Definition:
The Number which can be written in the form : p/q where p and q are integers and q ≠ 0, is called Rational Numbers. For Example : -2/3 , 4/7 , 3/5 , 4 , 7 etc. Here 4 and 7 are also Rational Numbers because it can be written in the form of p/q . We can write it as 4/1 or 7/1 .
What is the use of Rational Numbers?
In Mathematics, we frequently come across simple equations to be solved , For example , the equation
x + 2 = 5
is solved when x=3 , because this value x satisfies the given equation. the solutions 3 is natural number. On the other hand , for the equation:
x + 3 = 3
The solutions gives the Whole Number 0(zero). If we consider only natural numbers above equation cannot be solved. To Solve this type of equation we added number zero to the collection of natural numbers and obtained the whole numbers. Even whole numbers will not be sufficient to solve equations of type
x + 15 = 3
Above equation is solved when x = -12 , which is not whole number. This led us to think of integers (positive and negative) . Now consider the equation:
3x = 5
2x + 3 = 0
for which we cannot find solution from the integers.
We need the numbers 5/3 and -3/2 to solve above equation. This leads us to the collection of Rational Numbers.
Adding Two Rational Numbers:
Example: 1
5/7 + 2/5
In above example , there are two denominator 7 and 5 , We need LCM of these two numbers, And here it is 35. We use following method to solve this.
We get following result after calculate
It is our answer. Let's take some more example for practice.
Example : 2
Example : 3
Example : 4
Multiplication of Two Rational Numbers:
Multiplication and division of Rational Numbers are more easy than addition , Let's take some examples...
Example: 1
Example: 2
Some More Examples :
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