Properties of addition of rational numbers :
Students who would like to practice problems on adding rational numbers must be aware of the properties of adding rational numbers.
There are some properties of rational numbers like closure property, commutative property and associative property.
Let us explore these properties on the binary operation addition.
The sum of any two rational numbers is always a rational number. This is called ‘Closure property of addition’ of rational numbers. Thus, Q is closed under addition
If a/b and c/d are any two rational numbers, then (a/b) + (c/d) is also a rational number.
2/9 + 4/9 = 6/9 = 2/3 is a rational number.
Addition of two rational numbers is commutative.
If a/b and c/d are any two rational numbers,
then (a/b) + (c/d) = (c/d) + (a/b)
2/9 + 4/9 = 6/9 = 2/3
4/9 + 2/9 = 6/9 = 2/3
Hence, 2/9 + 4/9 = 4/9 + 2/9
Addition of rational numbers is associative.
If a/b, c/d and e/f are any three rational numbers,
then a/b + (c/d + e/f) = (a/b + c/d) + e/f
2/9 + (4/9 + 1/9) = 2/9 + 5/9 = 7/9
(2/9 + 4/9) + 1/9 = 6/9 + 1/9 = 7/9
Hence, 2/9 + (4/9 + 1/9) = (2/9 + 4/9) + 1/9
The sum of any rational number and zero is the rational number itself.
If a/b is any rational number,
then a/b + 0 = 0 + a/b = a/b
Zero is the additive identity for rational numbers.
2/7 + 0 = 0 + 2/7 = 27
(- a/b) is the negative or additive inverse of (a/b)
If a/b is a rational number,then there exists a rational number (-a/b) such that
a/b + (-a/b) = (-a/b) + a/b = 0
Additive inverse of 3/5 is (-3/5)
Additive inverse of (-3/5) is 3/5
Additive inverse of 0 is 0 itself.
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