Mathematics in Aviation Maintenance

The first and last terms of the proportion (the 3 and 8 in this example) are called the extremes. The second and third terms (the 4 and 6 in this example) are called the means. In any proportion, the product of the extremes is equal to the product of the means.

Formula: In the proportion 2:3 = 4:6, the product of the extremes, ; 2 × 6, is 12; the product of the means, 3 × 4, is also 12. An

inspection of any proportion shows this to be true.

Normally when solving a proportion, three quantities are known, and the fourth is unknown. To solve for the unknown, multiply the two numbers along the diagonal and then divide by the third number.

Example: Solve for X in the proportion given below.

Formula: 65 X ; = ; 80 100 ; First, multiply 65 × 100: 65 × 100 = 6500 ; Next, divide by 80: 6500 ÷ 80 = 81.25 ; Therefore, X = 81.25.

Example: An airplane flying 300 miles used 24 gallons of gasoline. How many gallons will it need to travel 750 miles?

The ratio here is: “miles to gallons;” therefore, the proportion is set up as:

Formula: Miles 300 = 750 ; Gallons 24 G

Formula: Figure 3-6 formula reference: Fraction, decimal-inch, and millimeter conversion chart. Examples: 1/64 inch = 0.015625 inch ≈ 0.397 millimeter; 1/32 inch = 0.03125 inch ≈ 0.794 millimeter; 1/16 inch = 0.0625 inch ≈ 1.588 millimeters; 1/8 inch = 0.125 inch = 3.175 millimeters; 1/4 inch = 0.25 inch = 6.35 millimeters; 1/2 inch = 0.5 inch = 12.7 millimeters; 3/4 inch = 0.75 inch = 19.05 millimeters; 1 inch = 25.4 millimeters. Source text: Fraction Decimal MM Fraction Decimal MM Fraction Decimal MM ; 1/64 0.015 0.396 1 1/64 1.015 25.796 2 1/64 2.015 51.196 ; 1/32 0.031 0.793 1 1/32 1.031 26.193 2 1/32 2.031 51.593 ; 3/64 0.046 1.190 1 3/64 1.046 26.590 2 3/64 2.046 51.990 ; 1/16 0.062 1.587 1 1/16 1.062 26.987 2 1/16 2.062 52.387 ; 5/64 0.078 1.984 1 5/64 1.078 27.384 2 5/64 2.078 52.784 ; 3/32 0.093 2.381 1 3/32 1.093 27.781 2 3/32 2.093 53.181 ; 7/64 0.109 2.778 1 7/64 1.109 28.178 2 7/64 2.109 53.578 ; 1/8 0.125 3.175 1 1/8 1.125 28.575 2 1/8 2.125 53.975 ; 9/64 0.140 3.571 1 9/64 1.140 28.971 2 9/64 2.140 54.371 ; 5/32 0.156 3.968 1 5/32 1.156 29.368 2 5/32 2.156 54.768 ; 11/64 0.171 4.365 1 11/64 1.171 29.765 2 11/64 2.171 55.165 ; 3/16 0.187 4.762 1 3/16 1.187 30.162 2 3/16 2.187 55.562 ; 13/64 0.203 5.159 1 13/64 1.203 30.559 2 13/64 2.203 55.959 ; 7/32 0.218 5.556 1 7/32 1.218 30.956 2 7/32 2.218 56.356 ; 15/64 0.234 5.953 1 15/64 1.234 31.353 2 15/64 2.234 56.753 ; 1/4 0.25 6.35 1 1/4 1.25 31.75 2 1/4 2.25 57.15 ; 17/64 0.265 6.746 1 17/64 1.265 32.146 2 17/64 2.265 57.546 ; 9/32 0.281 7.143 1 9/32 1.281 32.543 2 9/32 2.281 57.943 ; 19/64 0.296 7.540 1 19/64 1.296 32.940 2 19/64 2.296 58.340 ; 5/16 0.312 7.937 1 5/16 1.312 33.337 2 5/16 2.312 58.737 ; 21/64 0.328 8.334 1 21/64 1.328 33.734 2 21/64 2.328 59.134 ; 11/32 0.343 8.731 1 11/32 1.343 34.131 2 11/32 2.343 59.531 ; 23/64 0.359 9.128 1 23/64 1.359 34.528 2 23/64 2.359 59.928 ; 3/8 0.375 9.525 1 3/8 1.375 34.925 2 3/8 2.375 60.325 ; 25/64 0.390 9.921 1 25/64 1.390 35.321 2 25/64 2.390 60.721 ; 13/32 0.406 10.318 1 13/32 1.406 35.718 2 13/32 2.406 61.118 ; 27/64 0.421 10.715 1 27/64 1.421 36.115 2 27/64 2.421 61.515 ; 7/16 0.437 11.112 1 7/16 1.437 36.512 2 7/16 2.437 61.912 ; 29/64 0.453 11.509 1 29/64 1.453 36.909 2 29/64 2.453 62.309 ; 15/32 0.468 11.906 1 15/32 1.468 37.306 2 15/32 2.468 62.706 ; 31/64 0.484 12.303 1 31/64 1.484 37.703 2 31/64 2.484 63.103 ; 1/2 0.5 12.7 1 1/2 1.5 38.1 2 1/2 2.5 63.5 ; 33/64 0.515 13.096 1 33/64 1.515 38.496 2 33/64 2.515 63.896 ; 17/32 0.531 13.493 1 17/32 1.531 38.893 2 17/32 2.531 64.293 ; 35/64 0.546 13.890 1 35/64 1.546 39.290 2 35/64 2.546 64.690 ; 9/16 0.562 14.287 1 9/16 1.562 39.687 2 9/16 2.562 65.087 ; 37/64 0.578 14.684 1 37/64 1.578 40.084 2 37/64 2.578 65.484 ; 19/32 0.593 15.081 1 19/32 1.593 40.481 2 19/32 2.593 65.881 ; 39/64 0.609 15.478 1 39/64 1.609 40.878 2 39/64 2.609 66.278 ; 5/8 0.625 15.875 1 5/8 1.625 41.275 2 5/8 2.625 66.675 ; 41/64 0.640 16.271 1 41/64 1.640 41.671 2 41/64 2.640 67.071 ; 21/32 0.656 16.668 1 21/32 1.656 42.068 2 21/32 2.656 67.468 ; 43/64 0.671 17.065 1 43/64 1.671 42.465 2 43/64 2.671 67.865 ; 11/16 0.687 17.462 1 11/16 1.687 42.862 2 11/16 2.687 68.262 ; 45/64 0.703 17.859 1 45/64 1.703 43.259 2 45/64 2.703 68.659 ; 23/32 0.718 18.256 1 23/32 1.718 43.656 2 23/32 2.718 69.056 ; 47/64 0.734 18.653 1 47/64 1.734 44.053 2 47/64 2.734 69.453 ; 3/4 0.75 19.05 1 3/4 1.75 44.45 2 3/4 2.75 69.85 ; 49/64 0.765 19.446 1 49/64 1.765 44.846 2 49/64 2.765 70.246 ; 25/32 0.781 19.843 1 25/32 1.781 45.243 2 25/32 2.781 70.643 ; 51/64 0.796 20.240 1 51/64 1.796 45.640 2 51/64 2.796 71.040 ; 13/16 0.812 20.637 1 13/16 1.812 46.037 2 13/16 2.812 71.437 ; 53/64 0.828 21.034 1 53/64 1.828 46.434 2 53/64 2.828 71.834 ; 27/32 0.843 21.431 1 27/32 1.843 46.831 2 27/32 2.843 72.231 ; 55/64 0.859 21.828 1 55/64 1.859 47.228 2 55/64 2.859 72.628 ; 7/8 0.875 22.225 1 7/8 1.875 47.625 2 7/8 2.875 73.025 ; 57/64 0.890 22.621 1 57/64 1.890 48.021 2 57/64 2.890 73.421 ; 29/32 0.906 23.018 1 29/32 1.906 48.418 2 29/32 2.906 73.818 ; 59/64 0.921 23.415 1 59/64 1.921 48.815 2 59/64 2.921 74.215 ; 15/16 0.937 23.812 1 15/16 1.937 49.212 2 15/16 2.937 74.612 ; 61/64 0.953 24.209 1 61/64 1.953 49.609 2 61/64 2.953 75.009 ; 31/32 0.968 24.606 1 31/32 1.968 50.006 2 31/32 2.968 75.406 ; 63/64 0.984 25.003 1 63/64 1.984 50.403 2 63/64 2.984 75.803 ; 1 1 25.4 2 2 50.8 3 3 76.2

Therefore, to fly 750 miles, 60 gallons of gasoline is required.

Percentage means “parts out of one hundred.” The

Formula: percentage sign is “%.” Ninety percent is expressed as 90% ; (= 90 parts out of 100). The decimal 0.90 equals 90/100, or 90 ; out of 100, or 90%.

To express a decimal number in percent, move the decimal point two places to the right (adding zeroes if necessary) and then affix the percent symbol.

Example: Express the following decimal numbers as a percent:

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Aviation Maintenance Technician Handbook–General

Solving Proportions

Percentage

Expressing a Decimal Number as a Percentage