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Rule. First, seek how many times the divisor is contained in as many of the left hand figures us the dividend as are just necessary; (thai is, find the greatest figure that the divisor can be multiplied by, so as to provuce a product that shall not exceed the part of the divi-, dend used ;) when found, place the figure in the auntient ; multiply the divisur by this quuiient figure; place the product under la 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 fol. Ows : 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 rether, and add their p

dd their product to the se ainder, and reject the nines, and place the excess at lop. 4. Cast the nines ont or the dividend, and place the excess at bottom. Nute. If the sum is right, the top and bottom figures e ill be alike

Divisor. Dio. Quotient.

29) 10359(529 365,49640(136
145

365
Proof by
excess of 9's. 85

1314
5 .
58

1095
2X7
279

2190 261

2190

Remzins 18

0 Rem. Divisor. Div. Quotient. 95(85595(901 61)28609(469

736)863250(1172 472)251104(532

there remains 664. 9. Divide 1893312 by 912.

Ans. 2070 10. Divide 1893312 by 2076.

Ans. 912" 11. Divide 47254149 by 4674. Ans. 10110 Tomar 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. 30973383.. 16. Divide 280208122081 by 912314.

Quotient, 307140 141TT.
MORE EXAMPLES FOR EXERCISE.
Divisor. Dividend. Remainder.
234063)590624922(Quotient)83973

47614)3278791861
987654(988641654

-..0

CASE II. When there are ciphers at the right hand of the divisor, 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 wil have the truc remainder

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EXAMPLES.

1. Divide 4673625 by 21400. 2,1(00).167°36)25(2182127 true quotient by Restitution

428.

. 393

214

1796
1712

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6425 true rem. 2. Divide 379432675 by 6500. Ans. 583741474. 3. Divide 421400000 by 49000. Ans. 8600.

4. Divide 11659112 by 89000. Ans. 1317!?a. * 5. Divide 9187042 by 9170000. Ans. Isult75.

MORE EXAMPLES.
Divisor. Dividend. ' Remains.
- 125000)430250000( Quotient.) 0
120000)1495964781

j 70-178
901000)6543472307

j221230 720000)9870540000

1.534000

CASE III. Short Division is when the Divisor does not exceed 12. Rule.-Consider how many times the divisor is contained in tho krst tiyurc ur figures of the dividend, put the result under, and carry i inany lons to the next figure as there are oncs over. Divide every figure in tho same manner till the whole is finished.

EXAMPLES. Vivisur, Dividend.

2)1 13415 3)85494 4)39407, 5)94379

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Contractions in Division. When the divisor is such a number, that any two figurut in the Tible, being multiplied together, will produce it, die vide the given dividend by one of those figures ; the qủotiunt thence arising by the other; and the last quotient will be the answer.

NOTE. The total remainder is found by multiplying the dast remainder by the first divisor, and adding in the til: renundur.

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22.58–7
22:52_8

69

first rem. + True Quotient 22539.

True rem. fig 2. Divide 178464 by 16.

Ans. 11151. 3. Divide 467412 by 24.

Ans. 191751;. 4. Divide 942341 by 35.

Ans. 26921 5. Divide 79638 by 36.

Ans. 2212. 6. Divide 141872 by 48.

Ans. 30184. 7. Divide 937387 by 54.

Ans. 17359 4. 8. Divide 93975 by 84.

Ans. U11881. 9. Divide 1 15260 hy 108.

Ans. 1345. 11. Divide 1575:360 by 144.

Ans. 10940. 2. To divide by 10, 100, 1000, &c. RULE-Cutoff as many figures from the right hand of the dividen as there are ciphers in the divisor, and these figures so cut otf are the remainder; and the other figures of the dividend are the quotient.

EXAMPLES. 1. Divide 365 by 10. Ans. 36 and 5 remains 2. Divide 5762 by 100. Ans. 57 -- 62 rem. 3. Divide 763753 by 1000. Ans. 763 - 753 rem.

SUPPLEMENT TO MULTIPLICATION. 999: To multiply by a mixt number; that is, a whole number "joined with a fraction, as 81, 51, 63, &c. *** RULE.--Multiply by the whole number, and take t, d, f, &c. of 1. The valtiplicand, and add it to the product.

EXAMPLES. C Multiply 37 by 232.

Multiply 48 by 27. 2)37

48

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Questions 60 exercise Multiplication and Division. 1. What wili 9 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 contains 52 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 q yards ; how many ya. ds in the whole ? Ans. 873 yds. i u 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 selendar 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. 177335.

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