18. Short Method for Casting out 9's. After a little practice the casting out of 9's can be done with very much less trouble.

=

Looking at the first number (437) of § 17 we see at once that the excess is 5 because 7+3 10 (1 more than 9) and this 1 is added to the 4. This excess of 5 with the 5 of the next line gives 10 or an excess of 1. Add this to 7, giving 8. The 9 is disregarded. Proceeding this way we obtain 5 as the excess of the whole column of numbers.

The casting out of 9's is not an absolute test, since the result may be wrong in just such ways as to leave the excess unchanged. Thus 2912 and 2921 have the same excess. On the other hand, if the excess of all the numbers and of the sum are not the same, the result cannot be correct.

19. Check by Dividing Columns. An effective check in adding a long column of numbers is to add the whole column and then divide it into two columns, add each of these, and then add their sums.

WRITTEN EXERCISES

Copy and add the following columns of figures and check by casting out 9's. Also check as suggested in § 19. Remember that correct copying is as important as correct adding.

20. Horizontal Addition. — In order to save laborious copying it is sometimes necessary to add numbers horizontally. Thus 347 + 591 +260 + 495 + 398 = 2091.

Horizontal addition is just like vertical addition, except that it is necessary to take great care that numbers of the same order are added.

ORAL EXERCISES

Add the following horizontally; write down the sums but do not copy the figures to be added.

1. 145 169 + 847

2. 856 + 391 + 670

3. 319 + 1810 + 2780

5. 674 +592 + 547

6. 492 + 276 + 542

7. 192 + 1370 + 430

4. 5402900 + 8694

8. 1872476 + 896

21. Designing Blank Forms. The professional bookkeeper often has to design blank forms suited for his particular purpose. In designing such forms the following should be kept in mind:

1. The width of a column should allow about one eighth of an inch for each figure. If the column is to be added, it should be remembered that the sum is likely to contain one figure more (possibly two if the column is very long) than any of the figures to be added.

2. The height of the column should allow one inch for five numbers with at least a half inch over for ruling and writing the sum. 3. If the blank is intended for writing dollars and cents, a column one fourth inch wide must be ruled for writing the cents.

1. Write figures of the same order in a straight column, taking care that the first figures at the right are near the right margin of the space in which the numbers are written.

2 Look at a number once and then copy the whole number without looking at it again. Verify the accuracy of the copying by looking at the copied number and then at the original.

3. Take special care not to omit a number or to invert the order of two figures.

PROBLEMS

1. The following are the numbers of men, women, and children admitted to a series of baseball games:

a. Draw a blank form suitable for the above and copy the figures on this form.

b. Find the total number of men by horizontal addition, also the total number of women and the total number of children. Then add these totals to get the grand total for the series.

c. Find the total attendance each day and add these horizontally, to find the total for the series.

In the above example the total is found in two ways. Such problems are said to be self-checking.

To add a very long column, it may be broken up into several colThese may then be added and checked by horizontal addition, as is indicated in the example below.

umns.

2. Make an appropriate blank, copy, and find the sums and the total in the following:

SUMS

PROBLEMS

1. Following is a week's record of the sales of six clerks working in the same department in a large store. Make a blank, copy, and find totals as on page 17.

2. The numbers of boys in the Cleveland Academic high schools below normal age, of normal age, and above normal age, in a recent year, were as follows:

Make blank, copy, and find the totals.

3. The numbers of girls in the same schools and under the same conditions were as follows:

PROBLEMS

1. In a certain city the daily attendance in the grammar schools for one week was as follows: The Central School, 496, 512, 487, 506, and 503; at the Daly School, 243, 238, 251, 247, and 241; at the Hawthorne School, 491, 478, 473, 483, and 485; at the Lincoln School, 184, 192, 196, 189, and 191; at the Lowell School, 291, 287, 296, 289, and 293; at the Manual Training School, 212, 220, 218, 217, and 213; at the Prescott School, 317, 321, 324, 319, and 318; at the Roosevelt School, 518, 521, 524, 519, and 521; at the Whittier School, 98, 101, 103, 100, and 97; at the Willard School, 150, 161, 154, 158, and 153.

Design a proper blank for recording this attendance, copy, and add to find the total daily attendance for the city, the total for each school for the week, and the total for the city for the week.

2. In a department store in a small city the daily sales for one week were as follows: Men's clothing, $1489.50, $948.75, $859.25, $1046.40, $1147.60, and $1846.40; women's suits, etc., $742.60, $541.35, $962.20, $824.20, $730.60, and $1121.40; notions, $294.70, $187.65, $341.24, $541.70, $281.60, and $879.30; shoes, $364.80, $324.20, $478.20, $543.50, $521.70, and $849.75; groceries, $297.60, $304.75, $327.24, $378.40, $312.78, and $594.36; hardware, $719.60, $321.50, $217.20, $180.35, $479.80, and $1124.50; furniture, $1560, $581.50, $629.60, $2890.50, $1242.20, and $1938.40; farm implements, $316.50, $184.00, $867.90, $357.40, $740.00, and $1780.00.

Enter on a suitable blank the items just given. Find the total sales for each day for the whole store, the total sales for each department for the week, and the grand total for the week for the store.

3. Following is a week's record of the packages delivered daily by the wagons of a retail store: Wagon no. 1, 417, 391, 289, 326, 358, 317; wagon no. 2, 217, 293, 236, 327, 356, 410; wagon no. 3, 192, 341, 321, 376, 248, 354; wagon no. 4, 384, 307, 424, 375, 293, 214; wagon no. 5, 246, 238, 302, 316, 279, 285.

Enter on a suitable blank the items just given and find the totals.