Which of the following statements is NOT true with respect to the concept of Fractions ?

The correct option is It represents a part of a whole which is greater than 1.

Let us analyze the concept of fractions to understand why this statement is NOT true:

1. Definition of a Fraction:
A fraction represents a part of a whole or a part of a collection of objects. When referring to a single whole object, the whole is considered as 1 complete unit. Therefore, a fraction representing a part of a whole represents a quantity less than or equal to 1 (or equal to 1 when considering the entire whole). It does not represent a part of a whole that is greater than 1.

2. Analysis of the given statements:
• "It represents a part of a collection of same objects" - True. For example, 3 out of 5 apples in a basket can be represented as $\frac{3}{5}$ of the collection.
• "The mathematical notation of a fraction can be represented as a ratio" - True. A fraction such as $\frac{\mathrm{a}}{\mathrm{b}}$ expresses the ratio of part $$a to whole $$b (i.e., $$a : b).
• "The mathematical notation of a fraction can be represented as a division problem" - True. The fraction $\frac{\mathrm{a}}{\mathrm{b}}$ literally means $$a ÷ b.
• "It represents a part of a whole which is greater than 1" - NOT True. A single whole equals 1. A part of that single whole must be less than or equal to 1.

Hence, the statement that is NOT true with respect to fractions is "It represents a part of a whole which is greater than 1".