Every time an aviation maintenance technician (AMT) troubleshoots an electrical circuit, calculates a required torque value, or determines the correct fuel-to-oil mixture, algebra is working quietly in the background. Algebra is simply the branch of mathematics that uses letters — called variables or unknowns — to represent quantities we do not yet know. By setting up an equation and performing a series of legal operations on both sides, we can isolate that unknown and find its exact value. The FAA AMT General knowledge test expects applicants to demonstrate comfort with basic algebraic manipulation, and the skills tested on that exam are the same ones you will use every day on the flight line.
This article walks through the fundamental rules of solving algebraic equations, shows how those rules apply directly to maintenance formulas you will encounter in the shop, and highlights the specific traps the FAA test is known to set for unprepared students.
What an Equation Really Means
An equation is a mathematical statement that two expressions are equal, separated by an equal sign. Think of the equal sign as the fulcrum of a perfectly balanced scale. Whatever you do to one side of the scale — add weight, remove weight, multiply by a factor — you must do the same to the other side to keep it balanced. This single idea, sometimes called the Golden Rule of Algebra, governs every step of every solution: perform the same operation on both sides of the equation.
Variables in maintenance formulas are usually meaningful letters. In Ohm's Law, E represents voltage (electromotive force), I represents current, and R represents resistance. In the torque formula, T is torque, F is force, and D is distance. Recognizing these standard letters saves time and reduces errors on the bench and on the test.
How to Solve for an Unknown: The Core Technique
The goal of solving an equation is to get the unknown variable alone on one side of the equal sign, with a pure number on the other side. You achieve this by applying inverse operations — the opposite of whatever is being done to the variable. Addition and subtraction are inverses of each other; multiplication and division are inverses of each other.
Step-by-step approach
- Identify the unknown you need to find and circle it mentally.
- Look at what operations surround the unknown — is it being multiplied, divided, added to, or subtracted from something?
- Undo those operations in reverse order (think of peeling an onion from the outside in). If the unknown is multiplied and then added to, undo the addition first, then undo the multiplication.
- Apply each inverse operation to both sides simultaneously.
- Simplify until the variable stands alone, then read off the answer and attach the correct unit.
Always double-check by substituting your answer back into the original equation. If both sides come out equal, you solved it correctly.
Maintenance Formulas and How to Rearrange Them
Ohm's Law
The most commonly tested algebraic formula in the AMT General curriculum is Ohm's Law: E = I × R. This formula relates voltage (E, in volts), current (I, in amperes), and resistance (R, in ohms). If you need to find current when voltage and resistance are known, divide both sides by R:
E ÷ R = (I × R) ÷ R, which simplifies to I = E ÷ R.
If you need resistance and know voltage and current, divide both sides by I: R = E ÷ I. All three arrangements come from the same one equation — you are just rearranging the balance of the scale each time.
Power Formula
The electrical power formula states P = E × I, where P is power in watts. Rearranging: E = P ÷ I and I = P ÷ E. Combined with Ohm's Law, this gives rise to a family of equivalent formulas — sometimes called the Ohm's Law wheel — that allow you to solve for any one of the four quantities (E, I, R, or P) if you know any two others. For example, substituting E = I × R into P = E × I gives P = I² × R, and substituting I = E ÷ R gives P = E² ÷ R.
Torque Calculations
Torque is calculated as T = F × D, where T is torque (in inch-pounds or foot-pounds), F is the applied force (in pounds), and D is the distance from the pivot point (in inches or feet). If a technician needs to know what force to apply at a known wrench length to achieve a specified torque value, solve for F: divide both sides by D, yielding F = T ÷ D. A practical example: if the required torque is 480 inch-pounds and the torque wrench handle is 12 inches long, then F = 480 ÷ 12 = 40 pounds of applied force. This kind of rearrangement is tested directly on the FAA AMT General exam.
Area and Volume Formulas
Maintenance technicians calculate areas to determine material quantities (e.g., fabric or sheet metal) and volumes to determine fluid capacities. The area of a rectangle is A = L × W. If total area and length are known, solve for width: W = A ÷ L. The volume of a cylinder — relevant for checking oil sump capacity or hydraulic reservoir sizing — is V = π × r² × h. Solving for height: h = V ÷ (π × r²). Notice that even more complex-looking formulas still obey the same Golden Rule; you simply divide both sides by the entire group of terms that surrounds the unknown.
Mixture and Percentage Problems
Mixture problems appear in the context of fuel additives, hydraulic fluid dilution, and chemical cleaning solutions. The general relationship is Amount of component = Total volume × Percentage (as a decimal). For example, if a hydraulic system holds 4 gallons of fluid and a certain additive must make up 5 percent of the total, the required additive = 4 × 0.05 = 0.20 gallons. Rearranged, if you know the component amount and total volume, the percentage = component ÷ total. Converting between percentages and decimals (dividing by 100 or multiplying by 100) is a frequent source of errors on the test.
Why This Matters in the Shop
Algebraic errors in the maintenance environment carry real safety consequences. An incorrectly calculated torque value can result in fastener failure or overtorqued fittings that crack under vibration. An error in Ohm's Law can lead to undersized wire selection, causing thermal damage or fire. Improperly calculated fluid mixture ratios can compromise corrosion inhibition or lubrication. The FAA requires AMT applicants to demonstrate mathematical competency precisely because these calculations are not abstract — they determine whether an aircraft is airworthy.
Beyond safety, efficiency matters. A technician who can quickly rearrange a formula avoids unnecessary trips to a reference chart, reduces troubleshooting time, and presents a professional image of competence that supervisors and inspectors notice.
Key Numbers and Rules
- Golden Rule: Whatever you do to one side of an equation, do the same to the other side.
- Ohm's Law triangle: E = I × R; I = E ÷ R; R = E ÷ I — all three come from one formula.
- Power formulas: P = E × I; P = I² × R; P = E² ÷ R — derived by substitution.
- Torque formula: T = F × D — rearranges to F = T ÷ D or D = T ÷ F.
- Percentage as decimal: always divide the percent by 100 before multiplying (5% = 0.05, not 5).
- Order of operations (PEMDAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right) — apply this when simplifying either side of an equation.
- Inverse operations: to undo multiplication, divide; to undo division, multiply; to undo addition, subtract; to undo subtraction, add.
- Verification step: always substitute the answer back into the original equation to confirm both sides are equal.
Memory Aid
For Ohm's Law, technicians use the classic EIR triangle: write E on top, I and R side by side on the bottom. Cover the quantity you want to find — if you cover E, you see I × R (multiply); if you cover I, you see E over R (divide E by R); if you cover R, you see E over I (divide E by I). This visual shortcut works because it encodes the algebraic rearrangements in a spatial format that is fast to recall under pressure.
Common Test Traps
- Forgetting to convert units before calculating. Mixing inches and feet in a torque problem, or using percentage as a whole number instead of a decimal, produces a wrong answer even when the algebra is set up correctly.
- Dividing by the wrong quantity. When solving P = I² × R for R, students sometimes divide only by I instead of I², leaving an extra factor of I in the answer. Isolate the entire group attached to the unknown.
- Stopping one step short. Solving I = E ÷ R and leaving the answer as a fraction (e.g., 12/4) without completing the division (3 amperes) is a common careless error that costs points.
- Sign errors with subtraction. When a variable has a number subtracted from it — such as in a temperature correction formula — students sometimes add that number to both sides instead of adding it (i.e., they subtract a negative). Always think carefully about whether the operation is addition or subtraction.
- Misidentifying the unknown. The FAA test sometimes presents a formula with an uncommon variable isolated, or asks for a quantity that requires two rearrangement steps. Read the question carefully to confirm what you are actually solving for before beginning any manipulation.