John wanted Mary to measure the productivity of her department by averaging the income of all the sections weighted by the number of employees in each section. He gave her this formula to use:

A = #workers in section Alpha
a = income for section Alpha

B = #workers in section Beta
b = income for section Beta

C = #workers in section Gamma
c = income for section Gamma

Productivity = (A * a + B * b + C * c) / 3

When Mary used this formula, her figures were incorrect. Do you know why?

Mary computed the productivity this way:

P = 1 * 6000 + 5 * 1000 + 20 * 2000 / 3

P = 6000 + 5 * 1000 + 20 * 2000 / 3

P = 6005 * 1000 + 20 * 2000 / 3

P = 6005000 + 20 * 2000 / 3

P = 6005020 * 2000 / 3

P = 12010040000 / 3

P = 4003346666.67

She performed each calculation in the formula from left to right, but her result is much too large. Notice that when she multiplied by 1000 she included all the previous numbers.

John intended for Mary to solve the problem this way:

P = (1 * 6000 + 5 * 1000 + 20 * 2000) / 3

P = (6000 + 5 * 1000 + 20 * 2000) / 3

P = (6000 + 5000 + 20 * 2000) / 3

P = (6000 + 5000 + 40000) / 3

P = (51000) / 3

P = 17000

Definition:

An expression is a string of values and operators to be evaluated.

The right side of the formula given above is an expression. As the example illustrates, there are rules regarding the order of performing the operations in an expression. Mary was right to approach the problem from left to right but she needed to know about the order of precedence for the operators in an expression.

Follow the order below and you will always evaluate your expressions properly. Begin with the top and work your way down the list.