Standard Form of a Rational Number- How to create it.

 In this article, we will learn how you can easily create a standard form of a rational number if it is not given in the standard form.

A Rational number is said to be in standard form if and only if,

1. The numerator and denominator are co-prime , I. E., they should have no common factor other than 1.

2. The denominator of a rational number is positive.

For example-  

5/9 is written in the standard form of a rational number.

Because both 5 and 9 are co-prime numbers and its denominator 9 is positive. 

STEPS TO CONVERT GIVEN RATIO INTO AN STANDARD FORM-

METHOD 1- 

# Divide the numerator and the denominator of the given rational number by their common factors until the numerator and denominator become co-prime.

We can best understand by taking an example- 

Q. Convert 32/48 into a standard form.

Pick such number through which both numbers 32 and 48 can be divided I. E, 2

= 32÷2/ 48÷2  = 16/24 

Again pick such number through which both numbers can be divided I. E., again 2

= 16÷2/ 24÷2  = 8/12 

again, 8 ÷ 2/ 12÷2 = 4/6

again, 4÷2/ 6÷2 = 2/3

Now, both numbers 2 and 3 can't be easily divisible by any number except 1 I. E., both become co- prime so, this became standard form 

I.e., The standard form of 32/48 is = 2/3.

Q.Convert rational no. 48/72 into an standard Form. 

= 48/72 = 48÷2/72÷2 = 24/36 = 24÷2/36÷2 = 12/18 = 12÷ 2/ 18÷2 = 6/9 = 6÷3/9÷3 = 2/3 

Now, 2/3 both numbers 2 and 3 are not divisible by any number other than 1 so, it become the standard form.

METHOD 2- 

Divide  the numerator and the denominator  of the rational number by the HCF of the numerator and and the denominator.

Ex- Convert 12/16 into an standard Form. 

=Take HCF of 12 and 16 =4 

Now, divide by 4 in numerator and denominator.

= 12÷4/ 16÷4  = 3/4 

Now, both numbers are not divisible by no any number except 1 I. E., 3 and 4 are co- prime numbers, 

Hence , 3/4 is the standard form of 12/16.

METHOD 3: 

If the denominator of the given rational number is a negative number, then multiply the numerator and the denominator by -1.

For example- 

4/-9  = 4 × -1/ -9 ×-1  = -4/9 

Note- if denominator is negative then only you need to multiply by -1 in numerator and denominator .

Q1. Does Rational no. 7/8 ,into an standard Form. 

= Yes, 7 and 8 are co- prime and the denominator is positive. 

Q2. Does 6/-35, into an standard Form. 

= No, 6/ -35 is not written into an standard Form even though 6 and 35 are co- prime but due to denominator is present in negative.

Standard form of 6/-35 = 6×-1/ -35×-1 = -6/35 

Q3. Does 8/12 ,into an standard Form. 

= Since, it is not in standard form because they have 2 and 4 as common factors.

8÷4/12÷4 = 2/3 , The standard form of 8/12 is 2/3.

Q4. Does 39/91 into an standard form. 

= No, because both are divisible by 13 so, it is not written into an standard Form. 

Standard form of 39/91 = 39÷13/91÷13 = 3/7

Q5. Does 4/6  into an standard Form. 

= No, it is not written into an standard Form. 

Because both numbers are divisible by 2.

= 4÷2/6÷2 = 2/3  Now,  it is in standard form because both numbers are co- prime.

Q6. Is 4/-9 is written in Standard form?

= No, because number present in the denominator is negative due to this it is not in standard form.

Now, for converting it into an standard Form multiply by -1 in numerator and denominator simultaneously.

= -1×4/-1×-9  = -4/9