EXERCISES IN NOTATION.

27. Let the learner express the following numbers in figures by the French method:

1. One thousand, three hundred and fourteen.

2. Seventeen millions and thirty-six thousand. 3. Sixty-five trillions, four millions and six.

4. One hundred and fifty-three decillions, one hundred and forty-nine octillions, nine hundred and ninety-nine quintillions, forty-eight quadrillions, seven hundred and forty-seven thousand, nine hundred and ninety-nine.

28. Express the following numbers in figures by the English notation:

1. Fourteen billions; three hundred fifty-six thousand, two hundred and fifty-seven millions; five hundred and twenty-five thousand, seven hundred and forty-one.

2. Two quintillions; five thousand quadrillions; two hundred forty-two thousand, seven hundred and fifty-two millions hundred and fourteen.

; two

NOTE. These and other exercises will be varied and extended by the teacher as circumstances may dictate.

29. TABLE OF ROMAN NUMERALS.

(a) When two or more letters of equal value are united, or when a letter of less value follows one of greater, the sum of their values is indicated; thus, XXX= 30, LXV 65, CC = 200, etc.

(b) When a letter of less value precedes one of greater, the difference of their values is indicated; as, IX= 9, XL

etc.

40,

(c) When a letter of less value stands between two of greater value, the less is to be taken from that which follows it and the remainder to be added to that which precedes it; as, XIV = 14, CXL = = 140, etc.

EXERCISES IN ROMAN NOTATION.

30. Express the following numbers by letters:

6. One thousand, four hundred and forty-six. 7. One thousand, six hundred and forty-four. 9. The present year, A. D.

31. ADDITION is the putting together of two or more numbers of the same kind, to find their sum or amount.

32. This may be done by the following

RULE. Write the numbers in order, units under units, tens under tens, etc. Draw a line beneath, add together the figures in the units' column and, if the sum be less than ten, set it under that column; but, if the sum be ten or more, write the units as before and add the tens to the next column. Thus proceed till all the columns are added.

33. Ex. 1. Add together 27, 93 and 145.

OPERATION.

27

93

145

Having arranged the numbers, we add the column of units; thus, 5 and 3 are 8, and 7 are 15 units (= 1 ten and 5 units). The 5 units are placed under the column of units and the 1 ten is added to the column of tens; thus, 1 and 4 are 5, and 9 are 14, and 2 are 16 tens (= 1 hundred and 6 tens). The 6 tens are set under the tens and the 1 hundred is added to the 1 hundred in the third column, making 2 hundreds to be set under the third column.

265

34. PROOF. Having added several numbers together, it is desirable to TEST the ACCURACY of the work; this TEST is called the PROOF and is applied in several different ways. The usual mode is to begin at the TOP of the units' column and add DOWN

WARD.
ALIKE.

IF THE WORK IS RIGHT THE TWO SUMS WILL BE By this process we COMBINE the figures DIFFERENTLY, and HENCE shall PROBABLY detect any mistake which may have been made in adding UPWARD.

NOTE 1. The operation called proof, in this and the following Articles, only serves to strengthen the probability that the work is right.

ILLUSTRATION.

Ex. 10.
37684
48297
68746
94852

Sum, 249579

Proof, 2 49 579

In adding upward we say, 2 and 6 are 8, and 7 are 15, and 4 are 19, etc.; but, in adding downward, we say, 4 and 7 are 11, and 6 are 17, and 2 are 19, etc., thus obtaining the same result, but by different combinations.

If we do not obtain the same result by the two methods, one operation or the other is wrong-perhaps both—and the work must be carefully performed again.

NOTE 2. ·In adding it is NOT desirable to NAME the figures that we add; thus, in the above example, instead of saying 2 and 6 are 8, and 7 are 15, and 4 are 19, it is SHORTER and THEREFORE BETTER to say 2, 8, 15, 19; setting down the 9, say, 1, 6, 10, 19, 27, etc. etc.

NOTE 3. - Much of the labor of the practical accountant consists in adding up long columns of figures, and the learner should not rest satisfied till he can readily sum up such columns with unerring accuracy.

Ex. 15. Add 7435, 86424, 75, 987 and 14.

16. What is the sum of 9874, 625 and 49687428 ?

17. Add four hundred and fifty-six; eight thousand, four hundred and seventy-two; fifteen thousand, seven hundred and twenty-one; forty-three millions, seven hundred and thirty-three thousand, eight hundred and fifty-nine; and ten.

18. A owes to B $176, to C $8796, to D $549, to E $27, to F $5, to G $1111, to H $469 and to I $46978; how much does he owe?

19. What was the aggregate population of our country in 1790, 1800, 1810, etc., the population of each state and territory being as in the following table?