Properties of Rational Numbers (PDF)

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					        Properties of Rational Numbers
Properties of Rational Numbers

The rational numbers are closed under addition, subtraction, multiplication and
division by nonzero rational numbers. The properties are called closure
properties of rational numbers.

If 'm' and 'n' are two rational numbers then the addition, subtraction,
multiplication and division of these rational numbers is also a rational number,
then these numbers satisfy the closure law.

Let’s take an example of addition which satisfies the closure properties, 3+4=7
shows the closure property of real number addition because when we add the
real numbers to other real numbers the result is also real.


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This condition is necessary for all other operations like subtraction,
multiplication and division.

Identity Property of Rational Numbers

Rational numbers are the numbers which can be expressed in the form x/y,
provided y is not equal to zero and x,y are integers. Apart from the addition,
subtraction, multiplication and division, rational numbers show a specific
property which is called identity of rational numbers and such numbers are
called identity property of rational numbers.

There are two types of identity properties of rational numbers which are as
follows:

1. Additive identity

2. Multiplicative identity Additive Identity of rational numbers: Additive identity of
a rational number is basically a real number which when added to a rational
number does not change its value,

zero is called the additive identity for all rational numbers, for example let’s say
“Q” is a rational number equal to a/b Also if we add '0' to this rational number
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Q+0 = Q or a/b+0 = a/b, as we see from the result we get the same rational
number that is why zero is called the additive identity of rational numbers.
Multiplicative Identity:

Multiplicative identity of a rational number is such a real number which when
multiplied by a rational number, its value remains unchanged, '1' is called the
multiplicative identity for all rational numbers,

ex. Q×1 = Q, or a/b ×1 = a/b, as we can see from the example when rational
number 'q' is multiplied by 1, its value remains unchanged that is why 1 is called
the multiplicative inverse of rational numbers.
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posted:3/28/2012
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