Question

rational number properties under addition and division

Answer 1

hi,
The property of rational number under addition :-
you know how to add two rational numbers.Let us find a few pairs here.
-2/3+5/7=1/21and5/7+{-2/3}=1/21
so, -2/3+5/7=5/7+{-2/3}
you find that two rational numbers can be added in any order. we we say that addition is commutative for rational numbers. That is, for any two rational numbers a and b, a+b=b+a.
property of rational number under Division :-
is -5/4÷3/7=3/7÷[-5/4]?
you will find that expression on both sides are not equal.
so division is not commutative for rational numbers.
Thanks.. hope it helps.

Answer 2

over addition
1. closure :a/b +c/d is a rational number
2. commutative : a/b + b/c =b/c +a/b
3. associative : a/b + (b/c+ c/d ) = (a/b +b/c) +c/d they can be grouped in any order
4, property of 0: a/b +0 =a/b+0=a/b
5. negative of a rational number: if a/b is a rational number then (-a/b) is a rational number such that a/b + (-a/b)= 0
-a/b is the negative inverse of a/b

over division
1. if a/b and c/d are two rational numbers than a/b / c/d = a rational number
2. for any rational number a/b , a/b /1 =a/b and (-a/b)/1= -a/b
3. for every non zero rational number a/b , a/b / a/b = 1, (-a/b) / a/b = -1
a/a / (-1) = -a/b