Percentage — Study Notes for Assam TET Paper I

Overview

Percentage is one of the most frequently tested topics in the Mathematics section of Assam TET Paper I. It forms the foundation for understanding profit-loss, simple interest, and data interpretation problems that appear in the exam. The word "percent" comes from Latin "per centum" meaning "per hundred," so percentage is simply a way of expressing a number as a fraction of 100.

For primary-level teaching, you must not only solve percentage problems yourself but also understand how to make this concept accessible to young learners. Questions typically test your ability to convert between fractions, decimals, and percentages, calculate percentage increase or decrease, and apply percentages to real-life situations like discounts, marks obtained, or population changes.

Mastering percentage requires comfort with basic arithmetic operations and a clear understanding of the relationship between part, whole, and rate. Most exam questions can be solved quickly using standard formulas or mental math shortcuts once the core concepts are internalised.

Key Concepts

• **Percentage means "out of 100"**: When we say 25%, we mean 25 out of every 100, or 25/100, or 0.25 as a decimal.

• **The three quantities in any percentage problem**: Part (the portion we're finding), Whole (the total or base), and Rate (the percentage). If you know any two, you can find the third.

• **Percentage of a number**: To find x% of a number N, calculate (x/100) × N or equivalently (x × N)/100.

• **Converting fractions to percentage**: Multiply the fraction by 100. For example, 3/5 = (3/5) × 100 = 60%.

• **Percentage change always uses original value as base**: Whether increase or decrease, the change is calculated with respect to the original (initial) value, not the new value.

• **Successive percentage changes do not add directly**: A 10% increase followed by a 10% decrease does not return to the original — there is always a net change.

• **Percentage points vs percentage**: An increase from 20% to 25% is a rise of 5 percentage points, but a 25% increase in the rate itself.

Formulas / Key Facts

| Formula/Fact | Context | |--------------|---------| | Percentage = (Part/Whole) × 100 | Finding what percentage one number is of another | | Part = (Percentage × Whole)/100 | Finding a given percentage of a number | | Whole = (Part × 100)/Percentage | Finding the total when part and percentage are known | | Percentage Increase = [(New − Original)/Original] × 100 | When value goes up | | Percentage Decrease = [(Original − New)/Original] × 100 | When value goes down | | New Value after x% increase = Original × (100 + x)/100 | Quick calculation for increased value | | New Value after x% decrease = Original × (100 − x)/100 | Quick calculation for decreased value | | 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, 1/10 = 10% | Must-memorise fraction-to-percentage conversions |