Representing Rational Numbers using Scientific Notations

Rational numbers are the result of two integers or they can be represented in simple fraction form with the numerator and the denominator. They are the ratio of two integers like a/b. Rational number are countable numbers. In addition and subtraction we have to equalize the denominator but in multiplication and division there is no need to equalize the denominator. Let’s take some example of addition and subtraction:-

Note:-For adding and subtracting rational expressions we have to find LCMs of polynomials.

First take an example for addition when the denominator is equal:

A/C +      B/C   =   (A + B)/c

Now take an example of polynomials expression for adding.

= 5a/4a+1 + (11a + 4)/4a +1    

In the first step we will combine numerators together and in second step we will take the LCM of denominators if both denominator are same than LCM will also same.

= 5a/4a+1 + (11a + 4)/4a +1    

= (5a + 11a + 4)/4a + 1, in this we have combined numerators and common denominator

= 16a + 4/4a +1

Now we will reduce the above expression to the lowest term

16a + 4/4a +1

Common factor out 4

4(4a + 1)/4a +1

Divide out the common factor of 4a + 1

= 4

Let’s talk about subtraction of rational number:-

A/C -  B/C = (A – B)/C

Subtraction of polynomials expression:-

(4a² - 3a + 1)/a -   (3a² - 4a + 11)/a

First step will be same as I mention above, combine numerators together and in the next step put the common denominator over step 1

(4a² - 3a + 1- 3a² - 4a + 11)/a

Subtract every term of second num

(a^{2 –} 7a + 12)/ a

Then reduce the lowest term

a²- 7a +12

a now no common factor, so,

(a – 3) (a – 4).

Thus we can say, for adding and subtracting rational expressions we need to be able to find LCMs of polynomials.