THE ADDING OF SEVERAL COLUMNS. ART. 7. Considerable practice will enable the accountant to add two or more columns at one operation. There is often an advantage in adding in this manner. Beyond two columns, or at most three, the method may be more skillful than practical. The following will illustrate the method of adding two columns: 86 75 68 34 59 Ans. 322 Process.-59 plus 30=89, plus 4=93, plus 60=153, plus 8=161, plus 70=231, plus 5=236, plus 80=316, plus 6=322. It will be seen that the process consists simply in adding the tens first and then the units. By naming only the results, we have 89, 93; 153, 161; 231, 236; 316, 322. The units may be added first and then the tens, thus: 63, 93; 101, 161; 166, 236; 242, 322. Three or more columns may be added in a similar manner, thus: 223 425 384 256 Ans. 1288 Operation.-256+4=260, 260+80=340, 340+300=640, 640+5=645, 645+20=665, 665+400=1065, 1065+3= 1068, 1068+20=1088, 1088+200=1288. By naming only results, we have: 260, 340, 640; 645, 665, 1065; 1068, 1088, 1288. Examples. 1 Add 25, 68, 67, 83, 37, 46, 99, 87, and 34. 2. Add 38, 46, 92, 37, 83, 46, 52, 53, and 46. 3. Add 286, 356, 396, 423, 345, 660, and 780. 4. Add 384, 236, 112, 345, 784, 569, and 963. SUBTRACTION. ART. 8. Ex. 1. From 3084 take 2793. 29184 Minuend changed in form. 3084 Minuend. 2793 Subtrahend. 291 Remainder. Remarks.-1. That the changed minuend above is equivalent to the given minuend is evident from the fact that 30 hundreds +8 tens-29 hundreds +18 tens. 2. Upon the principle that the difference between two numbers is the same as the difference between these numbers equally increased, instead of changing the form of the minuend, we can add 10 to the minuend figure when it is less than the lower subtrahend figure, and add 1 to the next higher order of the subtrahend. It is plain that 1 added to a higher order is the same as 10 added to the next lower. We do not borrow this 10 however, nor do we pay any thing by adding the 1. These terms ought not to be used. Examples. 2. From 406309 take 347278. 3. From 100102 take 90903. 4. From 5000050 take St432. 5. From one billion take one million and one. 6. From 32670804 take 3867498. Proof by excess of 9's.-Add the figures of the multiplicand, casting out the 9's and setting the excess at the right. Proceed in the same manner with the multiplier, setting the excess under that of the multiplicand. Multiply these excesses together and cast the 9's out of the result. Then cast out the 9's in the original product, and, if the work is correct, the last two excesses will agree. Although this is not always an absolute test of the correctness of a result, it is sufficiently so for common purposes. Ex. 2. Multiply 23045 by 70800. 9. How many feet would a horse travel in 109 days at the rate of 35 miles per day? (A mile contains 5280 feet.) 10. How much can 508 men earn in 65 days, if each man receives 3 dollars per day? DIVISION. ART. 10. Ex. 1. Divide 2920464 by 60843. 60843)2920464(48 Quotient. 243372 486744 486744 Suggestion.-Make 6 your trial divisor and 29 your first trial dividend. The second trial dividend is 48. Ex. 2. Divide 2406874 by 30400. 30400)24068 74(79 Quotient. 2128 2788 2736 5274 Remainder. Examples. 3. Divide 304608 by 304. 4. Divide 6743207 by 6200. 5. Divide 340068 by 27. 6. Divide 84306200 by 308000. 7. Divide 8408 by 24. 8. Divide 345602 by 18. 9. Divide 4060703 by 33. 10. Divide 412304 by 30300. CONTRACTIONS IN MULTIPLICATION AND DIVISION. ART. 11. There are abbreviated methods of multiplying and dividing numbers, which the expert accountant can often use with great advantage. With a little practice a person may readily multiply by two, three, or even more figures, at a single operation. The process of division may be abbreviated in a similar though less practical manner. Many of these methods, together with their explanations, are too complex for insertion here. The living teacher can best present such processes. Unless the student is made familiar with them, they are of no practical importance. ART. 12. When the multiplier is 14, 15, 16, etc. Operation. 3425 × 15 51375 Product. Remark. It is not necessary to put down any part of the operation. The result may be written at once by the following RULE. Multiply by the unit's figure, adding, after the unit's place, the figures of the multiplicand. Eamples. 2. Multiply 34809 by 13. 8. Multiply 369403 by 14. ART. 13. When the multiplier is 31, 41, 51, etc. Ex. 1. Multiply 3425 by 51. Operation. 3425 × 41 13700 140425 Product. RULE. Multiply by the ten's figure and add the product to the proper orders of the multiplicand. Examples. 2. Multiply 3486 by 71. |