- Topics At a Glance
- Variables
- Variables as Unknown Quantities
- Variable Notations
- Constants
- Expressions and Equations
- Rearranging Expressions
- Commutative Properties
- Associative Properties
- Distributive Properties
- Factoring (Distributive Property in Reverse)
- Combining Like Terms
- Eliminating Parentheses
- Simplifying
- Equations, Functions, and Formulas
- Equations
- Functions
- Independent and Dependent Variables
- Formulas
- Applications to Toolbox
- Evaluating Expressions by Substitution
- Evaluating Formulas by Substitution
- Geometric Formulas
- Four-Sided Shapes
- Three-Sided Shapes
- Circles
- Unit Conversion
- Temperatures
- Weights
- Distances and Speeds
- Money
**In the Real World**- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

**I Like Practical Stuff; Why Should I Care?**

Hey, we like practical stuff, too! The great thing is that all of these formulas can be applied to real-world situations. That's good news if you live in the real world.

One thing the geometrical formulas are useful for is figuring out what amounts of materials are needed for projects such as carpeting floors:

How much carpet is needed to cover the floor shown in the picture below?

The area of the floor is the area of the rectangle plus the area of the square, which is

10(20) + 5^{2} = 225 square feet.

By the way, we think that 5 x 5 area on the right would make a splendid breakfast nook. Just something to consider.

The unit conversion formulas are useful when traveling or reading information from countries that use different, or "silly," units.

The simplification of algebraic expressions will be useful for later material. It is a simplify-now-understand-why-later sort of deal. Getting rid of parentheses and combining like terms often makes formulas easier to work with, especially formulas that we will use a lot.

Example 1

The perimeter |