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CASE IV.

29. When the multiplier is 1 and any number of ciphers after it, as 10, 100, 1000, &c.

Placing a cipher on the right of a number changes the units' place into tens, the tens into hundreds, the hundreds into thousands, &c., and therefore increases the number ten times.

Thus, 5 is increased ten times by making it 50. The addition of two ciphers increases a number one hundred times; the addition of three ciphers, a thousand times, &c. Thus, 6 is increased a hundred times by making it 600, and a thousand times, by making it 6000.

Hence, to multiply by 1 and any number of ciphers we have the following

RULE - Annex, or place on the right of the multiplicand as many ciphers as there are in the multiplier, and the number so formed will be the required product.

EXAMPLES.

1. Multiply 254 by 10.
2. Multiply 648 by 100.
3. Multiply 7987 by 1000.
4. Multiply 9840 by 10000.
5. Multiply 3750 by 100.

Ans. 2540.

Ans.
Ans. 7987000.

Ans.
Ans. 375000.

CASE V.

30. When there are ciphers on the right hand of one or both of the factors. In this case each number só formed may be regarded as a composite number, of which the significant figures will be one factor, and 1 with the requisite number of ciphers annexed, the other. Hence, we have the following

29. If you place one cipher on the right of a number, what effect has it on its value? If you place two, what effect has it? If you place threo ? And for any number of ciphers, how much will each increase it? How do you multiply by 10, 100, 1000, &c. ?

30. Whon there are ciphers on the right hand of one or both the factors, how do you multiply?

RULE. Neglect the ciphers and multiply the significant figures ; then place as many ciphers to the right hand of the product, as there are in both of the factors.

EXAMPLES.

(1.)
(2.)

(3.)
76400
7532000

416000
24
580

357000 1833600

148512000000 4. 4871000 x 270000. Ans. 1315170000000. 5. 296200 X 875000.

Ans. 6. 3456789 x 567090. Ans. 1960310474010. 7. 21200 x 70.

Ans. 8. 359260 X 304000.

Ans. 109215040000. 9. 7496430 X 695000.

Ans. 5210018850000.

APPLICATIONS. 1. There are ten bags of coffee, each containing 48 pounds: how much coffee is there in all the bags ?

Ans. 480 lbs. 2. There are 20 pieces of cloth, each containing 37 yards, and 49 other pieces, each containing 75 yards : how many yards of cloth are there in all the pieces ?

Ans. 4415 yards. 3. There are 24 hours in a day, and 7 days in a week: how many hours in a week ?

Ans. 168 hours. 4. A merchant buys a piece of cloth containing 97 yards, at 3 dollars a yard: what does the piece cost him?

Ans. 5. A farmer bought a farm containing 10 fields; three of the fields contained 9 acres each.; three other of the fields 12 acres each; and the remaining 4 fields, each 15 acres : how many acres were there in the farm, and how much did the whole cost at 18 dollars an acre ?

Ans.

The farm contained 123 ocres.

It cost 2214 dollars. 6. Suppose a man were to travel 32 miles a day: how far would he travel in 365 days ? Ans. 11680 miles..

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7. A merchant bought 49 hogsheads of molasses, each containing 63 gallons: , how many gallons of molasses were there in the parcel ?

Ans. 3087 gallons. 8. In a certain city, there are 3751 houses. If each house on an average contains 5 persons, how many inhabitants are there in the city ?

Ans. 18755 inhabitants. 9. If a regiment of soldiers contains 1128 men, how many men are there in an army of 106 regiments ?

Ans. 119568. 10. If 786 yards of cloth can be made in one day, how many yards can be made in 1252 days?

11. If 30009 cents are paid for one man's services, how many cents would be paid to 814 men, each man receiving the same wages ?

Ans. 24427326. 12. If in one granary there are 375296321 kernels, how many kernels would there be in 79024 granaries ?

13. If one farm costs 2730 dollars, how much would 8 farms cost?'

Ans. 21840. 14. Multiply 123456789 by 987654321.

15. What will 397 barrels of flour cost at 7 dollars a barrel ?

Ans. 2779 dollars 16. What will 596hhd. of sugar cost at '74 dollars å hhd.?

17. If a vessel sails 169 miles a day, how many miles will she sail in 576 days ?

Ans. 97344. 18. What will 687 yoke of oxen cost at 73 dollars a

yoke ?

19. If one man travels 74 miles in one day, how many miles will he travel in 365 days?

Ans. 27010. 20. What will 698 heifers cost at 14 dollars per head ? 21. Multiply 6176777 by 22222.

Ans. 137260338494. 22. What will 616783 yards of calico cost at 36 cents per yard ? 23. There are 320 rods in a mile; how

many

rods are there in the distance from St. Louis to New Orleans, which is 1092 miles ?

Ans. 349440. 24. What will 46000 bushels of potatoes cost at 34 cents per bushel ?

25. Supposé a book to contain 470 pages, 45 lines on each page, and 50 letters in each line : how many letters in the book ?

Ans. 1057500. 26. Supposing a crew of 250 men to have provisions for 30 days, allowing each man 20 ounces a day: how many ounces have they ?

27. There are 350 rows of trees in a large orchard, 125 trees in each row, and 3000 apples on each tree : how many apples in the orchard ? Ans. 131250000.

31. When a person sells goods he generally gives with them a bill, showing the amount charged for them, and acknowledging the receipt of the money paid ;, such bills are usually called Bills of Parcels.

BILLS OF PARCELS.

New York, Oct. 1, 1846. James Johnson

Bought of W. Smith. 4 Chests of tea, of 45 pounds each, at 1 doll. a pound. 3 Firkins of butter at 17 dolls. per firkin 4 Boxes of raisins at 3 dolls.

per

box 36 Bags of coffee at 16 dolls. each 14 Hogsheads of Molasses at 28 dolls. each

Amount 1211 dollars. Received the amount in full,

W. Smith.

Hartford, Nov. 1, 1846. James Hughes

Bought of W. Jones. 27 Bags of coffee at 14 dollars per bag 18 Chests of tea at 25 dolls."

per

chest 75 Barrels of shad at 9 dolls.

per

barrel 87 Barrels of mackerel at 8 dolls. per barrel 67 Cheeses at 2 dolls. each 59 Hogsheads of molasses at 29 dolls. per hogshead

Amount 4044 dollars. Received the amount in full, for W. Jones,

per

James Cross. 31. What are bills of parcels?

DIVISION OF SIMPLE NUMBERS.

32. Charles has 12 apples, and wishes OPERATION. to divide them equally between his four 12 brothers.

4 He gives one to each, which takes 4.

8 lst remain. Subtracting 4 from 12, 8 remains. " He

4 then gives another to each, which takes

4 2d remain. 4 more. He then gives one more to

4 each, which takes all his apples. 'He has thus divided them equally, and found

0 3d remain. that 12 contains 4, three times.

We can arrive at the same result by a shorter method, called Division.

Division is the process of finding how many times one number is contained in another. It is a short method of subtraction.

The number by which we divide is called the divisor. The number to be divided is called the dividend.

The number expressing how many times the dividend contains the divisor, is called the quotient.

If there is a number left, it is called the remainder, which is always less than the divisor.

33. There are three signs used to denote division. They are the following: 18-4 expresses that 18 is to be divided by 4.

expresses that 18 is to be divided by 4. 4) 18 expresses that 18 is to be divided by 4. When the last sign is used, a curved line is also drawn on the right of the dividend to separate it from the quotient, which is generally set down on the right.

32. When Charlos divides 12 apples equally, among his four brothers, how many does he give to each? How many times does 12 contain 4? Which number is the dividend? Which the divisor ? Which the quotient? What is division ? What is the number to be divided called? What is the number called by which we divide ? What is the answer called? What is the number called which is left? Is it greater or less than the divisor?

33. How many signs arethere in division ? Make them?

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