Properties Of Rational Numbers With Examples
Properties Of Rational Numbers With Examples
Rational numbers are the numbers which can be expressed in the form of p/q , where p and q
are the integer numbers and q <> 0.
There is a big list of Properties of rational numbers. Some of them are :
1. Identity Property of Rational Numbers.
2. Commutative property of rational numbers.
3. Associative property of rational numbers.
4. Closure property of rational numbers.
5. Dense property of rational numbers.
6. Property of zero.
Here we will study about Identity Property of Rational Numbers:
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a) Identity Property of Addition for Rational Numbers: According to this property, we say
that there exist a number 0 , which is cal ed Additive Identity, in which we say that if 0 is added
to any rational number, the result remains same. I.e. if p1/q1 is the rational number, then
p1/q1 + 0 = p1/q1
For example : if 4/7 is added to 0, the result is 4/7 itself
4/7 + 0 = 4/7
0 indicates additive identity, which means that if any rational number is added to its inverse,
we get the additive identity.
To find the additive inverse of any number the sign of the number is changed. SO we can say
that additive inverse or p/q is -p/q.
Let us take a rational number 3/7, its additive inverse will be -3/7. So we can say that if 3/7
and -3/7 are added we get 0 ( which is the additive identity).
Mathematically it is written as 3/7 + (-3/7) = 0
Again if -9 is the rational number , then -( -5) = 5 is its additive inverse. Thus we come to a
conclusion that -5 + ( 5 ) = 0
b) Identity Property of Multiplication for Rational Numbers: According to this property, we
say that there exist a number 1 , which is cal ed Multiplicative Identity, in which we say that if 1
is multiplied to any rational number, the result remains same. I.e. if p1/q1 is the rational
number, then p1/q1 * 1 = p1/q1
For example : if 4/7 is multiplied by 1, then the result is 4/7 itself
4/7 * 1 = 4/7
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1 indicates multiplicative identity, which means that if any rational number is multiplied to its
inverse, we get the multiplicative identity.
To find the multiplicative inverse of any rational number p/q, we change the numerator to
denominator and denominator is changed to numerator, i.e. q/p is the multiplicative inverse.
We can also get the multiplicative inverse of any number by dividing the number 1 by the
given rational number. Lets say 5 is the rational number, its multiplicative inverse wil be 1/5..
So we can sat 5 * 1/5 = 1
Let us take a rational number 3/7, its multiplicative inverse wil be 7/3. So we can say that if
3/7 and 7/3 are multiplied we get 1 ( which is the multiplicative identity).
Mathematically it is written as 3/7 * 7/3 = 1


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