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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

First, complete the operations inside the parentheses ( ).

Formula: N = 2 × [3 + 49] ; N = 2 × [52]

Second, complete the operations inside the brackets [ ].

Formula: N = 104
Figure 3-11. Converting between scientific and standard notation.
Figure 3-11. Converting between scientific and standard notation.

Order of Operation

In algebra, rules have been set for the order in which operations are evaluated. These same universally accepted rules are also used when programming algebraic equations in calculators. When solving the following equation, the order of operation is given below:

Formula: N = (62 – 54)2 + 62 – 4 + 3 × [8 + (10 ÷ 2)] + 25 + (42 × 2) ÷ 4 +3 /4
  1. Parentheses. First you must do everything in parentheses, ( ), starting from the innermost parentheses. If the expression has a set of brackets, [ ], treat these exactly like parentheses. If you are working with a fraction, treat the top as if it was in parentheses and the denominator as if it were in parentheses, even if there is none shown. From the equation above, completing the calculation in parentheses gives the following:
Formula: N = (8)2 + 62 – 4 + 3 × [8 + (5)] + 25 + (84) ÷ 4 + 3/4, ; then ; N = (8)2 + 62 – 4 + 3 × [13] + 25 + 84 ÷ 4 + 3/4 ; 2. Exponents. Next, clear any exponents. Treat any roots

(square roots, cube roots, and so forth) as exponents. Completing the exponents and roots in the equation

Formula: gives the following: ; N = 64 + 36 – 4 + 3 × 13 + 5 + 84 ÷ 4 + 3/4 ; 3. Multiplication and Division. Evaluate all of the

multiplications and divisions from left to right. Multiply and divide from left to right in one step. A common error is to use two steps for this (that is, to clear all of the multiplication signs and then clear all of the division signs), but that is not the correct method. Treat fractions as division. Completing the multiplication and division in the equation gives the following:

Formula: N = 64 + 36 – 4 + 39 + 5 + 21 + 3/4 ; 4. Addition and Subtraction. Evaluate the additions and

subtractions from left to right. Like above, addition and subtraction are computed left to right in one step. Completing the addition and subtraction in the equation gives the following:

Formula: X = 161 3/4

A commonly used acronym, PEMDAS, is used for remembering the order of operation in algebra. PEMDAS is an acronym for parentheses, exponents, multiplication, division, addition, and subtraction. To remember it, many use the sentence, “Please Excuse My Dear Aunt Sally.” Always remember, however, to multiply/divide or add/subtract in one sweep from left to right, not separately.

Figure 3-12. Total capacitance in a series circuit.
Figure 3-12. Total capacitance in a series circuit.

Order of Operation for Algebraic Equations

  1. Parentheses
  2. Exponents
  3. Multiplication
  4. Division
  5. Addition
  6. Subtraction