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Practical Questions in Subtraction.

1. What is the difference between 24567 and 7456?

Ans. 1711.

2. I lent a friend 2456 dolls. and received in dollars; what remains due?

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Ans. 1114 dolls. 3. A merchant owes 34323 dolls. his effects are worth but 22749 dollars; how much will he fall in debt?

Ans. 11574 dolls.

4. A merchant has an estate in his hands valued at 52394 dolls. he owes 31399 dolls. ; what is he worth after paying his debts? Ans. 20995. dolls.

5. A merchant sent a ship and cargo to sea, valued at 11497 dolls. and on her return, she and her cargo was valued at 16579 dolls.; what was his gain?

Ans. 5082 dolls. 6. A ship builder built a ship, which cost him 6241 dolls. and he sold her for 5927 dolls. ; what did he lose? ; Ans. 314 dolls.

7. A. borrowed of B. 9427 dolls. and he paid him at one time 4249 dollars, at another time 1427 dollars, and at another time 947 dollars; what remains due?

Ans. 2804.

SIMPLE MULTIPLICATION.

DEFINITION. Simple Multiplication is a compendious way of adding; as 9 multiplied by 6 is equal to 54, and is the same as if 9 were set down 6 times and added up.

The number to be multiplied is called the multiplicad The number given to multiply by, is called the multiplier.*

The number arising from the operation is called the product.

The following table must be committed to memory before any progress can be made in Multiplication.

*The multiplicand and multiplier are in general terms called Tactors.

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When the multiplier is a single figure.

RULE. Under the multiplicand write down the multiplier, in the place of units; draw a line underneath, and multiply every figure of the multiplicand, by the multiplier; observing to carry one for every ten to the next product. The whole product of the last figure multiplied, must be set down.

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Proor-Cast the nines from the multiplicand; and all that is over put at the right of a cross, (which is ade thus X); then cast the nine from the multiplier, I all that is over, put at the left of the cross; then cast the nines from the product, and put all that is over the top of the cross. Then multiply the figure on the left of the cross with the one on the right; cast the 9's from the product, and what is over, put at the bottom of

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the cross; and if the top and bottom figures are alike, the work is right.

NOTE. The preceding method of proof is liable to one error, viz. if any of the figures in the product should happen to be transposed, as if 468 in the product should happen to be written 648, the work would prove, and an error would still exist.

Second method of Proof. Divide the product by the multiplier, and if the work is right the quotient will be like the multiplicand. This method can be used only by those who have attained to a knowledge of division. CASE II.

When the multiplier consists of several figures. RULE Set down the multiplier under the multiplicand, units under units, &c. multiply each figure in the multiplier into every figure in the multiplicand, singly, as in case first, observing to set down the first figure of the product exactly under the figure by which you are multiplying; then add the several products together, their sum will be the product required.

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CASE III.

When there are cyphers at the right hand of the multiplicand, or multiplier, or both.

RULE Multiply by the figures only; and to the right of the product annex as many cyphers, as are equal to the number of cyphers in both factors.

Examples.

101200
200

Products.20240000

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No. Multiplicands.

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Practical Questions in Multiplication.

1. A man had a farm on which he raised 360 bushels of wheat; and he had another, on which he raised 6 times as much; what quantity did he raise on both of them? Ans. 2520 bushels.

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2. A man had an estate which he divided among sons as follows, viz. to the first eight, he gave 333 dol. lars each: to the ninth, he gave as much wanting 1000 dollars as to the other eight; I demand the value of the estate; and also the ninth son's share.

Value of the estate 4328 dolls.

The 9th son's share 1664 dolts. 3. A man sheared 364 sheep, six years successively, each sheep neated 3 pounds of wool per year: how much wool had he yearly; and how much in six years? Ans. Yearly 1092 pounds. In six years 6552 pounds. 4. I sold 342 tons of iron at 142 dollars per ton: I de and the price of the whole. Ans. 48564 dolls.

5. I sold 742 thousand of boards in the W. I. at 62 dollars per thousand; what did they come to ? Ans. 46004 dolls.

6. What will 6422 quintals of fish come to at 6 dolls. Ans. 38532, per quintal? 7. A man travelled 26 days, and each day, he travelled 37 miles; what distance did he travel in the whole time? Ans. 962 miles.

SIMPLE DIVISION.

DEFINITION-Simple Division teaches to find how many times a smaller number is contained in a larger. The number given to be divided, is called the dividend. The number given to divide by, is called the divisor. That number which expresses the number of times, that the divisor is contained in the dividend, is called the quotient, or answer.

If any thing is left after dividing, it is called the remainder.

LONG DIVISION.

Long division is when the Divisor is more than twelve. CASE I.

RULE.-Write down the dividend, on the right and left draw a curved line; on the left hand of the dividend write down the divisor; seek how many times the divisor can be had in a competent number of the first figures of the dividend, and place the figure expressing the number oftimes, at the right of the dividend; multiply the divisor by the same figure, and place the product under the first figures of the dividend, and subtract; to the remainder bring down the next figure of the dividend, and divide as before; and thus proceed until all the figures of the dividend are brought down; if at any time when you have brought down a figure the sum is still less than

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