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
