Algebra Chapter 1 Section 5: Formulas, Models, and Geometry

Here, I will describe some of the basics of algebraic manipulation.  First, we need to define a formula, which is any equation which uses letters to represent relationships between quantities.  An example of this is the area of a circle, $A=\pi r^{2}$.  You'll remember from Section 3 that we can solve for a variable.  The formula I used was the one relating masses of two object, their distance, a constant, and the Gravitational force.

To solve a formula for a particular variable or constant, perform the following steps:
  1. Multiply both sides by any denominator there happens to be in order to cancel out any denominator and clear any fractions.  Combine like terms.
  2. Using the addition principle, get every term with the variable to be solved for on one side of the equals sign and every other term on the other side of the equals sign.  Combine like terms again if necessary, which may include factoring.
  3. Solve for the variable by using the multiplication principle.
These formulas can be taken individually (one at a time) or together to form a mathematical model describing the real world.  In terms of problem solving from Section 4, the mathematical model comes from the translation step.

That's the end of this section.  If you have any questions, please leave them is the comments.  Like and share this post if you found it helpful.  And until next time, stay curious.

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