Art. 46, a part of them having the subtrahend above the minuend, without making a mistake, he may then strive for rapidity. A rapid calculator will subtract as fast as he can write the figures of the result.

It will be a great help to the student if he will reverse the addition table. At odd moments, when walking or working, let him say to himself, 6 from 11 is how much? 9 from 17 is what? etc., and in a short time the right answer will present itself without any mental effort whatever.

48. Addition and subtraction form an extremely important part of a bookkeeper's work. The books must balance, as it is termed; i. e., the sum of the columns on the debit side must exactly equal the sum of the columns on the credit side. If an error of even one cent is made it will manifest itself in the trial balance, and a day or more may be spent in finding the error. Hence, the importance of accuracy. It is also important that no time be wasted in adding the columns, and in subtracting the sums of the two columns to find the balance. To illustrate, we give part of a page of a ledger. The double vertical lines separate the debit side on the left from the credit side on the right.

Now, what the bookkeeper has to do is to add the two columns and subtract the less sum from the greater; then he must write the difference in the column that contains the less sum, and also write it under the total of the column containing the greater sum. This difference is indicated by the word balance. In order not to mar the appearance of the ledger, no figures except those written above should be used.

If the student were obliged to write the two sums on a piece of waste paper in order to subtract them, considerable time would be lost, and confusion would result. There is a much shorter and easier method, when it can be readily seen which column contains the greater sum. It is as follows:

In the above account it is readily seen that the debit, or left-hand, column is the greater. Hence, add this column, and write the result, $5,061.40, underneath (the period separates the dollars from the cents). Now add the extreme right-hand column-8, 16-and subtract 16 from the first figure (right-hand figure) of the total in the debit column. This figure is a cipher; hence, we prefix 2 to the cipher, making 20; whence, 2016 4, which write in the credit column, as shown. Now add the second column on the credit side, carrying the 2-thus, 2, 10, 13-obtaining 13 as the sum. Now subtract 13 from 4, the second figure of the total on the debit side. But 13 cannot be taken from 4; hence, we prefix 1 to the 4, and 13 from 14 leaves 1, which write in the second column on the credit side, as shown. Then add the third column of the credit side, first adding the 1 that was prefixed-thus, 1, 5, 10, 18-obtaining 18 as the sum; subtract 18 from 21 (prefixing 2) and get 3, which write in the third column on the credit side. The sum of the fourth column, with the 2 that was prefixed, is 20. Subtracting 20 from 6, prefixing 2 to the 6, getting 26, leaves 6, which write in the fourth column on the credit side. The sum of the fifth column, with the 2 that was prefixed, is 33. Subtracting 33 from 40, formed by prefixing 4 to 0, leaves 7, which write in the fifth column on the credit side. Carrying 4 to the sixth column and adding it to the 1 gives 5, and 5 from 5 equals 0. Hence, the balance is $763.14. If the work has been done correctly, the debit and credit sides, when added, should give the same total. Adding the credit side, the total is $5,061.40, the same as the debit side; hence, the work is correct.

49. The student will find the addition method of subtraction the best to use in this case. Thus, adding the first

column on the right, the sum is 16. The right figure of 5,061.40 is a cipher; hence, we write 2 before the cipher, getting 20, and say 16 and 4 is 20, and write the 4 on the credit side, as shown. Now, carrying the 2, the sum of the second column is 13, and 13 and 1 is 14, writing the 1 as before. Carrying the 1, the sum of the numbers in the third column is 18, and 18 and 3 is 21; write the 3 and carry the 2. The sum of the third column plus the 2 carried is 20, and 20 and 6 is 26; write the 6 and carry the 2. The sum of the fourth column plus the 2 carried is 33, and 33 and 7 is 40; write the 7 and carry the 4. The sum of the fifth column plus the 4 carried is 5, and 5 and 0 is 5.

The student should apply both methods in solving the following examples.

EXAMPLES FOR PRACTICE.

50. Let the student practice this method on the following examples, one of which is worked out. If it is not apparent which set of numbers is the greater, he should add up the two left-hand columns and be guided by the sums so obtained.

Ans.

(1) 34,047; (2) 110,790; (3) 31,726; (4) 662,270; (5) $94.50; (6) $250.02; (7) 1,864,953.

MULTIPLICATION.

51. To multiply a number is to add the number to itself a certain number of times.

52. Multiplication is the process of multiplying one number by another.

The number thus added to itself, or the number to be multiplied, is called the multiplicand.

The number that shows how many times the multiplicand is to be taken, or the number by which we multiply, is called the multiplier.

The result obtained by multiplying is called the product.

53. The sign of multiplication is X. It is read times, or multiplied by. Thus, 9 x 6 is read 9 times 6, or 9 multiplied by 6.

54. It matters not in what order the numbers to be multiplied together are placed. Thus, 69 is the same as 9 × 6.

MULTIPLICATION TABLE.

55. In the following table, the product of any two numbers (neither of which exceeds twelve) may be found.

This table should be carefully committed to memory.

Since 0 has no value, the product of 0 and any number is 0.