seventy-five thousand, six hundred and nineteen yards. many miles in length was the whole ?

How

Ans. 1520m. 1f. 36p. and lyd. 4. In the city of Pekin there are said to be seven bells, each weighing 120000lb.; and in Moscow there is one bell which weighs 127836/b.; another which weighs 286000lb. ; and a third which weighs 432000/b. Required the weight of each in tons. Ans. 531. 11cwt. 1gr. 20lb.; 57t. lcwt. 1gr. 16lb.; 128t. 11cwt. 1qr. 20lb.; and 192t. 17cwt. 16lb.

5. Suppose one person to lie in bed nine hours each day at an average, and another only six hours and a half; and suppose the latter to employ the time thus gained in reading and study, for 48 years; to how many years' study, of 12 hours each day, would the entire time gained be equivalent. Ans. 8 years, 121 days, and 8 hours.

6. The whole surface of the earth contains 196649494 square miles, and of these Europe is supposed to contain 4456065. Required the number of acres contained in each. Ans. 125855676160, and 2851881600. 7. In what time would a body move from the Earth to the Moon, at the rate of thirty-one miles per day; the mean distance being 238545 American miles?

Ans. 21 years, and 30 days. 8. In what time would a body moving with the velocity of sound, (which is known to move at the rate of 1130 feet per second,) pass from the Earth to the Sun, the distance being ninety-five millions of miles?

Ans. 14 years, 27 days, 15 hours, 50 min. 5,3 sec. 9. In how long time would a cannon ball, with the velocity of 1960 feet per second, move from the Sun to Uranus ?

1960

Ans. 155 years, 224 days, 5 hours, 46 min. 7,680 sec. 10. By the latest measurements, the Earth's mean diameter is found to be 7920 miles. How many yards, feet, and inches are contained in it?

Ans. 13924680 yds.; 41774040 ft.; 501288480 inches. 11. The number of penny-pieces which have been lately coined, and actually circulated in England, amounts to 40000000, each weighing exactly an ounce; of course, the halfpence of the same coinage weigh half an ounce, the farthings a quarter of an ounce. How many tons, &c. are in the above number of penny-pieces, and how many pounds sterling do they contain? Ans. 1116 tons, 1cwt. 1gr. 2016. weight; £166666 13s. 4d. value.

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12. The United States of America were declared Free and Independent 1609403328 seconds ago this present year, 1827; how many years have intervened since, allowing the year to consist of 365 days, 5 hours, 48 minutes, and 48 seconds? and in what year did that glorious event take place? Ans. 51 years ago; and in the year 1776, the period in which it happened.

CHAPTER III.

Compound Addition, Subtraction, Multiplication, and Division.

49. When the numbers to be added express quantities of the same kind, but of different denominations, the operation is called compound addition.

RULE.* Arrange the given quantities so that those in each column may be of the same denomination. Add the numbers of the lowest denomination together; reduce their sum to the next higher denomination; set the remainder below the column added, and carry the quotient to the next. Proceed thus with all the other denominations, except the highest, which is to be added in the same manner as in addition of whole numbers.

Either of the first two methods of proof given in the addition of whole numbers, (usually called Simple Addition,) may be employed in Compound Addition.

Federal Money.

Addition of Federal Money (if there are no fractions) is performed in the same manner as addition of whole num

*The reason of this rule is evident, from what has been said in addition of whole numbers: for instance, the addition of English money, as 1 in the pence is equal to 4 in the farthings; 1 in the shillings, to 12 in the pence; and in the pound, to 20 in the shillings; therefore carrying as directed, is nothing more than providing a method of placing the money arising from each column properly in the scale of denominations: and this reasoning will hold good in the addition of compound umbers of any denomination whatever.

bers; but it must be observed, that the cents are separated from the dollars by placing a point between them.*

Ex. 1. Add together the following sums: $35; $76.75; $109.06; and $300.29.

$ 35

76.75

109.06

300.29

$521.10

Here, 9 and 6 are 15, and 5 are 20, set down 0, and carry 2; again, 2 and 2 are 4, and 7 are 11, set down 1, and carry 1; then, 1 and 9 are 10, and 6 are 16, and 5 are 21, set down 1, place a point between the cents and the dollars, and carry 2; proceed as in sum, addition of whole numbers, and the amount, or sum will be 521 dollars, and 10 cents. 2. Add together the following sums: $9.12; $25.74; and $13.06.

Here 1 fourth and 3 fourths are 4 fourths, and, or 2 fourths, are 6 fourths; which divided by 4, the quotient is 1, and the remainder 2; this remainder, 2 fourths or, is set down, and the quotient figure 1 is added to the units of the cents.

$9.121 25.742 13.061

$47.931

-Ex. 6. What is the sum total of 33 dollars 13 cents, 676 dollars 33 cents, 171 dollars 19 cents, and 184 dollars 37 cents? Ans. $1065.02. Ex. 7. What is the sum of 18 cents, 37 cents, $1.183, 75 cents, 87 cents, 61 cents, $3.314, 432 cents, and 3. dollars? Aus. $10.18.

8. Bought an Arithmetic for 37 cents; a slate for 183 cents; a writing-book for 12 cents; a ciphering

* When there are fractional parts of a cent, such as,, or, find their amount in fourths, counting as 2 fourths, divide their sum by 4; the tient will be cents, and the remainder will be fourths of a cent, which set down, and carry the quotient figure to the units of cents; then proceed as in addition of whole numbers.

book for 25 cents; an English grammar for 37 cents a Geography for 374 cents; an Atlas for 50 cents; Walker's Dictionary for 62 cents; and an English Reader for 314 cents. What is the cost of the whole? Ans. $3.12.

9. A man borrowed a certain sum of money, and paid $376.27; the sum left unpaid was $127.37. What was the original debt? Ans. $503.75.

in all?

10. Laid out at market, in beef $1.37, in mutton 62 cents, in lamb 873 cents, in veal 50 cents, in fowl $1.12, in vegetables 183 cents. What was expended Ans. $4.683. 11. Expended in gloves $1.121, in stockings $3.871, in lace $12.374, in cambric $25.50, in muslin $6.75, in silk $15.624, and in shoes $1.621. What was the the whole sum spent?

12. Bought a cloak for $21, a shawl hat for $15 75, and sundry articles What is the whole cost?

English Money.

Ans. $66.87. for $29.35, a for $17.75. Ans. $83.85.

£ S. d. 39 18 73 51 12 41 79 19 101

2

8 7 111

43 13 93

375 16 10

In this example, the sum of the farthings is 14; which being di- Ex. 1. vided by 4, the farthings in a penny, the quotient is 3 pence; and the remainder, 2 farthings, or a halfpenny, is set down. The quotient, 3, is then added with the pence; the sum, 54, being divided by 12, the pence in a shilling, the quotient is 4 shillings, with a remainder of 6 pence, which is set down. The quotient, 4, is then added with the units of the shillings; the sum is 39, of which the latter figure is set down, and the tens being carried to the tens of the shillings, the sum is 8; which being divided by 2, because 2 tens, or 20 shillings, make a pound, the

Sum, 599 9 61*

* The proof is left to exercise the learner; and it will be proper to require him to perform it, not only in this example, but in all the exercises in this rule.

quotient is 4, which is added with the pounds, as in Simple Addition.*

In this example the halfpence amount to 5, or 2 pence halfpenny. In such examples, where all the fractional parts are halfpence, it is easier to call each a halfpenny than 2 farthings.

£ s. d.

2.

15 381

31 16 72

94 13 81

55 12 111 37 11 918

Sum, 234 18 91

When the columns are very long, the work becomes heavy and laborious; and therefore, in such a case, the given quantities may be separated into two or more divisions, as is suggested in page

5. Add together £71 13 4, £95 14 9, £31 16 3, £20, £13 0 3, and £1600.

Ans.

6. Required the sum of £13, 113d., 3s. 9d., £100, and 198. and 11 d.

Ans.

This table has been inserted, lest some teachers should consider the want of it an imperfection. It seems better, however, not to impose upon the learner the labour of committing it to memory, except perhaps a small part at the beginning.

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