TO THE TEACHER. Inability to write or copy numbers accurately is the cause of frequent mistakes. Dictate the above numbers, and then cause the work to be checked for accuracy and legibility. Make frequent use of dictation exercises of this kind.

NOTE. In offices the expression to "foot-up," meaning to "add,” is frequently heard; the sum is called the "footing."

17. Horizontal addition. In invoices and in arrangements of numbers in tabular form, it is sometimes necessary to add numbers horizontally. Care should be taken to combine figures of the same order: units with units, tens with tens, etc. Do not attempt to add horizontally if the numbers are very long; place a dot over each figure as it is added.

1. Find (a) the total native parentage, (b) the total foreign or mixed parentage, (c) the foreign whites, (d) the

total negro population, (e) the total population of each city. Check your work.

and by rows, and check the work by adding the vertical and horizontal totals and comparing the two amounts.

SUMMARY FOR WEEK ENDING JULY 25

CARPETS FURNITURE STOVES

BOOKS

DISHES

TOTAL

Mon.

$2436.15 $8654.72 $ 237.58 $ 972.15 $ 238.17

3. The number of pupils in school was as follows, as indicated by buildings and by grades. How many were there in each grade? in each building? Check your work.

SUBTRACTION

18. The most rapid method in subtraction is illustrated as follows: suppose you wish to subtract 3615 from 9521. 9521 Say to yourself: 5 and 6 (put down the 6) are 11, carry 1; 3615 2 (1 + 1 carried) and 0 (put down the 0) are 2; 6 and 9 (put down the 9) are 15; 4 (3 + 1 carried) and 5 are 9. Put down 5906 the 5.

In other words you are to find that number which added to 3615 will give 9521.

19. Ease and rapidity in subtraction will come with practice. Drill on the following, reading the differences at sight. The eighty results should be read in a minute and a half.

20. Checking. The best way to check subtraction is to add (upward) the remainder to the subtrahend, checking the result by the figures in the minuend as you do so. Thus in § 18,6 + 5 = 11 (check the 1), 0+ 1+1=2 (check), 9+6= 15 (check), 5+1 + 3 = 9.

21. A parenthesis, (), signifies that all quantities within it are to be considered together. A vinculum written over the numbers has the same effect. or 17

For example, 17 For example, 17 — (6 + 4), 64, means that the sum of 6 and 4 is to be subtracted from 17.

22. In making change, add to the amount of the purchase the amount necessary to equal the coin or bill tendered in payment.

1. If a man buys goods amounting to $2.53, and tenders a twenty-dollar bill, how will the cashier count out the change?

The cashier picks out, first 2, then 2 dimes, then a quarter, then a $2 bill, then a $5 bill, then a $10 bill (not two 5's), making $20. The change is counted out piece by piece, thus: $2.53, $2.54, $2.55, $2.65, $2.75, $3, $ 5, $ 10, $20.

23. To find the arithmetical complement of a number, subtract it from one unit of the next higher order. Thus, the