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.
After having gone through the stuff given above, we hope that the students would have understood "Properties of addition of rational numbers".
Apart from the stuff given above, if you want to know more about "Properties of addition of rational numbers", please click here
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
MATH FOR KIDS
HCF and LCM word problems
Word problems on quadratic equations
Word problems on comparing rates
Converting repeating decimals in to fractions