Operations with Integers and Rational Numbers
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Operations with Integers and Rational Numbers
If we look at any integer say 7, we find that 7 can be written as 7 /1, where 7
and 1 both are integers and the denominator 1 < > 0. So 7 is absolutely
expressed in form of a rational number.
Now, in this we are going to learn about operations with integers and rational
numbers. All mathematical operations namely addition, subtraction,
multiplication and division can take place with both integers and rational
numbers.
As integers all the properties of addition namely closure, commutative,
associative satisfy with rational numbers too.
There exist an additive identity 0 (zero), such that we add 0 to any rational
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number, the rational number remains unchanged. Similarly, there exists an
additive inverse for every rational number such that the sum of the number and
its additive inverse is zero.
In the same way, all subtraction properties of integers satisfy with rational
numbers.
To divide one rational number by another, we will convert the dividend to its
reciprocal and then the sum of division converts to the simple sum of
multiplication, which can be solved easily.
When we find the sum or the difference of any two rational numbers, we need to
first find the LCM of the denominators. On finding the LCM of denominators, we
change the rational number to its equivalent rational number such that the
denominator becomes equal to the LCM.
Finally addition or subtraction of the numerator can be done. Moreover to find
the product of two rational numbers is very easy. To look into it, we simply need
to multiply the numerator with the numerator and the denominator with the
denominator.
On getting the new rational number as the product, we convert it to the standard
form.
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