Standard Form of a Rational Number : A rational number is said to be in standard form if the common factor between numerator and denominator is only 1 and the denominator is always positive. Furthermore, the numerator can have a positive sign. Such Numbers are called Rational Numbers in Standard Form. Check out a few examples that illustrate the procedure of expressing Rational Number in Standard Form to be familiar with the concept even better.
What is the Standard Form of a Rational Number?
Usually, a rational number a/b is said to be in standard form if it has no common factors other than 1 between the numerator and denominator alongside the denominator b should be positive.
How to Convert a Rational Number into Standard Form?
Go through the below-listed guidelines to express a Rational Number into Standard Form. The Detailed Procedure is explained for better understanding and they are along the lines
Step 1: Have a look at the given rational number.
Step 2: Firstly, find whether the denominator is positive or not. If it is not positive multiply or divides numerator and denominator with -1 so that the denominator no longer remains negative.
Step 3: Determine the GCD of the absolute values of both numerator and Denominator.
Step 4: Divide the numerator and denominator with the GCD obtained in the earlier step. Thereafter, the rational number obtained is the standard form of the given rational number.
Solved Examples
1. Determine whether the following Rational Numbers are in Standard Form or Not?
(i) -8/23 (ii) -13/-39
Solution:
-8/23 is said to be in Standard Form since both the numerator and denominator doesn’t have any common factors other than 1. In fact, the denominator is also positive. Thus, the given rational number -8/23 is said to be in its Standard Form.
-13/-39 is not in standard form since it has common factor 13 along with 1. Moreover, the denominator is not positive. Thus we can say the given rational number is not in standard form.
2. Express the Rational Number 18/45 in Standard Form?
Solution:
Given Rational Number 18/45
Check for the denominator in the given rational number. Since it is positive you need not do anything.
Later find the GCD of the absolute values of numerator 18, denominator 45
GCD(18, 45) = 9
Thus, to convert the given rational number 18/45 to standard form simply divide both the numerator and denominator by 9
18/45 = (18÷9)/(45÷9)
= 2/5
Therefore, 18/45 expressed in standard form is 2/5.
3. Find the Standard Form of 12/-18?
Solution:
Given Rational Number is 12/-18
Check for the denominator in the given Rational Number
Since the denominator, -18 has a negative sign multiply both numerator and denominator with -1 to make it positive.
12/-18 = 12*(-1)/-18*(-1)
= -12/18
Find the GCD of absolute values of both numerator and denominator
GCD(12, 18) = 6
To convert a given rational number to its standard form multiply and divide both numerator and denominator by 6.
-12/18 = ((-12)÷6)/(18÷6)
= -2/3
Thus, the standard form of Rational Number 12/-18 is -2/3.
4. Reduce 3/15 to Standard Form?
Solution:
Given Rational Numbers is 3/15
Since the denominator is positive you need not do anything to change it to positive.
Find the GCD of absolute values of numerator and denominator of the given rational number.
GCD(3, 15) = 3
Divide numerator and denominator with GCD obtained.
3/15 = (3÷3)/(15÷3)
= 1/5
Therefore, 3/15 Reduced to Standard Form is 1/5.
