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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

To solve for N, subtract 17 from both sides.

Formula: N + 17 – 17 = 59 – 17 ; N = 42 ; N – 22 = 100

To solve for N, add 22 to both sides.

Formula: N – 22 + 22 = 100 + 22 ; N = 122 ; N ; -- = 50
Formula: 5 ; oth sides by 5. ; N × 5 = 50 × 5 ; N = 250

Solving for a Variable

Another application of algebra is to solve an equation for a given variable.

Formula: Example: Using the formula given in Figure 3-12, find the ; total capacitance (CT) of the series circuit containing three ; capacitors with ; C1 = 0.1 microfarad ; C2 = 0.015 microfarad ; C3 = 0.05 microfarad

First, substitute the given values into the formula:

Formula: 1 1 1 ; C T = 1 ; 1 = 1 ; 1 = 10 + 66.66 + 20 ; 1 ; 1 ; + ; + ; + ; + ; C1 C2 C3 0.1 0.015 0.05 ; Therefore, CT = 1/96.66 = 0.01034 microfarad. The microfarad ; (10-6 farad) is a unit of measurement of capacitance. This is

discussed in greater length in Chapter 12, Electricity.

Use of Parentheses

In algebraic equations, parentheses are used to group numbers or symbols together. The use of parentheses helps us to identify the order in which we should apply mathematical operations. The operations inside the parentheses are always performed first in algebraic equations.

Formula: Example: Solve the algebraic equation X = (4 + 3)2.

First, perform the operation inside the parentheses, which

Formula: is, 4 + 3 = 7. Then complete the exponent calculation ; X = (7)2 = 7 × 7 = 49.

When using more complex equations, which may combine several terms and use multiple operations, grouping the terms together helps organize the equation. Parentheses, ( ), are most commonly used in grouping, but you may also see brackets, [ ]. When a term or expression is inside one of these grouping symbols, it means that any operation indicated to be done on the group is done to the entire term or expression.

Formula: Example: ; Solve the equation N = 2 × [(9 ÷ 3) + (4 + 3)2]. Start with ; the operations inside the parentheses ( ), then perform the

operations inside the brackets [ ].

Formula: N = 2 × [(9 ÷ 3) + (4 + 3)2] ; N = 2 × [3 + (7)2]