Algebra rearranging operations help

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    Algebra Operations
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SUMMARY

The discussion focuses on the algebraic rearrangement of the formula SPI = EV / PV to derive EV = SPI * PV. The operation changes from division to multiplication when both sides of the equation are multiplied by PV, effectively eliminating PV from the denominator. This illustrates the principle that division can be interpreted as multiplication by the reciprocal, confirming the mathematical validity of the transformation.

PREREQUISITES
  • Understanding of basic algebraic operations
  • Familiarity with formulas involving Earned Value (EV), Planned Value (PV), and Schedule Performance Index (SPI)
  • Knowledge of reciprocal relationships in mathematics
  • Ability to manipulate equations and solve for variables
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  • Study algebraic manipulation techniques for rearranging equations
  • Learn about Earned Value Management (EVM) concepts and calculations
  • Explore the implications of SPI in project management
  • Review examples of reciprocal operations in algebra
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Students, project managers, and professionals in project management who need to understand the mathematical foundations of Earned Value Management and its application in performance measurement.

falcios
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How does this formula SPI = EV / PV rearrange to this formula EV = SPI * PV
Why does the operation change from multiply to divide?

Thanks for the help.
 
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We begin with:

$$SPI=\frac{EV}{PV}$$

If we next multiply both sides by $PV$, we get:

$$SPI\cdot PV=\frac{EV}{PV}\cdot PV=EV\cdot\frac{PV}{PV}=EV\cdot1=EV$$
 
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The answer to your "why" question is this:

Division is the same as multiplying by a reciprocal, that is:

[math]\frac{a}{b} = a*\frac{1}{b}[/math]
 

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