Part 4

Salesmen usually make change by addition. They have the money to count out, and in doing so they add to the amount of the purchase until they reach the amount of the bill presented. For example, if you buy something worth $3.35 and present a ten-dollar bill in payment, you will probably receive in return 5 cents, 10 cents, 50 cents, $1, and $5; the salesman saying 40, 50, $4, $5; $10. This method is least liable to error.

Accuracy and rapidity in counting out change can best be acquired by practice behind the counter or at the cash-desk.

Proof of Multiplication in Ten Seconds.

The unitate of a number is the sum of its digits reduced to a unit.

252 = 9 } = 54 = 9 321 = 6 } --- 252 504 756 ----- 80892 = 27 = 9

The unitate of the multiplier is 9 and the unitate of the multiplicand is 6; 6 times 9 equals 54, and the unitate of 54 is 9. Now the unitate of the product is found to be 9 also, which is a proof of the correctness of the work.

The Canadian Interest Rule.

4 | 724 181 × 11 = 19.91

This rule of computing interest appears in some Canadian text-books, and, though simply a modification of other rules, is worthy of notice. To find the interest on $724 for 5-1/2 months at 6 per cent., all you have to do is to divide by 4 and multiply by 11. The rule is to divide the principal by 4, and to multiply the quotient by one-third of the product of the rate by the time in months. Six times 5-1/2 = 33, and one-third of 33 is 11. If the time be expressed in years, multiply one-fifth of the principal by one-half the product of the rate by the number of years, and remove the decimal point one place to the left.

Table of Transposed Numbers.

DIFFERENCES.

9 { 10 21 32 43 54 65 76 87 98 { 01 12 23 34 45 56 67 78 89

18 { 20 31 42 53 64 75 86 97 { 02 13 24 35 46 57 68 79

27 { 30 41 52 63 74 85 96 { 03 14 25 36 47 58 69

36 { 40 51 62 73 84 95 { 04 15 26 37 48 59

45 { 50 61 72 83 94 { 05 16 27 38 49

54 { 60 71 82 93 { 06 17 28 39

63 { 70 81 92 { 07 18 29

72 { 80 91 { 08 19

81 { 90 { 09

90 { 100 { 010

99 { 100 { 001

Explanation of Foregoing Table.

The transposition of figures is a frequent cause of errors in proving accounts and balance sheets. This table is founded on the fact that all differences between transposed numbers are multiples of nine. The difference between the figures misplaced is equal to the quotient of the resulting error when divided by nine; thus, 91 - 19 = 72; 72 ÷ 9 = 8; 9 - 1 = 8, and the labor of searching for it may be confined to examining those figures the transposition of which would make the difference, as they are the only ones that can cause the error. Thus: if the error in the balance-sheet be 81 cents, it is possibly caused by a transposition, and the clerk can first examine the cents column of his books for items of 90 cents, or 09 cents, alone, with a strong probability of finding the cause of the error without further revision. Transpositions may occur in any decimal or integer place, and the differences caused thereby are divisible by nine without a remainder; but, beyond this table, the numbers ascend in regular progression, each difference increasing by nine, as follows:

108 { 120; 117 { 130; 126 { 140; etc. { 12 { 13 { 14

The quotient of the difference in a regular progression, when divided by nine, gives the figures transposed, thus: 130 - 13 = 117 ÷ 9 = 13, which are the figures to be sought for when a discrepancy of 117 is shown; but this will not apply to differences below 81, nor to mixed transpositions. An error divisible by two may be caused by posting an item to the wrong side of the ledger.

Short Method to Find the Interest of a Given Sum.

Reduce the time to months, and to the number thus found annex one-third of the days, which whole number multiplied by one-half of your principal will produce you the required interest in dollars, cents and mills, at 6 per cent. If days only are given, multiply one-third of the days by one-half of the principal for the required interest at 6 per cent. Note these exercises: