Calculating Percentages Quiz

Study Notes

Percentage represents a number as a fraction of 100.
Formula to calculate percentage:
[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 ]
Example: To find what percentage 20 is of 50:
[ \text{Percentage} = \left( \frac{20}{50} \right) \times 100 = 40% ]

Percentage Increase:
- Formula:
  [ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100 ]
- Example: If a price increases from 50to50 to 50to60:
  [ \text{Increase} = \left( \frac{60 - 50}{50} \right) \times 100 = 20% ]
Percentage Decrease:
- Formula:
  [ \text{Percentage Decrease} = \left( \frac{\text{Old Value} - \text{New Value}}{\text{Old Value}} \right) \times 100 ]
- Example: If a price decreases from 80to80 to 80to60:
  [ \text{Decrease} = \left( \frac{80 - 60}{80} \right) \times 100 = 25% ]

Rates express a quantity relative to another quantity (e.g., speed, density).
Common types of rates:
- Interest Rates: Cost of borrowing or the return on savings.
- Tax Rates: Percentage of income or value that must be paid as tax.
Rate Calculation Example: If a car travels 150 miles in 3 hours, the rate (speed) is:
[ \text{Rate} = \frac{150 \text{ miles}}{3 \text{ hours}} = 50 \text{ mph} ]

Simple interest is calculated on the principal amount only.
Formula:
[ \text{Simple Interest (SI)} = \text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)} ]
- Where R is expressed as a decimal.
Example: For a principal of $1,000 at an interest rate of 5% for 3 years:
[ \text{SI} = 1000 \times 0.05 \times 3 = 150 ]
Total amount after interest:
[ \text{Total Amount} = \text{Principal} + \text{Interest} ]
[ = 1000 + 150 = 1150 ]

Percentage expresses a value as a fraction of 100.
Formula for calculating percentage:
[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 ]
For instance, to calculate what percentage 20 is of 50, the result is 40%.

Percentage Increase:
- Formula:
  [ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100 ]
- Example of increase from $50 to $60 calculates to a 20% increase.
Percentage Decrease:
- Formula:
  [ \text{Percentage Decrease} = \left( \frac{\text{Old Value} - \text{New Value}}{\text{Old Value}} \right) \times 100 ]
- Example of decrease from $80 to $60 results in a 25% decrease.

Rates compare one quantity against another, commonly used in speed, density, etc.
Examples of rates include:
- Interest Rates: Represents cost of borrowing or returns on savings.
- Tax Rates: Percentage of income or value paid as tax.
Example rate calculation: A car traveling 150 miles in 3 hours has a speed of 50 mph.

Simple interest is based solely on the principal amount.
Formula for simple interest:
[ \text{Simple Interest (SI)} = \text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)} ]
- Rate (R) should be expressed as a decimal.
For a principal of $1,000 at 5% interest over 3 years, the simple interest amounts to $150.
Total amount after interest can be calculated as:
[ \text{Total Amount} = \text{Principal} + \text{Interest} = 1150 ]