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RULE. First, seek how many times the divisor is contained in as many of the left hand figures of the dividend as are just necessary; (that is, find the greatest figure that the divisor can be multiplied by, so as to produce a product that shall not exceed the part of the dividend used;) when found, place the figure in the quotient multiply the divisor by this quotient figure; place the product under that part of the dividend used; then subtract it therefrom, and bring down the next figure of the dividend to the right hand of the remainder; after which, you must seek, multiply and subtract, till you have brought down every figure of the dividend.

PROOF. Multiply the divisor and quotient together, and aad the emainder, if there be any, to the product; if the work be right, the sun will be equal to the dividend.*

* Another method which some make use of to prove division is as folows: viz. Add the remainder and all the products of the several quotient gures multiplied by the divisor together, according to the order in which hey stand in the work; and this sum, when the work is right, will be equal o the dividend.

A third method of proof by excess of nines is as follows, viz.

1. Cast the nines out of tre divisor, and place the excess on the left hand. 2. Do the same with the quotient, and place it on the right hand.

3. Multiply these two figures together, and add their product to the se ainder, and reject the nines, and place the excess at top.

4. Cast the nines out of the dividend, and place the excess at bottom. Note. If the sum is right. the top and bottom figures ll be alike

11. Divide 47254149 by 4674.

O Rem.

95(85595(901 736)863256(1172

there remains 664.

Ans. 2070

Ans. 912

Ans. 1011075:

12. What is the quotient of 330098048 divided by 4201

Ans. 78464.

13. What is the quotient of 761858465 'ivided by 846

Ans. 90001.

14. How often does 761858465 contain 90001 ?

Ans. 8465.

15. How many times 38473 can you have in 119184693 *

16. Divide 280208122081 by 912314.

Ans. 30973312.

MORE EXAMPLES FOR EXERCISE.

Quotient, 307140

When there are ciphers at the right hand of the diviser, cut off the ciphers in the divisor, and the same number of figures from the right hand of the dividend; then divide the remaining ones as usual, and to the remainder (if any) annex those figures cut off from the dividend, and you wil have the true remainder

EXAMPLES.

1. Divide 4673625 by 21400.

2,4(00)16736)25(218 true quotient by Restitution

428

8425 21400

Short Division is when the Divisor does not exceed 12. RULE. Consider how many times the divisor is contained in the rst figure or figures of the dividend, put the result under, and carry many tens to the next figure as there are ones over.

Divide every figure in the same manner till the whole is finished.

Contractions in Division.

When the divisor is such a number, that any two figures in the Table, being multiplied together, will produce it, divide the given dividend by one of those figures; the quo tient thence arising by the other; and the last quotient will be the answer.

NOTE. The total remainder is found by multiplying the last remainder by the first divisor, and adding in the fi remainder.

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

RULE.-Cut off as many figures from the right hand of the dividen as there are ciphers in the divisor, and these figures so cut off are th remainder; and the other figures of the dividend are the quotient.

SUPPLEMENT TO MULTIPLICATION.

To multiply by a mixt number; that is, a whole number jomed with a fraction, as 81, 51, 63, &c.

RULE.--Multiply by the whole number, and take 1,,, &c. of i: The multiplicand, and add it to the product.

Questions to exercise Multiplication and Division.

1. What will 93 tuns of hay come to, at 14 dollars a un ? Ans. $136. 2. If it take 320 rods to make a mile, and every rod ontains 5 yards; how many yards are there in a mile ?

Ans. 1760. 3. Sold a ship for 11516 dollars, and I owned & of her; what was my part of the money? Ans. $8637. 4. In 276 barrels of raisins, each 3 cwt. how many hundred weight?

5. In 36 pieces of cloth, each piece vards; how many yards in the whole? 6. What is the product of 161 multiplied

Ans. 966 cwt. containing 24 Ans. 873 yds. by itself?

Ans. 25921.

7. If a man spend 492 dollars a year, what is that per calendar month?

Ans. $41. 8. A privateer of 65 men took a prize, which being equally divided among them, amounted to 1191. per man; what is the value of the prize? Ans. £7785.

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