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Aviation Maintenance Technician Handbook–General

FAA-H-8083-30B Version 2023
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Chapter 3

Mathematics in Aviation Maintenance

Proportion Method:

Formula: 10.75 N ; = ; 12 100
Formula: To solve for N: N × 12 = 10.75 × 100 ; N × 12 = 1,075 ; N = 1,075 ÷ 12 ; N = 89.58 ; or ; N = (1,075 × 100) ÷ 12 ; N = 89.58

Therefore, the motor efficiency is 89.58%.

Finding a Number When a Percentage of it is Known

Example: Eighty ohms represents 52% of a microphone’s total resistance. Find the total resistance of this microphone.

Formula: Algebraic Method: ; 52% of N = 80 ohms ; 52% × N = 80 ; N = 80 ÷ 0.52 ; N = 153.846

The total resistance of the microphone is 153.846 ohms.

Proportion Method:

Formula: 80 = 52 ; N 100 ; To solve for N: N × 52 = 80 × 100 ; N × 52 = 8,000 ; N = 8,000 ÷ 52 ; N = 153.846 ohms ; or ; N = (80 × 100) ÷ 52 ; N = 153.846 ohms

Positive & Negative Numbers (Signed Numbers)

Positive numbers are numbers that are greater than zero. Negative numbers are numbers less than zero. [Figure 3-8] Signed numbers are also called integers.

Addition of Positive & Negative Numbers

The sum (addition) of two positive numbers is positive. The sum (addition) of two negative numbers is negative. The sum of a positive and a negative number can be positive or negative, depending on the values of the numbers. A good way to visualize a negative number is to think in terms of debt. If you are in debt by $100 (or, −100) and you add $45 to your account, you are now only $55 in debt (or −55).

Formula: Therefore: −100 + 45 = −55.

Example: The weight of an aircraft is 2,000 pounds. A radio rack weighing 3 pounds and a transceiver weighing 10 pounds are removed from the aircraft. What is the new weight? For weight and balance purposes, all weight removed from an aircraft is given a minus sign, and all weight added is given a plus sign.

Formula: 2,000 + −3 + −10 = 2,000 + −13 = 1,987

Therefore, the new weight is 1,987 pounds.

Subtraction of Positive & Negative Numbers

To subtract positive and negative numbers, first change the “–” (subtraction symbol) to a “+” (addition symbol), and change the sign of the second number to its opposite (that is, change a positive number to a negative number or vice versa). Finally, add the two numbers together.