Algebra

Algebra is the branch of mathematics that uses letters or symbols to represent variables in formulas and equations.

For example, in the equation D = V × T, where Distance = Velocity × Time, the variables are: D, V, and T.

Equations

Algebraic equations are frequently used in aviation to show the relationship between two or more variables. Equations normally have an equals sign (=) in the expression.

Example: The formula A = π × r2 shows the relationship between the area of a circle (A) and the length of the radius (r) of the circle. The area of a circle is equal to π (3.1416) times the radius squared. Therefore, the larger the radius, the larger the area of the circle.

Algebraic Rules

When solving for a variable in an equation, you can add, subtract, multiply or divide the terms in the equation, you do the same to both sides of the equals sign.

Examples: Solve the following equations for the value N.

3N = 21

To solve for N, divide both sides by 3.

3N ÷ 3 = 21 ÷ 3
N = 7
N + 17 = 59

To solve for N, subtract 17 from both sides.

N + 17 – 17 = 59 – 17
N = 42
N – 22 = 100

To solve for N, add 22 to both sides.

N – 22 + 22 = 100 + 22
N = 122
N5
= 50

To solve for N, multiply both sides by 5.

N5
× 5 = 50 × 5
N = 250

Solving for a Variable

Another application of algebra is to solve an equation for a given variable.

Example: Using the formula given in Figure 1-12, find the total capacitance (CT) of the series circuit containing three capacitors with

First, substitute the given values into the formula:

Figure 1-12. Total capacitance in a series circuit.

Therefore, CT = 1⁄96.66 = .01034 microfarad. The microfarad (10-6 farad) is a unit of measurement of capacitance. This will be discussed in greater length beginning on page 10^-51 in chapter 10, Electricity.