Addition of Rational Expression

Numbers which can be expressed in form of p / q where p and q are integers and q < > 0 are called rational numbers.  Rational expressions are the  expressions which consists of rational numbers. Various mathematical Operation on Rational Expression can be done like addition, subtraction, multiplication and division. We can do all operations on Rational numbers.
On doing addition of Rational Expressions, the output is also a rational number. In order to do Addition of Rational Expression, we first need to make the denominators of the operands same. For this we will first take the L.C.M. of all the denominators given in the expression. Then we try to replace all the denominators with the L.C.M.
For this we multiply both numerator and the denominator with some of the factors of the denominator, so that the denominator is the L.C.M. now. Then we proceed to the addition of the numerators, keeping the denominators same.
Let us look at the example:
Solve the given Rational Expression:   2 +  4/5  + (-3/10)
 Here we observe the three denominators are 1, 5 and 10. L.C.M. of these three numbers is 10.
So to make the denominator of 2 as 10, we multiply num. and denominator by 10
To make the denominator of  (4/5 ) as 10, we multiply both numerator and denominator by 2 and
 ( -3 / 10 ) already has 10 as the denominator.
Now we proceed:
 = 2 +  4/5  + (-3/10)
 = 2 *10/10   + ( 4 * 2 ) / (5 * 2 )   + ( -3 /10)
= 20 /10   + 8 /10 + (-3 /10 )
 = ( 20 + 8 -3 ) / 10
= 25 /10
= 5 / 2 Ans.

This is all about addition of rational numbers. In the nest article we will deal with Division of Rational Expressions.

Division of Rational Expressions

Rational numbers can be written in the form of p / q where p and q are integers and q <> 0. rational expressions is the series of rational numbers combined together with mathematical operators.  We can perform all mathematical operations namely addition, subtraction, multiplication and division on rational expressions and it comes under andhra pradesh board of secondary education. Division of Rational Expressions is very simple and follow a set pattern of steps. Before we start dividing rational expression, we will first understand the concept of reciprocal of rational number. By reciprocal of a rational number, we mean dividing 1 by a rational number. For instance:
  reciprocal of 4 / 7  = 1/ (4/7)
                                     = 7/4.
Always remember there is no reciprocal of zero (0) and reciprocal of 1 is always 1.
While dividing rational expression, we first  write the reciprocal of divident and replace divide sign by multiplication
Further, the sum changes into simple sum of multiplication and the numerator is multiplied by numerator, denominator by a denominator.
eg:  (-3/5) ÷ (4/10)
 we see that reciprocal of 4/10 is 10 / 4, so the above sum becomes :
= (-3/5) * (10/4)
= ( -3 * 10 ) / ( 5* 4)
= -30 /20
converting into lowest term we get
= -3 / 2 Ans.
Like division there are many rational expressions applications, Sometimes division of Rational Expression becomes the part of the expression with other operators. In such cases, we follow the rule of DMAS, where
D- stands for Division,
M- stands for Multiplication
A- stands for subtraction
S- stands for subtraction .
It means that division is the first mathematical operation to be followed in the given expression which is to be simplified.(want to Learn more about Rational Expressions,click here),
eg (-2/5) ÷ (2/6) * (3/7)
 First we solve (-2/5) ÷ (2/6)
                     = (-2/ 5) * (6/2 )
                     = (-2 * 6 ) / ( 5* 2)
                     = -12/10
 Ptting this in given equation we get:
     = ( -12/10) * ( 3/7)
= (-12 * 3) / (10 * 7)
= -36 /70
= -18/ 35 Ans.
This is all about the Division of Rational Expressions  and if anyone want to know about Simplifying Rational Expressions then they can refer to Internet and text books for understanding it more precisely.Read more maths topics of different grades such as Compound Inequalities in the next session here.