Theory:

"On the way to school today, Roshni looked at several things such, a bus, only half-filled with school children, a bus driver filling only a quarter of his fuel tank, a sweet and crunchy biscuit being shared equally among twin sisters. And, 'buy $$1$$ get $$2$$' offer for upcoming Christmas sale at the nearby shopping mall. While observing all these things, Roshni was half an hour late to her class.

Things Roshni observed are related to the concept of 'Fraction' in one way or another. While watching such things closely, Roshni realised that she was already introduced to this concept by her teacher. She saw the beauty of mathematics, every time she correlated the idea of fraction in daily life.

Introduction to fractions is an exciting concept in Mathematics. We do use the theory of FRACTIONS in our daily life with or without our knowledge."
Example:
1. To express time as quarter past 7, half past 3, and quarter to 10.

2. To mention the distance as half kilometre, 7 and half kilometre.

3. We use fractions to express the scores and marks of examination $\frac{450}{500}$.

4. To express progress or decline, we use fractions such as our economy contracted half percentage in this financial year.

5. We use a fraction to mention how much work has been completed, such half of the work, one third of the work.

6. We apply the fractions method to distribute the food such as a pizza and cake.
Let's dive into another example to understand this quite well.

David's friend visited his house. And his mother wanted to give an orange fruit to them. But she had only one orange.

If James came alone without his friends, she could have given the entire orange, but he did not. So she had to separate that fruit and gave it to them. But the question is, how?

She can separate the whole orange into four parts for the four people. Simply we are dividing one orange into four parts, that is $$1/4$$. If we are splitting in three parts, then the fraction is $$1/3$$.

What is mean by fraction?
A word fraction derived from the Latin word 'fratus' which means 'broken'. The Egyptians were the first people used fractions in about $$4000$$ years ago.
• Fraction is part of a whole number or a collection of certain things.
• Any number can be written as fractions. Fractions are a representation of the ratio between two numbers (numerator and denominator).
• It can be represented as $$p / q$$ where $$p$$ and $$q$$ are whole numbers, and $$q$$ $$≠$$ $$0$$ is known as a fraction.
Let us consider any number, say $$10$$, we can write it as $$10/1$$ or $$20/2$$ or $$50/5$$

Now let us consider any decimal, say $$0.5$$, we can write it as $$1/2$$ or $$2/4$$ or $$10/20$$

Hence, we say a fraction is a way of denoting a number in division form.

The number $$1$$ can be separated into two parts, that is $$(1/2) + (1/2)$$ or separated by four equal parts $$(1/4) + (1/4) + (1/4) + (1/4)$$
Example:
A pizza can be split into four pieces for four people, which is in a fraction of $$(1/4)$$. For two people, it can be split into two pieces $$(1/2)$$.

Now we gathered the basic idea of fractions and how we are using it in daily life. In the upcoming lessons, we will learn the types of fractions and other concepts related to fractions.