Percentage — Study Notes for OTET Paper I
Overview
Percentage is one of the most frequently tested topics in OTET Paper I Mathematics. It forms the foundation for many real-life calculations and connects directly to other arithmetic topics like profit-loss, simple interest, and data interpretation. Questions typically test your ability to convert between fractions, decimals, and percentages, calculate percentage increase or decrease, and solve word problems involving discounts, marks, and population changes.
For primary-level teaching, understanding percentage is essential because teachers must help young learners connect the abstract concept of "per hundred" to concrete situations like exam scores, discounts in shops, and recipe adjustments. Expect 2–4 questions on percentage or its direct applications in the exam. Mastery here also speeds up your work in related topics.
Key Concepts
- **Meaning of Percent**: "Percent" means "per hundred" or "out of 100." Writing 25% means 25 out of every 100 units.
- **Conversion Triangle**: Percentage ↔ Fraction ↔ Decimal are interchangeable. Moving fluently between these three forms is the core skill.
- **Base Value Matters**: Percentage is always calculated with respect to some base (original) value. Identifying the correct base is crucial in word problems.
- **Percentage Change**: When a quantity increases or decreases, the change is expressed as a percentage of the original value, not the new value.
- **Successive Percentage Changes**: When two percentage changes occur one after another, they cannot simply be added. The second change acts on the result of the first.
- **Percentage Points vs Percentage Change**: A rise from 20% to 25% is an increase of 5 percentage points but a 25% increase in the rate itself. Exam questions sometimes test this distinction.
- **Reverse Percentage Problems**: If a value after increase/decrease is given, finding the original requires working backwards using the percentage formula.
Formulas / Key Facts
**Basic Conversion Formulas**
- Percentage to Fraction: x% = x/100
- Fraction to Percentage: (a/b) × 100%
- Decimal to Percentage: Multiply by 100 (0.45 = 45%)
- Percentage to Decimal: Divide by 100 (45% = 0.45)
**Finding Percentage of a Quantity**
- x% of N = (x/100) × N
**What Percentage is A of B?**
- Percentage = (A/B) × 100%