unit arithmetic were developed over many centuries and are well documented in many textbooks in many different languages. In addition to the basic arithmetic functions encountered in decimal arithmetic, compound unit arithmetic employs three more functions: , in which a compound quantity is reduced to a single quantity—for example, conversion of a distance expressed in yards, feet and inches to one expressed in inches. , the inverse function to reduction, is the conversion of a quantity that is expressed as a single unit of measure to a compound unit, such as expanding 24 oz to . is the conversion of a set of compound units to a standard form—for example, rewriting "" as "". Knowledge of the relationship between the various units of measure, their multiples and their submultiples forms an essential part of compound unit arithmetic. Principles of compound unit arithmetic There are two basic approaches to compound unit arithmetic: where all the compound unit variables are reduced to single unit variables, the calculation performed and the result expanded back to compound units. This approach is suited for automated calculations. A typical example is the handling of time by Microsoft Excel where all time intervals are processed internally as days and decimal fractions of a day. in which each unit is treated separately and the problem is continuously normalized as the solution develops. This approach, which is widely described in classical texts, is best suited for manual calculations. An example of the ongoing normalization method as applied to addition is shown below. The addition operation is carried out from right to left; in this case, pence are processed first, then shillings followed by pounds. The numbers below the "answer line" are intermediate results. The total in the pence column is 25. Since there are 12 pennies in a shilling, 25 is divided by 12 to give 2 with a remainder of 1. The value "1" is then written to the answer row and the value "2" carried forward to the shillings column. This operation is repeated using the values in the shillings column, with the additional step of adding the value that was carried forward from the pennies column. The intermediate total is divided by 20 as there are 20 shillings in a pound. The pound column is then processed, but as pounds are the largest unit that is being considered, no values are carried forward from the pounds