Question

write five properties of rational numbers with example on each​

Answer 1

Answer:

Five Properties of Rational numbers are listed below:

Step-by-step explanation:

1) Properties of addition of rational numbers;

i) closure property: If two rational numbers are added together , the result will always be a rational number.

for example: 3/4 +5/6 = 9/12+ 10/12= 19/20(which is a rational number)

Hence property proved.

ii)Commutative property: the addition of any two rational numbers is commutative. That is a/b +c/d = c/d + a/b

for example: 3/4+5/6 = 9/12 + 10/12 = 19/ 20

now lets see if 5/6 +3/4 is also the same => 5/6+3/4 = 10/12 + 9/12 = 19/20

:. 3/4+5/6 = 5/6 +3/4

Hence property proved.

iii) Associative property- The addition of rational numbers is associative. that is a/b + (c/d + e/f ) = (a/b +c/d ) +e/f

for example: 2/3+(-5/6 +7/12) = 2/3 + ( -10/12 +7/12) = 2/3 +(-3/12) = 2/3-3/12 = 8/12 - 3/12 = 5/12

now lets see if (2/3 +(-5/6))+ 7/12 is also same =>(2/3 +(-5/6))+ 7/12 =                ( 4/6+(-5/6)) + 7/12 = -1/6 + 7/12 = -2/12 + 7/12 = 5/12

:.2/3+(-5/6 +7/12)= (2/3 +(-5/6))+ 7/12

Hence property proved

iv) Existence of additive identity of rational numbers- Additive identity of rational numbers is zro (0). When the additive identity is added to any rational number, it remains the same.

for example: 3/4+0 = 3/4 +0/4 = 3/4

Hence property proved.

v) Existence of additive inverse of a rational number- The opposite  of a rational number is called its additive identity.

For example- 3/5 its additive inverse is -3/5

-5/8 its additive inverse = 5/8

* THE SUM OF A RATIONAL NUMBER AND ITS ADDITIVE INVERSE = ADDITIVE IDENTITY= 0

NOTE- these were just the properties of rational numbers related to addition there are more properties related to subtraction, multiplication and division.

Hope my answer helped you.