You already know how to multiply. This unit is not here to teach you that.
It is here because a small set of calculations recur in aircraft maintenance, and getting one of them wrong produces a plausible number rather than an obvious error. That is the whole subject. A wrong answer that looks wrong is a nuisance; a wrong answer that looks right gets signed off, installed, and flown.
The Mechanic ACS says so itself. Three of its knowledge elements are qualified. Ratios, and proportion and percentage, each carry "including examples of where or how they may be used in relation to aircraft maintenance or system(s) operation." Algebra carries the same words, ending at "aircraft maintenance." The skills name their applications outright: not compute a volume but the volume of a cylinder and of a fuel tank; not convert units but inch-pounds to foot-pounds; not compare numbers but compute a compression ratio.
A general mathematics course would not satisfy this unit, and there is plenty of excellent free general mathematics available. What does not exist, and what this unit is, is the aviation framing the standard actually requires.
1. The failure mode this unit exists to prevent
Take three calculations from later units.
- A weight and balance computation with one arm entered positive instead of negative.
- A tank capacity in cubic inches reported as gallons.
- A torque figure in inch-pounds set on a wrench reading foot-pounds.
None of the three produces an error message. Each returns a number of about the right size, written down in the right units, on a form with the right boxes filled. The first moves a center of gravity to the wrong side of a limit. The second puts an aircraft into the air believing it has fuel it does not have. The third applies twelve times the intended torque, or one-twelfth of it.
Everything below is organized around that.
2. Areas and volumes: the arithmetic is easy, the shape is the skill
The handbook gives you the formulae and they are not difficult. The difficulty is elsewhere: deciding what shape the thing in front of you actually is.
- A cylinder is a cylinder — but engine specifications give you the bore, which is a diameter, and the volume formula wants a radius. Halving the bore is the single most common error in engine displacement calculations, and forgetting to halve it gives an answer four times too large. Four times, not twice, because the radius is squared.
- A wing is a trapezoid, not a rectangle, unless it is genuinely constant-chord. Root chord and tip chord differ, and the area uses their mean.
- A fuel tank is almost never a box. Real tanks are irregular, which is why the manufacturer publishes a capacity and a calibration rather than dimensions. Calculating a tank's volume from its dimensions is a training exercise; reading it from approved data is the job (GEN-I). Know how to do both, and know which one you may rely on.
The step that is not in the geometry
Volume comes out in cubic inches. Fuel is measured in gallons and loaded by pounds.
231 cubic inches = 1 US gallon, exactly. That single conversion is where tank and compartment problems are lost, because the geometry feels like the hard part and it is not.
Then weight: aviation gasoline is taken at 6 pounds per gallon and jet fuel at about 6.7, and those figures are what turn a volume into a weight and balance entry (GEN-C). Fuel density varies with temperature and grade, so these are planning figures, not measurements — which is itself worth knowing.
3. Ratio, proportion and percentage: what the ACS means by "aircraft applications"
The standard requires you to know where these are used. Here is where.
Ratio — compression ratio is the canonical case
Compression ratio compares two volumes: the space above the piston at the bottom of its stroke against the space at the top.
Understanding it as a ratio of volumes rather than as a formula to memorize is what makes an engine specification readable later in PP-A, and it is what lets you reason about why machining a cylinder head changes it.
Other ratios you will meet: gear ratios in accessory drives and propeller reduction; fuel/air ratio, which is a mass ratio and the subject of PP-I; and aspect ratio, which is span² ÷ area and connects straight back to §2.
Proportion — mixing, and scaling from a drawing
Two-part compounds are mixed by proportion, and the proportion is by weight or by volume depending on the product — never assume which. Getting it wrong produces a resin that cures to the wrong properties and looks correct (AF-B, GEN-G).
Scaling from a drawing is proportion too, and GEN-B warns why you should be careful: a drawing's stated dimensions govern, not its scale, because prints are reproduced at sizes their author did not intend.
Percentage — where it hides
Control surface hinge lines and balance weights are specified as a percentage of chord. Power settings are percentages of rated power. Humidity limits for finishing materials are percentages. In each case the percentage is of something, and naming that something is most of the work.
Algebra — the extension bar, which is the arithmetic that matters most
You will be asked, in the field and probably within a year, to torque a fastener you cannot reach with the wrench alone. Adding an extension in line with the handle increases the torque delivered at the fastener above what the wrench reads.
To get an actual torque at the fastener, using a wrench of length with an extension of length , you set the wrench to:
Set the wrench lower than the target, not higher. A mechanic who reasons "the extension makes it harder, so I should set it higher" over-torques the fastener — and GEN-E explains why that failure is invisible.
This is what element K6 means by algebra used in aircraft maintenance. It is one rearrangement
and it protects a joint.
4. Signed numbers are an airworthiness matter
The handbook covers positive and negative integers in a paragraph. Here is why the ACS lists
them twice — once as knowledge (K12) and once as a risk (R2).
In weight and balance, distances are measured from a datum, and the datum is chosen by the manufacturer for convenience. It is often ahead of the aircraft, so that every arm is positive — but not always. An arm forward of the datum is negative, and a moment is weight × arm, so the sign carries through to the total.
Enter one arm with the wrong sign and the arithmetic completes. There is no error. The center of
gravity simply lands somewhere it is not, possibly on the wrong side of a limit, and
GEN-C R4 explains what an out-of-limit center of gravity
does to an airplane.
Sign is not a detail of the notation. It is the difference between forward and aft.
5. Order of operations and rounding are risks, not rules
This is the part of the unit most likely to be dismissed, and the ACS anticipated that by classifying both as Risk Management rather than Knowledge.
Why precedence is a risk (R1)
Multiplication and division before addition and subtraction; brackets first. You know this.
The risk is not that you will forget it. The risk is that a wrongly ordered calculation returns a number. A weight and balance computation done in the wrong order does not fail — it produces a center of gravity, correctly formatted, in the right units, that is wrong. Compare that with a spanner that does not fit: the tool tells you immediately.
Any calculation whose result you cannot sanity-check is a calculation you must order carefully. Which leads directly to the habit this unit is really teaching, in GEN-H Procedures: every procedure ends with a check.
Why rounding is a risk (R3)
Two rules, and the second is the one that bites.
- Round at the end, not in the middle. Intermediate rounding accumulates, and it accumulates in one direction if you always round the same way.
- Never round toward a limit. If a measurement sits at 0.0625 and the limit is 0.062, the number does not become acceptable by being written as 0.06. A value at or beyond a limit is a rejection, and rounding is not a method of inspection (GEN-K).
The second rule is where rounding stops being arithmetic and becomes integrity, which is why
GEN-L K8 is not a separate subject from this one.
6. Notation: why fractions survive, and why binary appears
Fractions are not a legacy inconvenience
Drill sizes, sheet thickness, wrench sizes and fastener diameters are fractional and will remain so. You will read 3/16 on a drawing and reach for a drill marked in fractions, and you will also meet the same dimension as 0.1875 in a table of limits.
Fluency both ways is the requirement — not conversion as an exercise, but the ability to see
0.1875 and 3/16 as the same thing without stopping. Element S5 is that fluency.
Number drill sizes (#30, #40) and letter sizes sit alongside fractional ones and are not interchangeable with them. AF-A is where that matters, and the difference between a #30 and a 1/8 hole is the difference between a correct rivet fit and a loose one.
Binary, and why an airframe mechanic meets it
Element K8 includes binary, and it looks out of place until you reach
GEN-A K22 and K23. Digital systems represent state in binary;
built-in test equipment reports fault codes that are bit patterns; and a mechanic who can read
one is a mechanic who can isolate a failure to the right box rather than replacing three.
You are not being asked to program anything. You are being asked to recognize that a displayed code is a number in another base.
7. Two measurement systems on one aircraft
Element K7 asks when metric conversion may be necessary, and the honest answer is: more often
than the airframe suggests.
An airframe built to US customary units can carry an engine, an instrument or an avionics unit of European origin whose hardware, threads and specifications are metric. Manuals then mix the two, sometimes on the same page. Torque values may be given in newton-meters, dimensions in millimeters, and the fasteners you are holding will not tell you which system they belong to until you try one.
1 inch = 25.4 mm, exactly. That figure is a definition, not a measurement, and it is the one to hold.
The practical rule is GEN-B's: establish which system the document is in before you use any number from it, and never assume that because the airframe is imperial, everything bolted to it is.
8. What consumes this unit
Every explanation above exists because something later needs it. This unit's job is to be depended on, and a candidate who cannot see what it is for will not finish it.
| This unit | Is consumed by |
|---|---|
| Ratios, algebra, powers | GEN-A — Ohm's law, series and parallel resistance, power |
| Signed numbers, order of operations, moments | GEN-C — arms, moments, center of gravity |
| Areas, volumes, unit conversion | GEN-J — density altitude, horsepower, force and pressure |
| Torque conversion, the extension formula | GEN-E — torque and preload |
| Cylinder volume, compression ratio | PP-A, PP-I |
| Fractions and drill sizes | AF-A — rivet holes and sheet thickness |
| Rounding against a limit | GEN-K — serviceability judgment |
9. Where this sits in your own progress
This is the first unit of the free curriculum and it is deliberately first.
If the arithmetic here is comfortable, the rest of General is about aircraft rather than about mathematics, and you should move on to GEN-J.
If it is not comfortable, you have found that out for nothing, at the beginning, with the material to fix it in front of you — which is the whole point of publishing this before anyone asks you for money. Nobody is being turned away. You are being told what to work on.
License
CC BY-SA 4.0 (Licensing).