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.

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.

ASA AMT PrepwareASA – AMT General, Airframe and Powerplant Prepware for 2017.  Get ready for your FAA AMT Knowledge Exams with the most trusted source in aviation training.   Includes the contents of the Computer Testing Supplement, with the same FAA legends, figures, and charts you’ll be issued at the testing center before you take your official test.

Previous post:

Next post: