HOWARD'S ART OF RECKONING. ADDITION. ADDITION is the act of adding numbers. 15 Various suggestions have been made referring to improved methods of addition. In nearly every case the proposed improvement has been more fanciful than real. In practice, I have found no better or quicker method than the following: 3746 8743 6978 1256 3021 23744 Commence at the bottom of the right hand column; add thus, 7, 15, 18, 24; set down the 4 in unit's place, and carry the two tens to the second column; then add thus, 4, 9, 16, 24; set down the 4 in ten's place, and carry the two hundreds to the third column, and so on to the end. Never add in this manner: 1 and 6 are seven, and 8 are 15, and 3 are 18, and 6 are 24. It is just as easy to name the sum at once, omitting the name of each separate figure, and saves two thirds of time and labor. Book-keepers and others who have long columns of figures to add will find the following methods and suggestions acceptable. B 8 772 5 8 In adding long columns of figures, write in 4 the margin, lightly with pencil, opposite the 9 last figure added, the unit figure of the sum 6 immediately exceeding 100. By doing this the mind is never burdened with numbers beyond 100; and if interrupted in the work, it can be 4 resumed at the stage at which the interruption 6 occurred. The example in the margin shows the method; opposite the figure 7; the 2 indicating the column, so far, with the 7 included, 9 amounts to 102. 9 8 8 INSTANTANEOUS ADDITION BY COMBINATION. Write two, three, four, or more rows of miscellaneous figures, then write such figures as will make an equal number of nines in each column; under these again, write another row of miscellaneous figures. EXAMPLE 4987 2187 50 12 one 9. 5 2 6 3 two 9's. 7.8 1 2 three 9's. 4986 34983* RULE.-Bring down the last row, less the number of nines in each column, and prefix the number of nines. *This example has three nines in each column. Rule of addition for two columns at once: first practice adding two columns of two figures each, until you are able to grasp at a glance, and pronounce their Add from the left, and say three seven, four eight, twelve eight, &c., &c., instead of thirty-seven, forty-eight, one hundred and twenty-eight, &c., &c.; this habit is readily acquired and saves half the time. When you can instantly, at sight, name the sum of two pairs of figures, practice with gradually increasing columns of pairs, then take examples consisting of two or more columns of pairs. 36 2147 *The process is twelve six, one four naught; the 40 is put down and the 1 carried to the units column in the next pair, then ten naught, one four six. Any person who will PRACTICE this method, may add two columns with perfect ease; there is no royal road to this accomplishment: speed with precision can be attained only by persistent PRACTICE. Fives are always easy to add; so are 9's, when it is borne in mind that adding 9 to a sum places it in the next higher ten with the unit 1 less; thus, 17+ 9 = 26; 39 + 9 = 48; 63 + 9 = 72. SUBTRACTION is the process of finding the difference of two numbers by taking one number called the Subtrahend from another number called the Minuend. The answer is called the Difference or Remainder. RULE. Write the numbers so that the units in the subtrahend shall be directly under the units of the same order in the minuend; under, and in the same order, write the difference. 1694 Subtract 473 from 1694. 473 1221 To prove Subtraction, add the difference to the subtrahend; if correct, their sum=the minuend. MULTIPLICATION. MULTIPLICATION is the addition of several numbers in one act by adding to zero, one number called the Multiplicand, as many times as there are units in another number called the Multiplier. The answer is called the Product. Note.-The multiplier must be an abstract number. The base of our system of notation is 10; therefore numbers increase and diminish in a tenfold ratio; increasing from the decimal point to the left, and decreasing from the decimal point to the right; hence to multiply any number by 10, annex a cipher, or remove the point one place to the right. To multiply any number by 100, annex two ciphers, or remove the point two places to the right. To multiply any number by 1000, annex three ciphers, or remove the point three places to the right. MULTIPLICATION. 19 In multiplying be careful always to write the units, tens, etc., of the multiplier under the units, tens, etc., of the multiplicand, and the figures of the product in the same order. To find the product of two numbers, each expresed by two figures only. Multiply 54 by 32. 54 32 1728 Process.-First multiply the units figure of the multiplicand by the units figure of the multiplier, thus: 4 X 28; put the 8 in the units place in the product, then 5×2 + 4×3=22, put the units 2 on the left of the 8 and carry the other 2; then, 5×3+2=17, which, put down, making a total of 1728, the answer. The same method can be applied when the multiplicand has three or more figures. 163 24 3912 The steps are: 3 × 4 = 12, set down the 2 and carry the 1; (6 × 4) + (3 × 2) + 1 31; set down the 1, and carry the 3. (1 × 4) + (6 × 2) + 3 = 19; set down 9 and carry 1; 1 x 2 + 1 = 3, which place at the head of the line, making a total of 3912. When the multiplier can be resolved into two factors, it is sometimes shorter to multiply by each factor, than by the whole number. EXAMPLE, multiply 163 by 24. 8 × 3 = 24. 163 8 1304 3 3912 Ans. |