A most interesting beginning at such an inventory of the actual uses of arithmetic has been made by Wilson ['19] and Mitchell.[2] Although their studies need to be much extended and checked by other methods of inquiry, two main facts seem fairly certain. First, the great majority of people in the great majority of their doings use only very elementary arithmetical processes. In 1737 cases of addition reported by Wilson, seven eighths were of five numbers or less. Over half of the multipliers reported were one-figure numbers. Over 95 per cent of the fractions operated with were included in this list: 1/2 1/4 3/4 1/3 2/3 1/8 3/8 1/5 2/5 4/5. Three fourths of all the cases reported were simple one-step computations with integers or United States money. Second, they often use these very elementary processes, not because such are the quickest and most convenient, but because they have lost, or maybe never had, mastery of the more advanced processes which would do the work better. The 5 and 10 cent stores, the counter with "Anything on this counter for 25¢," and the arrangements for payments on the installment plan are familiar instances of human avoidance of arithmetic. Wilson found very slight use of decimals; and Mitchell found men computing with 49ths as common fractions when the use of decimals would have been more efficient. If given 120 seconds to do a test like that shown below, leading lawyers, physicians, manufacturers, and business men and their wives will, according to my experience, get only about half the work right. Many women, finding on their meat bill "7-3/8 lb. roast beef $2.36," will spend time and money to telephone the butcher asking how much roast beef was per pound, because they have no sure power in dividing by a mixed number. [2] The work of Mitchell has not been published, but the author has had the privilege of examining it. Test Perform the operations indicated. Express all fractions in answers in lowest terms. _Add:_ 3/4 + 1/6 + .25 4 yr. 6 mo. 1 yr. 2 mo. 6 yr. 9 mo. 3 yr. 6 mo. 4 yr. 5 mo. ----------- _Subtract:_ 8.6 - 6.05007 7/8 - 2/3 = 5-7/16 - 2-3/16 = _Multiply:_ 29 ft. 6 in. 7 × 8 × 4-1/2 = 8 ------------ _Divide:_ 4-1/2 ÷ 7 = It seems probable that the school training in arithmetic of the past has not given enough attention to perfecting the more elementary abilities. And we shall later find further evidence of this. On the other hand, the fact that people in general do not at present use a process may not mean that they ought not to use it.