The Concept of Fractions
If there is 1 loaf of bread, we can write this as 1.
If there are 2 loaves of bread, as 2.
If there are 3 loaves of bread, as 3, and so on.
In mathematics, each complete item is called a "whole" (represented by whole numbers: 0, 1, 2, 3...).
What if 1 whole loaf of bread is too much for me, and I only need "a part" that is less than 1—for example, half a loaf?
Or what if 1 loaf is not enough, but 2 loaves are too much?
How do we express these values in mathematics?
This is exactly why we need fractions (parts of a whole):
0 → 0 loaves
↓ (we need fractions here: values between 0 and 1)
1 → 1 whole loaf
↓ (we need fractions / mixed numbers here: values between 1 and 2)
2 → 2 whole loaves
In our world, not everything comes in whole amounts. We often need parts of a whole.
Fractions simply represent "parts of a whole".
So, how do we determine the exact mathematical value of a part? How do we know how much it is, or whether it is larger or smaller?
We know that a part is less than 1 whole, but exactly how big is it?
There is no rule that everything less than 1 whole has the same value. For example, 50 pence (50p) and 20 pence (20p) are both less than 1 Pound (£1.00), but they are not the same value!
To know the exact value of a part, let us look at how we divide a whole:
Suppose we divide a whole rectangle into 2 parts in two different ways:
In one, it is cut right down the middle into 2 equal parts.
In the other, one piece is large and the other is small (unequal parts).
Which shape do you think can represent "half"?
Think of it this way: If we call the first piece "half", then the other piece completing the whole would also have to be called "half".
This would create a mathematical contradiction: accepting two completely unequal pieces as equal!
Both pieces would be called "half", but they are clearly NOT equal to each other! In mathematics, this is impossible.
If a piece is cut unequally, is it worth 60 pence, 70 pence, or 80 pence? We cannot know what exact value it represents! Therefore, in order to know the exact mathematical value of parts, they must be divided into equal parts.
Unknown!
Unknown!
Definition of a Fraction:
"When a whole is divided into EQUAL parts, each part is called a fraction."
Only when we divide a whole into EQUAL parts can we be completely certain of the exact mathematical value of each part.
Now let's see how fractions work in the real world!
Examples in Real Life:
Classroom Example (Fractions of a Set): Let us consider our classroom of 20 students as 1 whole set, and divide it into 4 equal groups. Each group has 5 students and represents one equal part of the whole class.
🏫Step 0: Whole Classroom (20 Students)All 20 students together in 1 classroom form 1 Whole Set.
🧑🎓👋 Hi, I'm Tom!🧑🎓👋 Hi, I'm Emma!🧑🎓👋 Hi, I'm Leo!🧑🎓👋 Hi, I'm Maya!🧑🎓👋 Hi, I'm Noah!🧑🎓👋 Hi, I'm Olivia!🧑🎓👋 Hi, I'm Liam!🧑🎓👋 Hi, I'm Ava!🧑🎓👋 Hi, I'm Lucas!🧑🎓👋 Hi, I'm Mia!🧑🎓👋 Hi, I'm Ethan!🧑🎓👋 Hi, I'm Sophia!🧑🎓👋 Hi, I'm James!🧑🎓👋 Hi, I'm Isabella!🧑🎓👋 Hi, I'm Oliver!🧑🎓👋 Hi, I'm Amelia!🧑🎓👋 Hi, I'm Jack!🧑🎓👋 Hi, I'm Charlotte!🧑🎓👋 Hi, I'm Ben!🧑🎓👋 Hi, I'm Zoe!All 20 students together represent 1 Whole Set
Divided into 4 Equal Groups ↓Group 1Waiting...•••••5 students1 Equal Part14of classGroup 2Waiting...•••••5 students1 Equal Part14of classGroup 3Waiting...•••••5 students1 Equal Part14of classGroup 4Waiting...•••••5 students1 Equal Part14of classDivision Progress:0 of 4 parts dividedFraction:04of whole1/41/41/41/4The whole class of 20 students is divided into 4 equal groups. Each group represents one equal part (1/4)!
Money Example: Let us divide 1 Pound (£1.00 = 100 pence) into 5 equal parts:
1 Pound → 20p + 20p + 20p + 20p + 20p.£1.001 Whole Pound (£1.00)= 100 pence (The Whole Amount)Divided into 5 Equal Coins ↓20p20 pence1 Equal Part20p20 pence1 Equal Part20p20 pence1 Equal Part20p20 pence1 Equal Part20p20 pence1 Equal PartFive 20 pence coins together make the whole £1.00. Each coin is one of the 5 equal parts!
Pizza Example: Let us divide a pizza into equal slices.
Divided into 4 equal slices! Each slice represents one equal part of the whole pizza.
💡 A Note on Learning Fractions
In school, teachers often introduce fractions using pizza slices. But remember: a fraction is not just about pizza!
Any whole object, amount of money, number, or measurement in our world can be divided into equal parts and represented as a fraction. Whenever something is a part of a whole, we are looking at a fraction:
- ⏰Time on a clock: 1 whole hour is 60 minutes. Half an hour (30 minutes) or a quarter of an hour (15 minutes) is an equal part of 1 whole hour.
- 🏃Distances & Numbers: A 100-meter race is 1 whole track. Reaching the 50-meter mark means you have completed an equal part of the whole distance.
- 🥤Liquids & Volume: 1 whole litre bottle of water poured equally into 4 identical glasses divides the water into equal parts of the whole litre.
- 🔋Batteries & Gauges: A full phone battery or a car's fuel tank is 1 whole capacity. Half a tank or battery is a fractional part of the whole.
- 📦Groups & Sets: A box of 12 coloured pencils is 1 whole pack. Taking 3 pencils means you are holding a part of the whole collection.
No matter what example you choose, the golden rule of mathematics never changes: whenever a whole is shared equally, each piece is an equal part of the whole!
Special Parts: Halves and Quarters
We can divide a whole into countless pieces, and we cannot give a special name to every single one! But in our daily lives, there are certain equal divisions we use so frequently that mathematics and everyday speech have given them special names.
🌗 1. Half
If we divide a whole into 2 equal parts, each part is called a half.
2 equal halves joined together make 1 whole!
🍕 2. Quarter
In the same way, if we divide a whole into 4 equal parts, each part is called a quarter.
Four 25p coins (4 quarters) make £1.00 (1 whole pound)!
4 equal quarters joined together make 1 whole!
Ready to Divide? The Equal Splitter Challenge!
Position the dividers to split objects into equal pieces. Can you make every part completely equal?