Additive properties of rational numbers
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Rational numbers, integers and whole numbers are non commutative under subtraction and division. Role of zero and one- 0 is the additive identity for rational numbers.
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Associative property of addition of rational numbers:
While adding three rational numbers, they can be grouped in any order.
Thus, for any three rational numbers a/b, c/d and e/f, we have
(a/b + c/d) + e/f = a/b + (c/d + e/f)
For example:
Consider three rationals -2/3, 5/7 and 1/6 Then,
{(-2/3 + 5/7) + 1/6} = {(-14 + 15)/21 + 1/6} = (1/21 + 1/6) = (2 + 7)/42
= 9/42 = 3/14
and {(-2/3 + (5/7 + 1/6)} = {-2/3 + (30 + 7)/42} = (-2/3 + 37/42)
= (-28 + 37)/42 = 9/42 = 3/14
Therefore, {(-2/3 + 5/7) + 1/6} = {-2/3 + (5/7 + 1/6)}
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