Improper Fractions

Fractions form an integral part of our lives. Fraction is part of a whole. Hence, in a fraction we have two numbers. One on the top called numerator and the other on the bottom called denominator.
We classify fractions as proper fractions and improper fractions based on the values of numerator.

Improper fractions: 
Fractions with numerator greater than the denominator are called improper fractions.
Example: 13/4, 12/5
How to simplify improper fractions:
This is nothing but reducing improper fractions.
As the numerator is greater than the denominator in improper fractions, when we do the long division of this fraction, we will be getting a quotient greater than 1 and a remainder.
We can generalize the simplification by an algorithm:
Step 1: Perform the long division
Step 2:
Example: Simplify the improper fraction 18/7

Step 2:  Simplified form of the mixed fraction is


Improper fractions:

Improper fractions have two parts on simplification. The part which does not have denominator is called whole part and the part with denominator is called fractional part. The other name for the simplified improper fraction is mixed fraction.
Mixed fraction has both whole number part and a fractional part.

Adding improper fractions:
We adopt four steps to add improper fractions.
Step 1: Find the Least common multiple of the denominators
Step 2: Find the equivalent fractions of individual fractions such that the denominators of both the fractions are same.
Step 3: Add both the numerators and write the common denominator
Step 4: Simplify the improper fraction if need be
Example: 11/3 + 5/4
(11 x 4)/(3 x 4) + (5 x 3)/ (4 x 3)
= (44/12) + (15/12)
= 59/12
=4 11/12

Multiplying Improper Fractions
In this, the method adopted is as same as in multiplication of proper fractions. We follow three steps to evaluate the product of two improper fractions.
Step 1: Multiply both the numerators and write the result in numerator
Step 2: Multiply both the denominators and write the result in denominator
Step 3: Simplify if need be
Multiply 15/7 and 4/3
Step 1: Numerator = 15 x 4 = 60
Step 2: Denominator = 7 x 3 = 21
Step 3: Required product = 60/21 = 3 x 20/ 3 x7 = 20/7 = 2 6/7

Dividing Improper Fractions
In this as well, we follow the general rules of division of fractions.
Step 1: Write the first fraction
Step 2: Find the multiplicative inverse of the second fraction
Step 3: Multiply the results of steps 1 and 2 following the algorithm of multiplication of fractions.
Example:
Divide 15/ 7 by 4/3
Step 1: 15/7
Step 2: Multiplicative inverse of 4/3 is ¾
Step 3: 15/7 x 3/4 = (15 x 3)/ (4 x 7) = 45/28.
What is an improper fraction?
Improper fractions are those whose numerators are greater than denominators. The value of improper fractions is always greater than one.