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handbook

Aviation Maintenance Technician Handbook–General

FAA-H-8083-30B Version 2023

Chapter 3

Mathematics in Aviation Maintenance

Formula: (7 – 1) = (7 × 5 – 1 × 8) = (35 – 8 ) = (35 – 8) = 27 ; 8 5 8 × 5 5 × 8 40 40 40 40

Therefore, 27⁄40 is the minimum droop.

Multiplication of Fractions

Multiplication of fractions does not require a common denominator. To multiply fractions, first multiply the numerators. Then, multiply the denominators.

Example:

Formula: 3 × 7 × 1 = 3 × 7 × 1 = 21 ; 5 8 2 5 × 8 × 2 80

The use of cancellation when multiplying fractions is a helpful technique. Cancellation divides out or cancels all common factors that exist between the numerators and denominators. When all common factors are cancelled before the multiplication, the final product is in the simplest form.

Formula: Example: ; 2 1 ; ( 14 × 3 ) = (14 × 3) = ( 2 × 1) = 2 ; 15 7 15 7 5 × 1 5 ; 5 1

Division of Fractions

Division of fractions does not require a common denominator. To divide fractions, first change the division symbol to multiplication. Next, invert the second fraction. Then, multiply the fractions.

Example: Divide 7⁄8 by 4⁄3

Formula: ( 7 ÷ 4 ) = ( 7 × 3 ) = ( 7 × 3) = 21 ; 8 3 8 4 8 × 4 32

Example: In Figure 3-2, the center of the hole is in the center of the plate. Find the distance that the center of the hole is from the edges of the plate. To find the answer, the length and width of the plate should each be divided in half. First, change the mixed numbers to improper fractions:

Formula: 5 7/16 inches = 87/16 inches ; 3 5/8 inches = 29/8 inches

Then, divide each improper fraction by 2 to find the center of the plate.

Formula: 87 ÷ 2 = 87 × 1 = 87 inches ; 16 1 16 2 32 ; 29 ÷ 2 = 29 × 1 = 29 inches ; 8 1 8 2 16

Finally, convert each improper fraction to a mixed number:

Formula: 87 = 87 ÷ 32 = 2 23 inches ; 32 32 ; 29 = 29 ÷ 16 = 1 13 inches ; 16 16

Therefore, the distance to the center of the hole from each of the plate edges is 2 23⁄32 inches and 1 13⁄16 inches.

Reducing Fractions