Question

Explain about all the properties in rational numbers like closure, commutativity, associativity and distributive.
Also proof it by giving examples.

Answer 1

commutative property_ addition) a+b =b+a
3+4=4+3 7=7
_ multiplication)a×b=b×a
3×4=4×3 12=12

asociative property_addition)(a+b)+c=a+(b+c)
(2+3)+4=2+(3+4)
5+4 = 2×7
9 =9
_ multiplication) (a×b)×c=a×(b×c)
(2×3)×4 = 2×(3×4)
6×4 = 2×12
24 = 24

distrbutive prop. addition)a×(b+c)= a×c+a×c
10×(12+14) =10×12+10×14
120+140
160



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