Algebra is a mathematical method used for calculation of unknown values. In algebra, variables, generally represented by a letter of the alphabet, stand in for unknown values in an equation. Through a series of steps, the user can isolate the variable to determine its value. While often part of the high school math curriculum, many students wonder how algebra knowledge will be applied to real-life situations. Calculating the value of a total from a known percentage can be a valuable tool for determining the total number of voters in an election or calculating the total salary based on a percentage raise.
Understand the meaning of a percentage. The word percent comes from a Latin word meaning "for each 100." Percentages are essentially a fraction, with the denominator as 100. For example, 2% is equal to 2/100, or 2 for each 100.
Note the value of the percentage. If your given information states that 2% = 80, know that 2 for each 100 is the same as 80 for each of the unknown value.
Create an equation that shows the fractional relationship between the percentage and its value. Use the variable x to represent the unknown total. For the given example, 2/100 = 80/x.
Cross-multiply the equation to bring the variable to one side of the equation as a whole number. Multiply values diagonal from each other in the equation 2/100 = 80/x to create the whole number equation of 2x=8000.
Isolate the variable by dividing both sides of the equation by the co-efficient, 2. On the left side, 2x/2 = x. On the right side 8000/2 = 4000. The resulting solution is x = 4000.
Check your work by introducing the value of x into the original equation, 2/100 = 80/x. Replace x with 4000 and solve both sides of the equation to ensure that it balances. Use a calculator or sheet of paper to show that 2/100 = 0.02 and 80/4000 = 0.02.
TL;DR (Too Long; Didn't Read)
Cross-multiplication is a shortcut that combines two steps of the algebraic solution process. When 2/100=80/x is cross multiplied to create 2x=8000, it is the same result as multiplying the entire equation by the product of the denominators, 100 and x, to come up with a common denominator and then reducing the equation to lowest terms.
The steps outlined in the algebraic solution for percentage totals allow you to derive a simple method for determining totals from a percent in the future. Multiply the given percentage value by 100 and divide that product by the percent. This method will work in any instance where a percentage and its value are given. For example, when 2%=80, multiply 80 by 100 and divide by 2 to achieve the solution of 4000.
Percentages may be written as fractions or decimals. For example, 2/100=0.02