What is a Fraction?
A fraction represents a part of a whole — or more generally, a division of one quantity by another. Every fraction you write or read consists of exactly two numbers and a line between them.
The Anatomy of a Fraction
Numerator (top number) — how many equal parts you have.
Denominator (bottom number) — how many equal parts the whole is divided into.
The line between them is called the fraction bar (or vinculum) and means ÷.
3/4 — the whole is cut into 4 equal parts; you have 3 of them.
A Fraction as Division
Every fraction is also a division. 3/4 means 3 ÷ 4 = 0.75. This connection is why fractions and decimals are interchangeable.
Real-Life Examples
| Situation | Fraction | Meaning |
|---|---|---|
| Pizza sliced into 8 pieces, you eat 3 | 3/8 | You ate 3 out of 8 equal slices |
| 1 hour, 15 minutes used | 15/60 = 1/4 | A quarter of the hour has passed |
| 20 students, 7 absent | 7/20 | 7 out of 20 are absent |
| Filling a 500 ml bottle with 200 ml | 200/500 = 2/5 | 2/5 of the bottle is filled |
Key Vocabulary
| Term | Meaning | Example |
|---|---|---|
| Numerator | Top number — parts taken | 3 in 3/4 |
| Denominator | Bottom number — total equal parts | 4 in 3/4 |
| Unit fraction | Numerator is 1 | 1/5, 1/8, 1/100 |
| Proper fraction | Numerator < denominator | 3/7 |
| Improper fraction | Numerator ≥ denominator | 9/4 |
Why the Denominator Cannot Be Zero
Division by zero is undefined. So a denominator of zero makes no sense — you cannot split something into zero parts. Always check that the denominator is a non-zero number.
Key Takeaways
- A fraction shows part of a whole: numerator ÷ denominator.
- The denominator tells you the size of each equal part.
- The numerator tells you how many of those parts you are considering.
- Fractions and division are the same operation written differently.
- Zero denominators are always invalid.
Practice Questions
- A cake is cut into 12 equal slices. You eat 5. Write this as a fraction.
- In 3/8, which is the numerator and which is the denominator?
- Write “7 divided by 11” as a fraction.
- A class of 30 students has 18 girls. What fraction are girls?
- Why can you not write 5/0?