Adding Rational Numbers
With the Same Denominator
Add the numerators together and the denominator is maintained.
With a Different Denominator
Properties of the Addition of Rational Numbers
The result of adding two rational numbers is another rational number.
a + b
The way in which the summands are grouped does not change the result.
(a + b) + c = a + (b + c)
The order of the addends does not change the sum.
a + b = b + a
4. Additive identity:
The 0 is the neutral element in the addition because every number added to it gives the same number.
a + 0 = a
5. Additive inverse:
Two numbers are opposites if they are added together and the result is zero.
a + (−a) = 0
The opposite of the opposite of a number is equal to the same number.
As a result of these properties, the subtraction of two rational numbers is defined as the addition of the minuend plus the opposite of the subtrahend.
a − b = a + (−b)