Percents

Understanding Percentages:

• Definition: A percentage is a way to represent a part of a whole, with the whole being equal to 100%. The word "percent" means "per hundred." So, when you express a value as a percentage, you are essentially comparing it to 100.

• Percent Symbol: The percent symbol is %, and you place it after the number to indicate a percentage. For example, 25% represents 25 out of every 100.

• Converting Fractions to Percentages: To convert a fraction to a percentage, you can multiply the fraction by 100. For example, to convert 1/4 to a percentage, you multiply by 100: (1/4) * 100 = 25%. So, 1/4 is 25%.

Calculating Percentages:

• Finding a Percentage of a Number: To find a percentage of a number, you can use the following formula:
  Percentage = (Part / Whole) * 100%

  • Part: The value that is a part of the whole.

  • Whole: The total value or the whole.

• For example, to find 20% of 80, you use the formula: (20/100) * 80 = 16.

• Finding the Whole Given a Percentage: To find the whole when you know a part and the percentage, you can use this formula:
  Whole = (Part / Percentage) * 100%
  For example, if 15 is 25% of a certain number, you can find the whole using the formula: (15 / 25) * 100% = 60.

• Finding the Percentage Increase or Decrease: To find the percentage increase or decrease between two values, use this formula:
  Percentage Change = ((New Value - Old Value) / Old Value) * 100%

  • New Value: The updated or final value.

  • Old Value: The initial or starting value.

• For example, if a product's price increased from $50 to $60, you can find the percentage increase as follows: 

((60 - 50) / 50) * 100% = 20%.

Applications of Percentages:

Percentages are widely used in various everyday scenarios:

• Discounts: When you shop, discounts are often expressed in percentages to show how much you save on a purchase.

• Interest Rates: In finance, interest rates on loans, savings accounts, and investments are usually given in percentages.

• Probability and Statistics: Percentages are used to represent probabilities and frequencies in statistical analysis.

• Grade Systems: In education, grades are often assigned as percentages.

• Medical and Health Data: Percentages are used to represent risk factors, recovery rates, and more in the healthcare field.

Understanding percentages is essential for making informed decisions, comparing values, and interpreting data in various fields. Practicing percentage calculations and their applications will help you become proficient in working with percentages.