General (1-4)

Reducing Fractions
A fraction needs to be reduced when it is not in “lowest terms.” Lowest terms means that the numerator and denominator do not have any factors in common. That is, they cannot be divided by the same number (or factor).
To reduce a fraction, determine what the common factor(s) are and divide these out of the numerator and denominator. For example when both the numerator and denominator are even numbers, they can both be divided by 2.

Example: The total travel of a jackscrew is 13⁄16 inch. If the travel in one direction from the neutral position is 7⁄16 inch, what is the travel in the opposite direction?

 

 

 

The fraction 6⁄16 is not in lowest terms because the numerator (6) and the denominator (16) have a common factor of 2. To reduce 6⁄16, divide the numerator and the denominator by 2. The final reduced fraction is 3⁄8 as shown below. 

 

 

 

 

Therefore, the travel in the opposite direction is 3⁄8 inch.
Mixed Numbers A mixed number is a combination of a whole number and a fraction.
Addition of Mixed Numbers To add mixed numbers, add the whole numbers together. Then add the fractions together by finding a common denominator. The final step is to add the sum of the whole numbers to the sum of the fractions for the final result.
Example: The cargo area behind the rear seat of a small airplane can handle solids that are 43⁄4 feet long. If the rear seats are removed, then 2 1⁄3 feet is added to the cargo area. What is the total length of the cargo area when the rear seats are removed? 

 

 

 

Subtraction of Mixed Numbers
To subtract mixed numbers, find a common denominator for the fractions. Subtract the fractions from each other (it may be necessary to borrow from the larger whole number when subtracting the fractions).
Subtract the whole numbers from each other. The final step is to combine the final whole number with the final fraction.

Example: What is the length of the grip of the bolt shown in Figure 1-3? The overall length of the bolt is 31⁄2 inches, the shank length is 31⁄8 inches, and the threaded portion is 15⁄16 inches long. To find the grip, subtract the length of the threaded portion from the length of the shank. 

 

 

 

To subtract, start with the fractions. Borrowing will be necessary because 5⁄16 is larger than 1⁄8 (or 2⁄16). From the whole number 3, borrow 1, which is actually 16⁄16. After borrowing, the first mixed number will now be 2 18⁄16. (Because, 3 1⁄8 = 3 2⁄16 = 2 + 1 + 2⁄16 = 2 + 16⁄16+ 2⁄16 = 2 18⁄16.)

 

 

 

 

 

 

 

Therefore, the grip length of the bolt is 1 13⁄16 inches.
(Note: The value for the overall length of the bolt was given in the example, but it was not needed to solve the problem. This type of information is sometimes referred to as a “distracter” because it distracts from the information needed to solve the problem.)