Percentage — Study Notes for Bihar TET Paper I

Overview

Percentage is one of the most scoring and frequently tested topics in Bihar TET Paper I Mathematics. It forms the foundation for understanding profit-loss, discount, simple interest, and data interpretation — all of which appear in the exam. A primary-school teacher must be able to explain percentage concepts to young learners and solve standard calculation problems quickly.

The topic tests two core skills: converting between fractions, decimals, and percentages, and applying percentage concepts to real-life situations like increase, decrease, and comparison. Bihar TET typically includes 2–3 direct questions on percentage or its applications. Mastering this topic also helps in the pedagogy section when discussing how to teach commercial mathematics to children.

For exam success, focus on memorising common fraction-percentage equivalents, understanding the concept of "base value," and practising word problems involving percentage change.

Key Concepts

• **Meaning of Percent**: "Percent" means "per hundred." Writing 25% means 25 out of every 100, or 25/100.

• **Conversion Rule**: To convert percentage to fraction, divide by 100. To convert fraction to percentage, multiply by 100. For example, 3/4 = (3/4) × 100 = 75%.

• **Percentage of a Quantity**: To find x% of a number N, calculate (x/100) × N. For example, 20% of 150 = (20/100) × 150 = 30.

• **What Percent One Number is of Another**: If A is what percent of B, then answer = (A/B) × 100. For example, 45 is what percent of 180? Answer = (45/180) × 100 = 25%.

• **Percentage Increase**: When a value increases from old to new, percentage increase = [(New − Old)/Old] × 100.

• **Percentage Decrease**: When a value decreases from old to new, percentage decrease = [(Old − New)/Old] × 100.

• **Base Value Matters**: Always identify which quantity is the "base" (denominator). A common exam trap is confusing the base in increase vs decrease problems.

• **Successive Percentage Change**: When two percentage changes occur one after another, the net effect is NOT the simple sum. Use the formula for combined effect.

Formulas / Key Facts

| Concept | Formula | |---------|---------| | Percentage to Fraction | x% = x/100 | | Fraction to Percentage | (a/b) × 100 % | | x% of N | (x × N)/100 | | A is what % of B | (A/B) × 100 | | % Increase | [(New − Old)/Old] × 100 | | % Decrease | [(Old − New)/Old] × 100 | | New value after x% increase | Original × (100 + x)/100 | | New value after x% decrease | Original × (100 − x)/100 | | Successive change of a% and b% | Net effect = a + b + (ab)/100 % |