Theory:

1. Dividing a fraction by another fraction:
To divide a fractional number with another fractional number, follow the steps below:
 
Step 1: Take the reciprocal of the divisor.
 
Step 2: Multiply the reciprocal of the divisor with the dividend to get the new numerator and denominator of the fraction.
  
Reciprocal of a fraction: The reciprocal of a fraction can be obtained by interchanging the numerator and denominator of the fraction. For example, reciprocal of 12 is 21 The non-zero numbers whose product with each other is \(1\) are called the reciprocals of each other that is, 12×21=1. Hence, 12 and 21 are reciprocals of each other.
 
Let us find the value of 1256=?
 
Step 1: Take the reciprocal of divisor (56)=65.
 
Step 2: Multiply the dividend (12) by 65=12×65=35
 
\(\frac{\text{New Numerator}}{\text{New Denominator}}\) \(=\) 35
2. Division of the whole number by a fraction:
Dividing a whole number by a fraction will follow the same procedure as dividing a fraction by another fraction.
Example:
Let us find 1÷14
Step 1: Reciprocal of the divisor, 14 is 41
Step 2: Multiply the dividend (\(1\)) by 41=1×4=4.
3. Division of a fraction by a whole number:
Dividing a fractional number by a whole number will follow the same procedure as dividing a fraction by another fraction.
Example:
Let us find 14÷1.
 
Step 1: Reciprocal of the divisor, \(1\) is \(1\).
 
Step 2: Multiply the dividend 14 by 1=14.
4. Division of mixed fractions:
First, convert the mixed fractions to improper fractions and divide the fractions.
Example:
Convert 4105 to an improper fraction.
 
Step 1: Numerator of improper fraction \(=\) (denominator of the proper fraction \(×\) whole number) \(+\) numerator of a proper fraction.
 
\(= 5 × 4 = 20 + 10 = 30\).
 
Step 2: Denominator of improper fraction \(=\) denominator of the mixed fraction.
 
The denominator of improper fraction \(= 5\).
 
Improper fraction \(= 30 / 5 = 6\).
 
Thus,  4105 \(= 6\).