General (1-3)

Subtraction of Fractions
In order to subtract fractions, they must have a common denominator.

 

 

If the fractions do not have the same denominator, then one or all of the denominators must be changed so that every fraction has a common denominator.

Example: The tolerance for rigging the aileron droop of an airplane is 7⁄8 inch ± 1⁄5 inch. What is the minimum droop to which the aileron can be rigged? To subtract these fractions, first change both to common denominators.
The common denominator in this example is 40. Change both fractions to 1⁄40, as shown, then subtract. 

 

 

 

 

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. 

 

 

 

The use of cancellation when multiplying fractions is a helpful technique which 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 will be in lowest terms. 

 

 

 

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: In Figure 1-2, 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: 

 

 

 

 

 

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

 

 

 

Finally, convert each improper fraction to a mixed number: 

 

 

 

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.