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

Ans. 480 pounds. 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. 4. A merchant buys a piece of cloth containing 97 yards, at 3 dollars a yard; what does the piece cost him?

Ans. 291 dollars. 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 ?

The farm contained Ans. { 123 acres.

It cost 2214 dollars. 6. À merchant bought 49 hogsheads of molasses, each containing 63 gallons : how many gallons of molasses were there in the parcel ?

Ans. 3087 gallons. 7. Suppose a man were to travel 32 miles a day how far would he travel in 365 days?

Ans. 11680 miles. * person sells goods he generally gives 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, 1832. 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

DIVISION OF SIMPLE NUMBERS. $39. Having two unequal numbers, we may subtract the lesser from the greater. If the remainder be greater than the least number, that number may be subtracted from it, and these subtractions may be continued till the remainder becomes the least. For example, take the numbers

12 12 and 4. Having taken 4 from 4 12, the remainder is 8: which, be

8 lst remain. ing greater than 4, 4 can be again

4 subtracted. The second remain

4 2d remain. der is 4; and from this, 4 can be

4 again subtracted, and the third remainder is 0. Now the number 0 3d remain. 4 has been taken three times from 12. The number 12, therefore, contains 4 three times,

er.

$ 40. Take the numbers 27 and 27 8. In this example, 8 is taken 3 8 times from 27, and there is a re

19 1st remain. mainder of 3.

8 By continued subtraction we

11 2d remain. can always find how many times

8 one number is contained in another, and also, what is left when it 3 3d remain. is not contained an exact number of times.

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

§ 41. DIVISION explains the manner of finding how many times a less number is contained in a great

It is a short method of subtraction.
The less number is called the divisor.
The greater number is called the dividend.

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

The number which is left, when the dividend does not contain the divisor an exact number of times, is called the remainder.

§ 42. There are three signs used to denote division. They are the following:

18-4 expresses that 18 is to be divided by 4. y

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.

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Let the following table be committed to memory. It is read 2 in 2, 1 time; 2 in 4, 2 times, &c.

DIVISION TABLE.

2 in 2 1 time 2 in 4 2 times 2 in 6 3 times 2 in 8 4 times 2 in 10 5 times 2 in 12 6 times 2 in 14 7 times 2 in 16 8 times 2 in 18 9 times 3 in 3 1 tine 3 in 6 2 times 3 in 9 3 times 3 in 12 4 times 3 in 15 5 times 3 in 18 6 times 3 in 21 7 times 3 in 24 8 times 3 in 27 9 times 4 in 4 1 time 4 in 8 2 times 4 in 12 3 times 4 in 16 4 times 4 in 20 5 times 4 in 24 6 times 4 in 28 7 times 4 in 32 8 times 4 in 36 9 times 5 in 5 1 time 5 in 10 2 times 5 in 15 3 times 5 in 20 4 times 5 in 25 5 times 5 in 30 6 times

5 in 35 7 times 5 in 40 8 times 5 in 45 9 times 6 in 6 1 time 6 in 12 2 times 6 in 18 3 times 6 in 24 4 times 6 in 30 5 times 6 in 36 6 times 6 in 42 7 times 6 in 48 8 times 6 in 54 9 times 7 in 7 1 time 7 in 14 2 times 7 in 21 3 times 7 in 28 4 times 7 in 35 5 times 7 in 42 6 times 7 in 49 7 times 7 in 56 8 times 7 in 63 9 times 8 in 8 1 time 8 in 16 2 times 8 in 24 3 times 8 in 32 4 times 8 in 40 5 times 8 in 48 6 times 8 in 56 7 times 8 in 64 8 times 8 in 72 9 times 9 in 9 1 time 9 in 18 2 times 9 in 27 3 times

9 in 36 4 times 9 in 45 5 times 9 in 54 6 times 9 in 63 7 times 9 in 72 8 times 9 in 81 9 times 10 in 10 1 time 10 in 20 2 times 10 in 30 3 times 10 in 40 4 times 10 in 50 5 times 10 in 60 6 times 10 in 70 7 times 10 in 80' 8 times 10 in 90 9 times 11 in 11 1 time 11 in 22 2 times 11 in' 33 3 times 11 in' 44 4 times 11 in 55 5 times 11 in 66 6 times 11 in 777 times 11 in 88 8 times 11 in 99 9 times 12 in 12 1 time 12 in 24 2 times 12 in ' 36 3 times 12 in 48 4 times 12 in 60 5 times 12 in 72 6 times 12 in 84 7 times 12 in 96 8 times 12 in 108 9 times

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Divisor
Dividen.

Ex. 1. Divide 86 by 2.

Place the divisor on the left of the divilend, draw a curved line 2) 86 between them, and a straight line

43 quotient. under the dividend.

Now, there are 8 tens and 6 units to be divided by 2. We say, 2 in 8, 4 times, which being 4 tens we write the 4 under the tens. We then say, 2 in 6, 3 times, which are 3 units, and must be written under the 6. The quotient therefore, is 4 tens and 3 units, or 43.

2. Divide 729 by 3.
In this example there are 7 hundreds 2

3) 729 tens and 9 units, all to be divided by 3. Now,

Set

243 we say 3 in 7,2 times and 1 over. down the 2, which is hundreds, under the 7. But there is 1 hundred or 10 tens not yet divided. We put the 10 tens with the 2 tens, making 12 tens, and then say,

3 in 12, 4 times, and write the 4 in the quotient, in the tens place; then say 3 in 9, 3 times. The quotient therefore is 243.

3. Divide 729 by 9.

In this example we say 9 in 7 we cannot, but 9 in 72, 8 times, which are 8 tens: then

81 9 in 9, 1 time.

"The quotient is therefore 81.

9) 729

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