Podcast
Questions and Answers
What is the percentage of 25 out of 200?
What is the percentage of 25 out of 200?
A percentage increase from $30 to $45 represents a 50% increase.
A percentage increase from $30 to $45 represents a 50% increase.
False
What is the formula to calculate simple interest?
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.
The ______ of a value is calculated by dividing the part by the whole and multiplying by 100.
Signup and view all the answers
Match the following terms with their definitions:
Match the following terms with their definitions:
Signup and view all the answers
If a product's price decreases from $100 to $75, what is the percentage decrease?
If a product's price decreases from $100 to $75, what is the percentage decrease?
Signup and view all the answers
If a car travels 300 miles in 6 hours, its speed is 50 mph.
If a car travels 300 miles in 6 hours, its speed is 50 mph.
Signup and view all the answers
What is the total amount after interest if the principal is $2,000 with a simple interest of $300?
What is the total amount after interest if the principal is $2,000 with a simple interest of $300?
Signup and view all the answers
To find the _____, subtract the old value from the new value, divide by the old value, and multiply by 100.
To find the _____, subtract the old value from the new value, divide by the old value, and multiply by 100.
Signup and view all the answers
What is the simple interest on a principal of $500 at a rate of 4% over 2 years?
What is the simple interest on a principal of $500 at a rate of 4% over 2 years?
Signup and view all the answers
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
-
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 ]
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
