Percentages

Understanding Percentages

  • A percentage is a way of expressing a number as a fraction of 100. It’s often denoted using the percent sign, “%”.
  • Therefore, “50%” means 50 per 100, or simply 1/2, and “25%” means 25 out of a 100 or 1/4.
  • Percentages are widely used in practice, such as calculating discounts, interest rates, and changes in values.

Calculating a Percentage of a Quantity

  • To calculate a percentage of a quantity, multiply that quantity by the percentage (expressed as a decimal).
  • A common memory aid is: “percentage of” translates to “times”. For example, if you wish to find 15% of 60, calculate 15/100 * 60 or 0.15 * 60.

Expressing One Number as a Percentage of Another

  • To express one number as a percentage of another, divide the first number by the second number, and then multiply the result by 100.
  • For instance, to find what percentage 45 is of 180, calculate (45 ÷ 180) * 100.

Percentage Increase and Decrease

  • A percentage increase or percentage decrease calculates the proportion of change in a quantity.
  • A percentage increase involves finding a certain percentage of a quantity and then adding that to the original quantity.
  • Conversely, a percentage decrease involves calculating a certain percentage of a quantity and then subtracting that from the original quantity.
  • To calculate a percentage increase or decrease, subtract the original from the new value, divide that by the original value and then multiply by 100.

Compound Interest and Exponential Growth

  • Compound interest is an application of percentages that involves exponential growth.
  • When interest is compounded, it’s calculated as a percentage of the current value, not the original value. Therefore, compounded amounts grow faster than linear amounts.
  • The formula to calculate the amount, A, after t years, given a principal amount P, an annual interest rate r (expressed as a decimal), and the number of compounding periods n, is A = P * (1 + r/n)^(nt).

Using Percentages in Real-Life Situations

  • Demonstrating proficiency in using percentages is critical owing to their widespread application in day-to-day life.
  • This includes understanding measurements in graphs and statistics, interpreting changes and differences in quantities, calculating discounts or profit margins and understanding financial concepts such as depreciation and inflation.