplication table