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4. As in Simple Addition.
Q. Where do you place the separatrix ?

A. Directly under the separating points above

More Exercises for the Slate.

* James bought 2,5 cwt. of sugar, 23,265 cwt. of hay, and 14,2657 cwt. of rice; now much did he buy in all? A. 30,0307

owt.

3. James is 14 years old, Rufus 15, and Thomas 16 what is the sum of all their ages? A. 46,5 years.

255

4. William expended for a chaise $255, for a wagon $37, for a bridle $10, and for a saddle $11; what did these amount to? A. $304,455.

5. A merchant bought 4 hhds. of molasses; the first contained 621 gallons, the second 72,5 gallons, the third50 gallons, and the fourth 5570 gallons; how many galloną did he buy in the whole? A. 240,6157 gallons.

6. James travelled to a certain place in 5 days; the first day he went 40 miles, the second 28 miles, the third 421 miles, the fourth 2200 miles, and the fifth 29 miles how far did he travel in all? A. 162,0792 miles.

7. A grocer, in one year, at different times, purchased the Following quantity of articles, viz. 427,2623 cwt., 2789,00065 swt., 42,000009 cwt., 1,3 cwt., 7567,126783 cwt., and 897,62 cwt.; how much did he purchase in the whole year? A. 11724,309749

twt.

8. What is the amount of fo, 245, 61000, 245000 Tobboo Too0, 427100000, 40, 100000, and 1925? 4. 2854,492472.

9. What is the amount of one, and five tenths; forty-five, and three hundred and forty-nine thousandths; and sixteen aundredths? A. 47,009.

SUBTRACTION OF DECIMALS.

1 LIV. 1. A merchant, owing $270,42, paid $192,625; how much did he then owe?

OPERATION.

$270,42
$192,625

Ans. $77,795

For the reasons shown in Addition, we proceed to subtract, and point off as in Subtraction of Federal Money

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Ilence we derive the following

RULE.

Q. How do you write the numbers down?
A. As in Addition of Decimals.
Q. How do you subtract?

A. As in Simple Subtraction.

Q. How do you place the separatrix ?
A. As in Addition of Decimals.

More Exercises for the Slate.

1. Bought a hogshead of molasses, containing 60,72 gallons ; how much can I sell from it, and save 19,999 gallons for my own use? A. 40,721 gallons.

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2. James rode from Boston to Charlestown in 4,75 minutes, Rufus rode the same distance in 6,25 minutes; what was the difference in the time? A. 1,5 min.

3. A merchant, having resided in Boston 6,2678 years, stated his age to be 72,625 yrs. How old was he when he emigrated to that place? A. 66,3572 yrs.

Note. The pupil must bear in mind, that, in order to obtain the answer, the Agures annexed to each question, are first to be pointed off, supplying ciphers, if secessary, then added together as in Addition of Decimals.

4. From ,65 of a barrel take ,125 of a barrel-525; take of a barrel-45; take,45 of a barrel-2; take,6 of a barrel-5; take 12567 of a barrel-52433; take 26 of a barrel-39, 4. 2,13933 barrels.

5. From 420,9 pipes take 126,45 pipes-29445; take,625 of a pipe-420275; take 20,12 pipes-40078; take 1,62 pipes41923, take 419,89 pipes-101; take 419,8999 pipes-10001 4.1536,7951 pipes.

MULTIPLICATION OF DECIMALS.

LV. 1. How many yards of cloth in 3 pieces, each piec containing 20 yards?

OPERATION.

20,75

3

Ans. 62,25 yds.

the multiplier also we

In this example, since multiplication is a short way of performing addition, it is plain that we must point off as in addition, viz. directly under the separat ing points in the multiplicand; and, as either factor may be made the multipli cand, had there been two decimals in must have pointed off two more place

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for decimals, which, counting both, would make 4. Hence, we must always point off in the product as many places for desi mals, as there are decimal places in both the factors.

2. Multiply 25 by,5.

OPERATION.

,25:

,5

In this example, there being 3 decimal places in both the factors, we point off 3 places in the product, as before directed, The reason of this will appear more evi. dent by considering both the factors common fractions, and multiplying by ↑ XLI., thus, ,25%, and 5o; now, foto ts, which, written decimally, is,125, Ans., as before

Ans. 125

3. Multiply,15 by,05.
OPERATION.
,15

,05

In this case, there not being so many figures in the product as there are deci mal places in both the factors (viz. 4), we place two ciphers on the left of 75, to make as many. This will appear evident by the following;,15%, and To; then 1% 180-100,0075, Ans., the same

Ans. ,0075

before.

=

From these illustrations we derive the following

RULE.

Q. How do you multiply in Decimals?

A. As in Simple Multiplication.

Q. How many figures do you point off for decimals in the product? A. As many as are in both the multiplicand and multiplier.

Q. If there be not figures enough in the product for this purposa, How would you proceed?

A. Prefix ciphers enough to make as many.

Q. What is the meaning of annex?

A. To place after.

Q. What is the meaning of prefix?

A. To place before.

More Exercises for the Slate.

4. What will 5,66 bushels of rye cost, at $1,08 a bushel? $6,1128, or $6, 11 c., 27 m.

How many gallons of rum in,65 of a barrel, each baszál

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Dontaining 31 gallons-20475. In 8 of a barrel ?-252. 42 of a barrel?-1323. In ,6 of a barrel 189. In 1126,3 barrels ?-3548475. In 1,75 barrels ?-55125. In 125,626789 barrels ?-39572438535. A. 39574,9238535 gallons.

6. What will 8,6 pounds of flour come to, at $,04 a pound?344. At $,03 a pound?-258. At $,035 a pound?-301. At 3,0455 a pound?-3913. At $,0275 a pound?-23650 4. $1,5308.

7. At $,9 a bushel, what will 6,5 bushels of rye cost?-585 What will 7,25 bushels ?-6525. Will 262,555 bushels?2362995. Will ,62 of a bushel?-558. Will 76,75 bushels? 69075. Will 1000,0005 bushels ?-90000045. Will 10,0000 bushels ?-9000045. A. 1227,307995.

DIVISION OF DECIMALS.

LVI. In multiplication, we point off as many decimal in the product as there are decimal places in the multiplicand and multiplier counted together; and, as division proves mul tiplication, by making the multiplier and multiplicand the divisor and quotient, hence there must be as many decimal places in the divisor and quotient, counted together, as there are decimal places in the dividend.

1. A man bought 5 yards of cloth for $8,75; how much was it a yard? $8,75-875 cents, or 100ths; now, 875+5=175 ents, or 100ths,=$1,75, Ans.

OR

By retaining the separatrix, and dividing as in whole nam Bers, thus:

OPERATION.

5)8,75

Ans. $1,75

As the number of decimal places in the divisor and quotient, when counted together, must always be equal to the decimal places in the dividend, therefore, in this example, as there are no decimals in the divisor, and two in the dividend, by pointing off two decimals in the quotient, the number of decimals in the divisor and quotient will be equal to the dividend, which produces the same result is before.

2. At $2,50 a barrel, how many barrels of eider can I have for $11 $111100 cents, or 100ths, and $2,50 250 cents, 100ths then, dividing 100ths by 100ths, the quotient will evi dently be a whole number thus:

OPERATION.

250) 1100 (4488 barrels, Ans. 1000

In this example, we have for an an swer 4 barrels, and 188 of another barrel. But, instead of stopping here in the process, we may bring the remain

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der, 100, into tenths, by annexing a cipher (that is, multiplying by 10), placing a decimal point at the right of 4, a whole number, to keep it separate from the 10ths, which are to follow. The separatrix may now be retained in the divisor and dividend, thus:

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