In the previous write-up, we learnt how to read and write a fraction. Here, we will understand what does a fraction mean.
A fraction is a ratio of two natural numbers and written as p/q, where q is not equal to zero. A fraction consists of two parts, numerator and denominator, where denominator is not equal to zero.
Assumption:- p/q is a collection of p number of equal sized objects and the size of each object is 1/q unit. Collectively, the size of all the objects is p/q units.
Explanation:- The numerator part of the fraction represents the number of equal sized objects or group of objects whereas the denominator part of the fraction represents the size of each object or group of objects. and the fraction represents collectively the size of all the objects or groups of objects. let’s take some examples to understand the concept better.
Example 1:– 3/4 – A collection of three equal sized objects, where the size of each object is 1/4 and collectively the size of all the objects is 3/4.
3/4 = 1/4 + 1/4 + 1/4 (three objects of the same size)
Example 2:- 7/6 meters – A collection of seven equal sized objects, where the size of each object is 1/6 meters and collectively the size is 7/6 meters.
7/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 (seven objects of same size)
Example 3:- 4/5 students – A collection of four equal sized group of students, where the size of each group of students is 1/5 of the total number of students (unit size) and collectively the size of all the groups of students is 4/5.
4/5 = 1/5 + 1/5 + 1/5 + 1/5 (four groups of students of the same size)
Example 4:- 4/3 of a cake. A collection of four equal sized cakes, where the size of each cake is 1/3 of one whole cake (unit size) and collectively the size of all four cakes is 4/3. Let’s explore it further. Take a cake and first divide it into three equal parts. Each part represents 1/3 of the cake. Now take one more piece of cake of the same size 1/3. Total pieces of cake are four now and the size of each piece is 1/3. Therefore, the collective size of all four pieces of cake is 4/3.
4/3 = 1/3 + 1/3 + 1/3 + 1/3 ( four pieces of cake of the same size)