Fractions & Percentages
Fractions and percentages are two different ways of expressing the same idea: parts of a whole. They appear everywhere — marks in exams, discounts in shopping, probabilities, statistics, and data analysis.
In this lesson, you will understand fractions and percentages visually, learn how they are related, and know exactly when and how to use each one.
What Is a Fraction?
A fraction represents a part of a whole and is written as:
a / b
- a → numerator (how many parts we have)
- b → denominator (total equal parts)
For example, 3/4 means 3 parts out of 4 equal parts.
The shaded part visually shows the fraction.
Types of Fractions
Fractions are commonly classified into different types:
- Proper fraction: numerator < denominator (3/5)
- Improper fraction: numerator ≥ denominator (7/4)
- Mixed number: whole number + fraction (1 3/4)
All three represent values greater than or less than one, just written in different forms.
Equivalent Fractions
Two fractions are equivalent if they represent the same value, even though they look different.
Example: 1/2 = 2/4 = 4/8
Equivalent fractions are created by multiplying or dividing both numerator and denominator by the same number.
Fractions as Decimals
Fractions can be converted to decimals by dividing the numerator by the denominator.
| Fraction | Decimal |
| 1/2 | 0.5 |
| 1/4 | 0.25 |
| 3/5 | 0.6 |
This conversion is heavily used in computing and data processing.
What Is a Percentage?
A percentage represents a fraction with denominator 100.
Example: 25% = 25/100 = 1/4
The word “percent” literally means per hundred.
Percentages make comparison very easy, which is why they are used in statistics, business, and analytics.
Converting Between Fraction, Decimal, and Percentage
| Fraction | Decimal | Percentage |
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/5 | 0.6 | 60% |
These three forms represent the same value, just expressed differently.
Real-Life Uses of Fractions & Percentages
- Shopping: discounts (20% off)
- Education: marks (45/50 = 90%)
- Data Science: proportions and ratios
- Business: growth and profit margins
Practice Questions
Q1. Write 3/4 as a percentage.
Q2. Convert 40% into a fraction.
Q3. Which is larger: 2/3 or 60%?
Quick Quiz
Q1. What does “percent” mean?
Q2. Is 0.2 equal to 20%?
Quick Recap
- Fractions represent parts of a whole
- Percentages are fractions out of 100
- Decimals, fractions, and percentages are interchangeable
- Visual understanding makes comparison easy