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2. A father left his 6 children 2436 dollars to be equally them; how many dollars had each ?

livided among

Operation.

Dividend.

Divisor 6) 2 4 3 6

Quotient 4 0 6 Ans.

Here 6, the divisor, is not contained in 2, the first figure of the dividend; therefore we join the 2 (thousands) to the 4 (hundreds) making 24 (hundreds ;) and 6 is contained in 24 (hundreds) 4 (hundred) times. Then 6 is not contained in 3, the tens of the dividend, therefore we put a cipher under, (that is, in the quotient,) and join the 3 (tens) to the 6 (units,) making and 6 is contained in 36, 6 times. Ans. Each had $406,

36;

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9. How many times is 6 contained in 7326? Ans. 1221. 10. How many times is 5 contained in 4565? Ans. 913. 11. How many times is 7 contained in 84637 ?

Ans. 12091.

12. Divide the number 9784 into 8 equal parts.

Quot. 1223. Quotient 30502.

13. Divide 366024 by 12. 14. If 7 dollars will buy 1 barrel of flour, how many bar

rels of flour may be bought for $3822 ?

Ans. 546.

15. A market man received 2943 cents for melons that he sold at 9 cents apiece; how many did he sell? Ans. 327. 16. How many times is 7 contained in 6680, and how many over? Ans. 954 times, and 2 over. 17. A merchant has $5122 to purchase flour with; how many barrels can he buy at 8 dollars a barrel, and how many dollars will he have left? Ans. 640 barrels and 2 dollars left. 18. A prize of 3825 dollars was divided equally among 4 men; how much was each man's part?

Note. We divide the 3825 dollars among the 4 men, and find that each must have 956 dollars, and there is $1 left, which we must divide. Now if we divide 1 dollar into 4 equal parts, each part will be of a dollar.

Ans. Each man must have 956 dollars.

Had this remainder been 3 dollars, it is evident that each man would have had 3 times of a dollar, that is of a dollar, more; and in all cases where there is a remainder, we may obtain the true quotient by placing the divisor under the remainder, with a line between, as above.

Thus

Remainder 1

Divisor 4

shows that the divisor 4 is contained

in the remainder one fourth of a time.

19. How many cwt. of rice, at 4 dollars a cwt., may be bought for 947 dollars? Ans. 236 cwt. 20. How many cwt. of sugar, at 9 dollars per cwt., can be bought for 2944 dollars?

Ans. 327. 21. How many barrels of pork, at 11 dollars a barrel, be bought for 2478 dollars?

can

Ans. 225

barrels.

LONG DIVISION.

When the divisor exceeds 12, we cannot conveniently perform the operation in the mind; we therefore set the quotient figures on the right hand of the dividend, and write down the whole computation at full length, and this is called long division.

RULE.

I. Find how many times the divisor is contained in the least number of the left hand figures of the dividend, that will contain it once, or more: place the figure expressing the number of times, to the right hand of the dividend for the first quotient figure.

H. Multiply the divisor by this quotient figure, and place the product under that part of the dividend used, and subtract it therefrom.

III. Bring down the next figure of the dividend to the right hand of the remainder, and divide this number as before. Thus proceed till you have brought down, and divided, all the figures of the dividend.

Note. 1. If the product of the divisor by any quotient figure, be greater than that part of the dividend used, it shows that the quotient figure is too large, and must be diminished. If the remainder at any time be equal to or

To divide by 10, 100, 1000, &c.

RULE.

Cut off as many figures from the right hand of the dividend as there are ciphers in the divisor, and the figures cut off are the remainder, and the other figures of the dividend are the quotient.

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1. If a man divide 4280 dollars equally among his five children; how many dollars will each receive? Ans. 856. 2. Suppose 125 acres of land cost 4125 dollars, how many dollars is that an acre?

Ans. $33.

3. What number multiplied by 125, will make 17125?

Ans. 137.

4. If you were to divide 1875 dollars equally among 15 men, how many dols. would you give each one? Ans. $125. 5. If 24 hogsheads of molasses cost 456 dollars, what is that a hogshead? Ans. $19.

6. What number multiplied by 7, will make 2436 ?

Ans. 348.

7. A drover purchased oxen, at $28 a head, to the amount of 6972 dollars; how many did he purchase? Ans. 249. 8. A prize of 294630 dollars is to be divided equally among 138 soldiers; how many dollars will each one have? Ans. '2135.

Questions.

1. What does Simple Division teach? 2. How many principal parts has division ?

3. What is meant by dividend? 4. What is meant by divisor? 5. What is the quotient? Is the remainder greater, or less than the divisor?

6. What is Short Division? (Repeat the Rule.)

7. How do you prove division? 8. How may the remainder, after division, be expressed?

9. What is the Rule for Long Division? 10. When there are ciphers at the right hand of the divisor, how may we proceed?

11. When the divisor is a composite number, how may we proceed?

12. How is the true remainder found? 13. When the divisor is 10, 100, or 1000, &c., how would you proceed?

14. Write the sign of division on your slate.

REDUCTION OF FEDERAL MONEY.

The changing of numbers from one name to another, without altering their value, is called Reduction.

EXAMPLES.

1. Reduce 148 dollars to cents and mills.

Thus, 14800 cents.

To reduce dollars to cents, mul

=

148000 mills. tiply by 100, because 1 dollar 100 cents. That is, we annex 2 ciphers, and the whole will be cents. (See Rule for multiplying by 10, 100, &c. page 37.) And to reduce cents to mills, we annex 1 cipher, and the whole will be mills: therefore to change dollars to mills, we annex 3 ciphers.

2. In 1386 dollars 8 cents, how many cents?

Therefore, if the sum Thus, 138608 cents. Ans. consists of dollars and cents, join them together as a whole number, and the whole will be cents. (In this example, the cents being less than 10, we write a cipher before them, or in the tens' place, which must always be done in like cases.) And, if the sum consists of dollars, cents and mills, join them together in like manner, and they will express so many mills.

Thus, 25 dollars, 41 cents, 5 mills = 25415 mills. 3. In 138608 cents, how many dollars and cents?

Thus, $1386, 08 = 1386 dols. 08 cents. Ans.

lar.

To reduce cents to dollars, we divide by 100, because 100 cents 1 dol

(See Rule for dividing by 10, 100, &c. page 48.) That is, we cut off 2 figures to the right hand, and those on the left hand will be dollars; and to reduce mills to dollars, we point off three figures to the right; and those on the left will be dollars, and those on the right will be cents and mills.

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Thus, 25415 mills $25,41,5, or 25 dols. 41 cts. 5 m. 4. Reduce 125 dollars to cents.

5. Reduce 12550 cents to dollars.

Ans. 12500 cents.

Ans.

6. Reduce 568 dollars, 9 cents, to cents.

Ans. 56809 cents.

7. Reduce 56809 cents to dollars. Ans.

8. Reduce 25 dollars, 58 cents, 8 mills to mills.

Ans. 25588 mills.
Ans.

Ans. 450000 mills.

9. Reduce 25588 mills to dollars. 10. Reduce 450 dollars to mills. 11. Reduce 3598 mills to dollars. 12. Reduce 95410 cents to dollars. Ans.

Ans.

$3,598.

$954,10.

Ans. 96125 mills.

13. Reduce $96 12 cents to mills.
14. In 96125 mills, how many dollars and cents?

Ans. 96 dols. 12 cts.

15. Write down 125 dols. and 9 mills as a whole number.

Ans. 125009 mills.

MULTIPLICATION OF FEDERAL MONEY.

RULE.

Multiply the given sum as in whole numbers, and place the separating point as many figures from the right hand in the product, as it is in the given sum, or multiplicand.

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Ans.

$ cts. mls.

Ans.

51 27 5 367 50

Ans.

3. Multiply $1 46 cts. 5 m. by 35.
4. Multiply 3 dols. 75 cts. by 98.
5. Multiply $31, 98 c. 1 m. by 156.
6. Multiply 81 dols. 5 cts. by 195.
7. Multiply $156, 28 c. 3 m. by 75.
8. Multiply 13 dols. 5 m.
by 29.
9. Multiply 25 dols. 314 cts. or $253,15, by 365.

4989 03 6 Ans. 15804 75 Ans. 11721 22 5 Ans. 377 14 5

Ans. $9239,975.

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