MATH

Percentage Increase

The amount expressed as a percentage that denotes the increase from the original value to the new value, calculated as: ( \text{Percentage Increase} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100 )

Percentage Decrease

The amount expressed as a percentage that denotes the decrease from the original value to the new value, calculated as: ( \text{Percentage Decrease} = \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \times 100 )

Discounted Price

The price after applying a discount, calculated as: ( \text{Discounted Price} = \text{Original Price} - \text{Discount} )

Sale Price

The final price after discount applied to the original price, calculated as: ( \text{Sale Price} = \text{Original Price} \times (1 - \frac{\text{Discount Rate}}{100}) )

Sales Tax

An additional amount of money added to the original price, calculated as: ( \text{Sales Tax} = \text{Price} \times \frac{\text{Tax Rate}}{100} )

Commission

A fee paid to an agent or salesperson for their services, calculated as: ( \text{Commission} = \text{Sale Amount} \times \frac{\text{Commission Rate}}{100} )

Finding the Percentage of a Number

To find the percentage of a number, multiply the number by the percentage (expressed as a decimal), calculated as: ( \text{Percentage of a Number} = \text{Number} \times (\frac{\text{Percentage}}{100}) )

Solving Problems Involving Rates

Involves calculating the relationship between quantities; common formulas may include ( \text{Rate} = \frac{\text{Distance}}{\text{Time}} )

Distance Formula (D = S x T)

Distance is calculated by multiplying speed (S) by time (T), expressed as: ( D = S \times T )

Simple Interest

Interest calculated on the principal amount only, expressed as: ( I = P \times R \times T ) where I is interest, P is principal, R is the rate (as a decimal), and T is time.