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

In ¶ XII. it was observed, that annexing 1 cipher to any num ber multiplied it by 10, 2 ciphers by 100, &c. Now, Division being the reverse of Multiplication, what will be the effect, if we cut off a cipher at the right of any number? A. It must decrease, or divide it by 10.

What will be the effect, if we cut off two ciphers? A. It will be the same as dividing by 100.

Why does it have this effect? A. By cutting off one cipher or figure at the right, the tens take the units' place, and hundreds the tens' place, and so on.

RULE I. What, then, is the rule for dividing by 10, 100, &c. ? A. Cut off as many places or figures at the right hand of the dividend, as there are ciphers in the divisor.

II. What are the figures cut off?. A. The remainder
III. What are the other figures? A. The quotient.

Exercises for the Slate.

1. A prize, valued at 25526 dollars, is to be equally divided among 100 men; what will be each man's part?

OPERATION.

255 26

255-2

dollars.

2. Divide 1786582 by 10000. A. 1788582.

3. Divide 87653428 by 10; by 100; by 1000; by 10000; by 100000;

8

428

by 1000000. A. Remainder to each, fo, BARE, -53428, 653 428 Quotients, total, 9739257.

653428

↑ XX. When there are ciphers at the right hand of

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In this example we have a divisor, 80, which is a composite number; (thus, 8 times 10 are 80 ;) how, then, may we proceed to divide by 10, one of the component parts? A. By cutting off one place at the right hand of the dividend, as in XIX.

How do you obtain the 62? obtain the 62 ? A. By dividing the 496 by 8, as

usual.

RULE I. As any number, which has a cipher or ciphers at the right, can be produced by two other numbers, one of which may be either 10, 100, 1000, &c., how, then, would you proceed to de

:

vide when there are ciphers at the right of the divisor? A. Cut them off, and the same number of figures from the right of the dividend.

II. How do you divide the remaining figures of the dividend? A. As usual.

III. What is to be done with the figures of the dividend which are out off? A. Bring them down to the right hand of the remainder.

Exercises for the Slate.

2. How many oxen, at 30 dollars a head, may be bought for 38040 dollars? A. 1268.

267

95876

3. Divide 783567 by 2100. A. 2100 rem. 4. Divide 2082784895876 by 1200000. A. T28868σ rem. 5. Divide 7942851265321 by 12500000.

6. Divide 18515952875 by 112000. A.

A. 1265324 rem. TI2000 rem.

12500000

875

Miscellaneous Questions on the foregoing.

Q. What is the subject which you have now been attending to called? A. Arithmetic.

Q. From what you have seen of it, how would you define it ? A. It teaches the various methods of computing by numbers. Q. What rules have you now been through? A. Notation or Numeration, Addition, Subtraction, Multiplication, and Di

vision.

Q. How many rules do these make?

Q. What are these rules sometimes called? A. The fundamental rules of arithmetic.

Q. Why? A. Because they are the foundation of all the other rules.

Q. To denote the operation of these different rules, we have certain characters; what is the name of these characters ? A. Signs.

Q. What do two horizontal straight lines signify; thus, 100 cents = 1 dollar? A. Equal to: as, 100 cents 1 dollar, read, 100 cents are equal to 1 dollar.

Q. What does a horizontal line crossing a perpendicular tell you to do; thus, 6+10=16? A. To add thus, 6+10-16, read, 6 and 10 are 16.

Q. What else does this sign denote? A. A remainder after dividing

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Q. What does one horizontal straight line tell you to do; thus, 8-6-2? A. To subtract: thus, 8-6-=2, read, 6 from 8 leaves 2.

Q What do two lines, crossing each other in the form of the Roman letter X, tell you to do; thus, 6×8=48? A. To multiply: thus, 6×8=48, read, 6 times 8 are 48.

Q. What does a horizontal line, with a dot above and below it, tell you to do; thus, 8÷2-4? A. To divide; thus, 8-2-4, read, 2 in 8, 4 times.

Q. By consulting ¶ XVII. you will perceive that division may be represented in a different manner; how is this done ? A. By writing the divisor under the dividend, with a line between them; thus, =2, read, 4 in 8, 2 times.

8

Q. What does 15 signify, then? 20 signify? 36? 42 ? 108? 144? 35?

Let me see you write down on the slate the signs of Addition, Subtraction, Multiplication, and Division.

Perform the following examples on the slate, as the signs indicate.

1. 87834+284+65+32+100-88315, Ans.

2. 876345723-267001345-609344378, Ans.

3. 692784578×27839421=19286721529249338, Ans. 4. 202884150÷÷4025-50406, Ans.

5. 2600-600-2000+1828-3828, Ans.

6. 3600-400-3200×4-12800, Ans.

7.260900890-20000, Ans.

8. 18836-18, Ans.

9. 18836+1+15+20—28, Ans.

10. What is the whole number of inhabitants in the world, there being, according to Hassel, in each grand division as follows;-in

Europe, one hundred and eighty millions;
Asia, three hundred and eighty millions;
Africa, ninety-nine millions;

America, twenty-one millions;
Australasia, &c. two millions?

A. 682000000.

11. What was the number of inhabitants in the following New England towns in 1820, there being in

Portland,

Portsmouth,

Salem,

8,581;;

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7,327;

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12,731 ;

New Haven,

492,031.

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12. What was the number of inhabitants in the following

towns, there being in

New York,

123,706;

Norfolk,

Philadelphia,

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Baltimore,

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Washington,

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Albany,

12,630; New Orleans,

8,478;

12,067;

24,780 ;

7,523;

27,176?

A. 400,461.

13. How many more inhabitants were there in New York than Philadelphia? Philadelphia than Baltimore? Baltimore than Boston? Boston than New Orleans? New Olreans than Charleston? Charleston than Albany? Albany than Providence? Providence than New Haven? A. Total, 115,379.

14. At 73 cents a bushel, what will 42 bushels of salt cost? What will 800 bushels? A. 61466 cents. 15. What will 2970 bushels? What 8900 bushels? A. 866510 cents.

16. James had 37 cents, William 10 times as many as James, Rufus 15 times as many as William, Thomas 26 times as many as Rufus, Harry 45 times as many as Thomas, and Stephen 24 times as many as Harry; how many did they all have? A. 162487757.

17. There are 60 minutes in one hour; how many hours are there in 120 minutes? In 4800 minutes? A. 82 hours. 18. In 172800 minutes? In 1036800 minutes? A. 20160 hours.

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1. At 10 mills a yard, how many cents will 4 yards of cloth

cost? Will 6 yards? Will 8?

2. How many mills are 2 cents? 3 cents? 4 cents? 5 cents? 8 cents? 8 cents? 12 cents?

3. How many cents are 2 dimes? 5 dimes? 6 dimes 2007 dimes? 11 dimes?

4. How many dimes are 2 dollars? 5 dollars? 7 dollars? 10 dollars? 12 dollars?

5. How many eagles are 20 dollars? 30 dollars? 40 dol

lars?

60 dollars? 80 dollars? 100 dollars? 120 dollars?

60 dollars?

A. 61.

Ꭿ. 12.

Q. How many cents are 43 pence?

Q. How many cents are 9 pence?

Q. How many cents are 18 pence, or of a dollar? A. 25.

Q. How many cents is of a dollar?

Q. How many cents is of a dollar?

Q. How many cents is one dollar?
Q. How many cents is a pistareen?
Q. How many cents is half a pistareen?
Q. How many 9 pences in a dollar?

Q. How many 4 pence-halfpennies in a dollar?

A. 50.

A. 75.

A. 100.

Ꭿ. 20.

A. 10.

A. 8.

Ꭿ. 16.

6. You buy 4 yards of cloth for $1, and give the shopkeeper two fifty-cent bits; how much change must he give you ?

7. You buy some calico to the amount of 17 cents, and give the clerk a pistareen; how much change must he give you? 8. You give a pistareen for 1 fish; how many cents must you give for 2? For 3? For 5? For 5? For 7? For 9? For 12? 9. What will 2 yards of ribbon come to in cents, at 4 pence a yard? At 9 pence? At of a dollar? At a dollar? At of a dollar?

Q. What is the coin of the United States called? A. Federal Money.

Q. When established? A. A. D. 1786.

Q. By what authority? A. Congress.

Q. Which is the money unit? A. Dollars.

Q. What place do dollars occupy, then? A. The place of

units.

Q. How are dollars distinguished from dimes, cents, and mills? A. By a comma, or separatrix, at the right of dollars. Q. What are the figures on the left of dollars? A. Eagles. Q. What is the first figure on the right of dollars? A. Dimes.

Q. What is the second figure? A. Cents.

Q. What is the third figure? A. Mills.

Q. How many of these coins are real? A. 4.

Name them. A. The eagle, the dollar, the dime, and the

cent.

Q. Which is a gold coin? A. The eagle.

Which are the silver coins? A. The dollar and the dime. Q. Which is a copper coin? A. The cent.

Which is imaginary? A. The mill, as there is no piece

of money of that denomination *

*There are, however, half eagles, and half dimes, real coins.

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