Percentage Guide & Practice

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1. Fundamentals & Definitions

The word "Percentage" means "per hundred". It is a fraction whose denominator is always 100.

• Symbol: %
• Example: 20% means 20/100 or 0.20.

Fraction to Percentage Conversion

To express a fraction a/b as a percent: (a/b * 100)%

• 1/2 = 50%
• 1/3 = 33.33% (or 33 1/3%)
• 1/4 = 25%
• 1/5 = 20%
• 1/6 = 16.66%
• 1/8 = 12.5%
• 1/10 = 10%
• 1/12 = 8.33%

Percentage to Fraction Conversion

To express x% as a fraction: x / 100

• 20% = 1/5
• 25% = 1/4
• 40% = 2/5
• 75% = 3/4

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2. Core Concepts & Formulas

A. Comparison of Quantities

To express Quantity 1 as a percentage of Quantity 2: Formula: (Quantity 1 / Quantity 2) * 100

B. Percentage Increase/Decrease

• Increase: [(New Value - Old Value) / Old Value] * 100
• Decrease: [(Old Value - New Value) / Old Value] * 100

C. Consumption and Expenditure

If the price of a commodity increases by R%, then the reduction in consumption needed to keep expenditure constant: Formula: [R / (100 + R)] * 100%

If the price decreases by R%, the increase in consumption allowed: Formula: [R / (100 - R)] * 100%

D. Population and Depreciation

Let P be the present population/value and R be the annual rate of change.

• Value after n years: P * (1 + R/100)^n (Use - for depreciation)
• Value n years ago: P / (1 + R/100)^n (Use - for depreciation)

E. Comparative Income

• If A is R% more than B, then B is less than A by: [R / (100 + R)] * 100%
• If A is R% less than B, then B is more than A by: [R / (100 - R)] * 100%

F. Successive Changes

If a value increases/decreases by X% and then by Y%: Net Change: [X + Y + (XY / 100)]% (Note: Use positive values for increase and negative values for decrease/discount)

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