Every task an aviation maintenance technician (AMT) performs — from calculating torque values and fuel loads to measuring precise dimensions for component replacement — depends on a solid command of basic mathematics. Among the most fundamental skills are working fluently with whole numbers, fractions, and decimals. These are not merely classroom abstractions; a misplaced decimal point when calculating a drilling dimension or a botched fraction conversion when reading a micrometer can lead to a part that does not fit, a fastener that is overtightened, or a system that fails in flight. Understanding each number type and how to move between them is a foundational requirement for the FAA Aviation Mechanic General knowledge test and for safe, professional maintenance work.
This article walks through each number type in depth, explains the arithmetic operations that appear most often in AMT work, and highlights the conversion techniques and pitfalls that the FAA knowledge test consistently tests.
Whole Numbers and Their Operations
A whole number is any non-negative integer: 0, 1, 2, 3, and so on — no fractional or decimal parts. In aviation maintenance, whole numbers appear in part counts, torque specifications given in whole foot-pounds, and integer unit conversions. The four fundamental operations — addition, subtraction, multiplication, and division — must be performed accurately and in the correct order when expressions combine several operations.
The correct order of operations is a critical discipline. In a multi-step expression, multiplication and division are performed before addition and subtraction. Operations inside parentheses are always resolved first. For example, if a work order requires 3 rivets per panel and there are 8 panels, plus 4 extra rivets for trim, the total is (3 × 8) + 4 = 24 + 4 = 28 rivets — not 3 × (8 + 4). Misapplying the order of operations is one of the most common sources of arithmetic errors on the FAA General test.
Division of whole numbers also introduces the concept of a remainder. When 25 bolts must be shared equally among 4 assemblies, 25 ÷ 4 = 6 remainder 1. That remainder can be expressed as a fraction (6 and 1/4) or as a decimal (6.25), which leads directly into the other two number types.
Fractions: Structure and Arithmetic
A fraction represents a part of a whole and consists of a numerator (top number, showing how many parts are selected) and a denominator (bottom number, showing how many equal parts the whole is divided into). Fractions are everywhere in aircraft maintenance: drill bit sizes, fastener diameters, and sheet metal thicknesses are routinely expressed in fractional inches — for example, a 3/16-inch drill or a 1/8-inch rivet.
Types of Fractions
A proper fraction has a numerator smaller than its denominator (e.g., 5/8). An improper fraction has a numerator equal to or greater than its denominator (e.g., 9/4). A mixed number combines a whole number and a proper fraction (e.g., 2 and 1/4). Converting between improper fractions and mixed numbers is a routine AMT skill: to convert 9/4 to a mixed number, divide 9 by 4 to get 2 remainder 1, yielding 2 and 1/4. To reverse the process, multiply the whole number by the denominator and add the numerator: (2 × 4) + 1 = 9, so 9/4.
Adding and Subtracting Fractions
Fractions can only be added or subtracted when they share a common denominator. The least common denominator (LCD) is the smallest number divisible by both denominators. To add 1/4 and 3/8, recognize that the LCD is 8. Convert 1/4 to 2/8, then add: 2/8 + 3/8 = 5/8. For mixed numbers, handle the whole number parts and the fractional parts separately, borrowing from the whole number column when necessary during subtraction.
Multiplying and Dividing Fractions
Multiplying fractions is the most straightforward operation: multiply numerators together and denominators together, then simplify. For example, 3/4 × 2/5 = 6/20, which reduces to 3/10. Dividing by a fraction means multiplying by its reciprocal. To divide 3/4 by 1/2, flip the divisor (1/2 becomes 2/1) and multiply: 3/4 × 2/1 = 6/4 = 3/2 = 1 and 1/2. In a maintenance context, this comes up when dividing a total material length by a fractional piece size to determine how many pieces can be cut.
Reducing Fractions
Always reduce fractions to their lowest terms. Find the greatest common factor (GCF) shared by the numerator and denominator and divide both by it. The fraction 12/16 has a GCF of 4, so it reduces to 3/4. Reducing fractions makes comparison and further calculation easier and is expected on the FAA knowledge test.
Decimals: Structure and Arithmetic
A decimal is another way to express a fraction whose denominator is a power of 10 (10, 100, 1,000, etc.). The decimal point separates the whole number part on the left from the fractional part on the right. Each position to the right of the decimal point represents a successively smaller power of ten: tenths, hundredths, thousandths, and so on. A torque specification of 23.75 foot-pounds means 23 and 75/100 (or 3/4) of a foot-pound.
Adding and subtracting decimals requires aligning the decimal points vertically before performing the operation. Multiplying decimals follows integer multiplication rules, with the total number of decimal places in the product equal to the sum of decimal places in both factors. For example, 2.5 × 1.4 = 3.50; each factor has one decimal place, so the product has two. Dividing decimals involves moving the decimal point in the divisor to make it a whole number, then moving the dividend's decimal point the same number of places.
Converting Between Fractions and Decimals
AMT work constantly requires moving between fractions and decimals. To convert a fraction to a decimal, simply divide the numerator by the denominator. The fraction 3/8 = 3 ÷ 8 = 0.375. To convert a decimal to a fraction, write the decimal digits as the numerator over the appropriate power of 10, then reduce. The decimal 0.625 = 625/1000, which reduces to 5/8 (dividing by the GCF of 125).
Some fractions commonly encountered in aviation maintenance and their decimal equivalents are worth committing to memory:
- 1/2 = 0.500
- 1/4 = 0.250
- 3/4 = 0.750
- 1/8 = 0.125
- 3/8 = 0.375
- 5/8 = 0.625
- 7/8 = 0.875
- 1/16 = 0.0625
- 3/16 = 0.1875
These conversions are not just test material — a mechanic reading a micrometer must often convert a decimal reading to a fractional drill size to select the right bit from the rack.
Why This Matters in Aviation Maintenance
The stakes of arithmetic accuracy in aircraft maintenance are high. Consider a few representative examples. When calculating the proper torque for a fastener, an error that transposes digits — say, reading 35.7 foot-pounds as 37.5 — results in either an under-torqued joint (risk of loosening in service) or an over-torqued fastener (risk of thread damage or bolt failure). When fabricating a sheet metal patch, misreading a fractional dimension by a single graduation on a ruler can mean a piece that does not cover the required area or that interferes with adjacent structure. When computing fuel quantities that involve decimal-based fuel density values (pounds per gallon), even small rounding errors can compound across large volumes. These are not hypothetical concerns — they are the reason the FAA tests AMT candidates specifically on arithmetic accuracy.
Key Numbers and Rules
- Order of operations: Parentheses first, then multiplication and division (left to right), then addition and subtraction (left to right).
- LCD rule: To add or subtract fractions, find the least common denominator before combining numerators.
- Reciprocal rule: To divide by a fraction, multiply by its reciprocal (flip the divisor).
- Decimal places in products: The total decimal places in the product equals the sum of decimal places in both factors.
- Fraction-to-decimal conversion: Divide numerator by denominator.
- Decimal-to-fraction conversion: Write digits over the appropriate power of 10, then reduce using the GCF.
- Reducing fractions: Divide both numerator and denominator by their GCF until no common factor remains other than 1.
Common Test Traps
- Skipping the common denominator: Adding numerators directly without finding a common denominator is a classic mistake. Always convert fractions to equivalent forms with the same denominator before adding or subtracting.
- Misplacing the decimal point: When multiplying or dividing decimals, counting decimal places incorrectly shifts the answer by a factor of 10. Always double-check by estimating — does 2.5 × 1.4 seem closer to 3.5 or 35? Reasonableness checks catch these errors.
- Forgetting to reduce: The FAA test often presents answer choices as both the unreduced fraction and the fully reduced equivalent. Always simplify to lowest terms.
- Improper-to-mixed conversion errors: When converting an improper fraction to a mixed number, students sometimes add the remainder to the denominator instead of keeping it as the new numerator. Remember: the remainder becomes the numerator of the fractional part.
- Order of operations errors with mixed expressions: When a problem mixes addition, multiplication, and parentheses, rushing through the arithmetic without following the correct sequence reliably produces a wrong answer that appears among the distractors.