Multiplying Rational Numbers
The product of two rational numbers is another rational number that has:
As a numerator, the multiplication of the numerators.
As a denominator, the multiplication of the denominators.
Properties of the Multiplication of Rational Numbers
The result of multiplying two rational numbers is another rational number.
a · b
The way in which the factors are grouped does not change the result.
(a · b) · c = a · (b · c)
The order of the factors does not change the product.
a · b = b · a
4. Multiplicative Identity:
The 1 is the neutral element in the multiplication because every number multiplied by it gives the same number.
a ·1 = a
5. Multiplicative inverse:
A number is the reciprocal of another if multiplied by each other, the product is the muliplicative identity.
The product of a number and a sum is equal to the sum of the products of this number for each of the addends.
a · (b + c) = a · b + a · c
Removing a common factor:
It is the reverse of the distributive property.
a · b + a · c = a · (b + c)