SHOP ARITHMETIC CHAPTER I COMMON FRACTIONS 1. Why We Use Fractions. When we find it necessary to deal with things that are less than one unit, we must use fractions. A machinist cannot do all his work in full inches because it is generally impossible to have all measurements in exact inches. Consequently, for measurements less than 1 in., he uses fractions of an inch; he also makes use of fractions for measurements between one whole number of inches and the next whole number. If a bolt is wanted longer than 4 in. but shorter than 5 in., it would be 4 in. and a fraction of an inch. This fraction of an inch might be nearly a whole inch or it might be a very small part FIG. 1.-Scale used for measurement of piece of steel. 3 of an inch. The system used to designate parts of a unit is easily seen by looking at a machinist's scale or at a foot rule of any sort. Each inch on the scale is divided into a number of equal parts. A wooden foot rule usually has 8 or 16 parts to each inch, while a machinist's steel scale has much finer divisions. Now, if we want to measure a piece of steel which is not an inch long, we hold a scale against it, as in Fig. 1, and find out how many of these divisions of an inch it takes to equal the length of the piece. The scale in Fig. 1 is 3 in. long, and each inch is divided into 8 parts. We see that this piece of steel is as long as five of these eight parts of an inch, or we say that it is "fiveeighths" of an inch long. |