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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 ; (thai is, find the greatest figure that the divisor can be multiplied by, to as to produce a product that shall not exceed the part of the divi-, dend used ;) when found, place the figure in the entient ; maliiply the divisur by this quuiient figure ; place the product under liral 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 add the 'emainder, if there be any, to the product; if the work be right, the wum will be equal to the dividend.*

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* 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 suin, when the work is right, will be equal o the dividend.

A third method of proof bv excess of nines is as follows, viz. 1. Cast the nines out of'lr.e 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 to ether, 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. Nute. If the sum is right. the top and Lotlom figures ill be alike

365, 19640(136

365

Divisor. Div. Quotient.

2910359(529

145 Proof by excess of 9's.

85 5

58 2 X7

279 5

261

1314
1095

2190
2190

Ans. 10110 1011:

Remains 18

0 Rem. Divisor. Div. Quotient.

95(85595(901 61)28609(469

730)863250(1172 472)251104(532

there remains 661. 9. Divide 1893312 by 912.

Ans. 2070 10. Divide 1893312 by 2076.

Ans. 912 11. Divide 47254149 by 4674. 12. What is the quotient of 330098048 divided by 420';

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"

Ans. 30973**i. 16. Divide 280208122081 by 912314.

Quotient, 307140,14 TT
MORE EXAMPLES FOR EXERCISE.
Divisor. Dividend.

Remainder.
234063)5906249221 Quotient)83973

47614)3278791860 ) 9182 987654(988641654 ) ---0

CASE II. When there are ciphers at the right hand of the divisci, 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) an. nex those figures cut off from the dividend, and you will have the truc remainder

EXAMPLES

1. Divide 4673625 by 21400. 2.4(00).16730)25(21877. true quotient by Restitution

428.

393
214

1796
1712

8425 true rem. 2. Divide 37943:2675 by 6500. Ans. 583741474 3. Divide 121400000 by 49000. Ans. 8000. 4. Divide 11059112 by 89000. Ans. 1311 5. Divide 9187642 by 9170000. Ans. 1917874 7°

MORE EXAMPLES.
Divisor. Dividend.

Remains.
125000)430250000( Quotient.) 0
120000)1-195964787

76.178 901000)654347230

1221230 720000)9876540001

)55-3-4000

CASE III. Short Division is when the Divisor does not exceed 12.

RvlE.-Consider how many times the divisor is contained in tho frst siguro ur figures of the dividend, put thu result under, and carry is many lens to the next figure as there ae ones over.

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

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Contractions in Division. When the divisor is such a number, that any two figurce in the Tible, being multiplied together, will produce it, divide the given dividend by one of those figures ; the qúotient thrice 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 tii: remurder.

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22.58-7
22:52_8

63

first rem. + True Quotient 2:25896.

True rem. 653 2. Divide 178464 by 16.

Ans. ||151. 3. Divide 467412 ly 24.

Ans. 194475.7. 4. Divide 942341 by 35.

Ans. 269215'. 5. Divide 79638 by 36.

Ans. 2212 6. Divide 14.1872 by 48.

Ans. 301846 7. Divide 937387 by 54.

Ans. 1735934 R. Divide 93975 by 84.

Ans. 111881. !). Divide 145260 hy 109.

Ans. 1345. 10. Divide 1575:360 by 144.

Ans. 10940. 2. To divide by 10, 100, 1000, &c. R1118.-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 the remainder; and the utier ligures of the divisiond are the quotient.

¿XAMPLES. 1. Divide 365

Ans. 36 and 5 remains 2. Divide 5762

hy 10.
by 100.

Ans. 57 3. Divide 763753 by 1000. Ans. 763

62 rem. 753 rem.

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SUPPLEMENT TO MULTIPLICATION. To multiply by a mixt number; that is, a whole number jured with a fraction, as 81, 51, 61, &c. - Kule.--Multiply by the whole number, and take 4, , #, &c. of 1. The waltiplicand, and add it to the product.

EXAMPLES
Multiply 37 by 23.

Multiply 48 by 27. 2)37

48
23

23;

184 111 74

24=; 12-=

96

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2
8691 Answer.

132 Ans. 3 Multiply 211 by 50

Ans. 10655.. 4. Multiply 2464 by 8.

Ans. 20533) 5. Multiply 345 by 19.

Ans, 6598. 6. Multiply 6497 by 5.

Ans. 33413 Questions co exercise Multiplication and Division. 1. What will 9 tuns of hay come to, at 14 dollars a

Ans. $136, 2. If it take 320 rods to make a mile, and every rod contains 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?

Ans. 966 cwt. 5. In 36 pieces of cloth, each piece containing 241 7., yards ; how many ya.ds in the whole ?

Ans. 873 yds. 6. What is the product of 161 multiplied by itself?

Ans. 25921. 7. If a man spend 492 dollars a year, what is that per talendar month ?

Ans. $41. 6. 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. £7735.

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