Percentage — Study Notes for CG TET Paper I
Overview
Percentage is one of the most practical and frequently tested topics in CG TET Paper I Mathematics. It forms the foundation for understanding profit-loss, simple interest, and data interpretation — all of which appear in the syllabus. For a primary school teacher, mastery of percentage is essential because it connects classroom mathematics to real-life situations like discounts, marks calculation, and population data.
In CG TET, expect 2–4 questions directly or indirectly involving percentage. Questions typically test basic conversion (fraction to percentage), finding percentage of a quantity, percentage increase/decrease, and simple word problems. The pedagogy section may also ask how to teach percentage using real-life examples from the Chhattisgarh context — local market prices, agricultural yield data, or school attendance figures.
Your goal: be fluent in quick mental calculations, understand the concept deeply enough to explain it to Class 4–5 students, and avoid common calculation traps.
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Key Concepts
- **Definition**: Percent means "per hundred." Writing 25% means 25 out of 100, or 25/100 = 0.25.
- **Fraction-Percentage-Decimal Triangle**: Any fraction can be written as a percentage by multiplying by 100. Any percentage can be written as a decimal by dividing by 100. Example: 3/4 = 75% = 0.75.
- **Base Value Concept**: When we say "20% of 150," the number 150 is the base. Always identify the base clearly in word problems.
- **Percentage Change**: Increase or decrease is always calculated on the original (initial) value, not the new value.
- **Successive Percentage**: When two percentages apply one after another, they don't simply add. You must apply them step by step.
- **Reversibility**: If a value increases by x%, to restore it you don't decrease by x%. The reverse percentage is different because the base changes.
- **Percentage Points vs Percentage**: If pass percentage rises from 60% to 75%, the increase is 15 percentage points, but the percentage increase is (15/60) × 100 = 25%.
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Formulas / Key Facts
| Concept | Formula | |---------|---------| | Percentage of a number | x% of N = (x/100) × N | | Fraction to percentage | (a/b) × 100 % | | Percentage to fraction | x% = x/100 (simplify) | | Percentage increase | [(New − Old)/Old] × 100 | | Percentage decrease | [(Old − New)/Old] × 100 | | New value after increase | Old × (1 + x/100) | | New value after decrease | Old × (1 − x/100) | | Successive change (a% then b%) | Net effect = a + b + (ab/100) % | | Reverse of x% increase | Decrease by [x/(100+x)] × 100 % | | Reverse of x% decrease | Increase by [x/(100−x)] × 100 % |