In solving problems the process should be not merely indicated, but all the figures necessary in solving each problem should be given in full. The answers to each problem should be indicated by writing “Ans.” after it. =Arithmetic= is the science of numbers. =A Number= is the result of the comparison (also called measurement) of a magnitude or quantity with another magnitude or quantity of the same kind supposed to be known. =A Concrete Number= is one the nature of the unit of which is known. =Denominate Number.=--A concrete number the standard of which is fixed by law or established by long usage. =An Abstract Number= is one of which the nature of the unit is unknown. =How to Read Numbers.=--The right way to read 101,274, etc., is one hundred one, two hundred seventy-four, etc. =The Decimal Point.=--A period, called decimal point, is placed in a mixed number between the integral part and the decimal portion which follows. It should never be omitted. =Roman Numbers.=--I stands for 1, V for 5, X for 10, L for 50, C for 100, D for 500 and M for 1,000. =Abbreviations.=--A smaller unit, written to the left of a greater one, is subtracted from the latter, as: IV = 4 (IV is marked IIII on clock and watch dials); IX = 9; XC = 90; CD = 400, etc. Sometimes a Roman number is surmounted by a dash or vinculum; it then expresses thousands, as IX = 9,000. Addition. =Addition.=--Operation which consists in taking in any order all the units and portions of units of several numbers and forming with them a single number called their Sum or Total. =Addition of Long Columns of Numbers.=--When long columns of numbers are to be added, the student should endeavor to add more than one figure at a time. He may pick those which aggregate 10, 15, 20, etc., and add the intermediate figures when convenient. =Sign of Addition.=--The sign of addition is the horizontal-vertical or Roman cross + placed between all the numbers to be added; it is read Plus. =To Prove an Addition.=--The shortest way to prove an addition is to do it over again from bottom to top. =Sign of Equality.=--The sign of equality is two short equal horizontal parallels =; it reads Equal. Subtraction. =Subtraction.=--An operation which consists in taking from a number called =minuend= (m) all the units and parts of units contained in another number called =subtrahend= (s). The result is called the =difference= (d) of the two numbers or the =remainder= of their subtraction. =Sign of Subtraction.=--The sign of subtraction is a horizontal dash - placed between the minuend, written first, and the subtrahend. Thus: 84 - 38 = d; 84 - 38 = 46. Generally m - s = d. =To Prove a Subtraction.=--Add from bottom to top the difference and the subtrahend; the sum must equal the minuend. Multiplication.