
Set of Rational Numbers Q={x/x =p/q, p, q¹0 are relatively prime integers}.
Properties of Rational Numbers in AdditionCommutative property: For any two rational numbers a/b, c/d we have a/b+c/d = c/d+a/b where a, b, c, d are integers and b, d are not equal to zero. Associative Property:For any three rational numbers a/b, c/d, e/f we have a/b+(c/d+e/f) = (a/b+c/d)+e/f, where a, b, c, d, e, f are integers and b, d, f are not equal to zero. Identity: For any rational number a/b where b¹0, we have 0+a/b = a/b+0 = a/b. Here zero is the identity element for addition in rational numbers. Inverse: For any nonzero rational number p/q there exists a unique rational number p/q such that p/q+(p/q) = 0. p/q, p/q are additive inverses. Each one is called the additive inverse of the other. Properties of Rational Numbers in MultiplicationFor any two rational numbers a/b c/d their product a/b*c/d is also a rational number.
Commutative Property:
Associative Property:
Identity:
Inverse: If the product of two numbers is one, we say that each number is the multiplicative inverse of the other(Except for zero). Directions: Answer the following questions. Also write five examples of each property. 