Questions and Answers
What is the percentage of 25 out of 200?
A percentage increase from $30 to $45 represents a 50% increase.
False
What is the formula to calculate simple interest?
SI = P * R * T
The ______ of a value is calculated by dividing the part by the whole and multiplying by 100.
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Match the following terms with their definitions:
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If a product's price decreases from $100 to $75, what is the percentage decrease?
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If a car travels 300 miles in 6 hours, its speed is 50 mph.
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What is the total amount after interest if the principal is $2,000 with a simple interest of $300?
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To find the _____, subtract the old value from the new value, divide by the old value, and multiply by 100.
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What is the simple interest on a principal of $500 at a rate of 4% over 2 years?
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Study Notes
Calculating Percentages
- 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 and Decrease
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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% ]
- Formula:
-
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% ]
- Formula:
Application of Rates
- 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} ]
Calculate and Use Simple Interest Formula
- 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 ]
Calculating Percentages
- 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 and Decrease
-
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.
- Formula:
-
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.
- Formula:
Application of Rates
- 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.
Calculate and Use Simple Interest Formula
- 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 ]
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Description
Test your knowledge on calculating percentages, including percentage increase and decrease, with practical examples. Understand the formulas and apply them to real-world scenarios to enhance your mathematical skills.
