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Remains 18

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

736)863256(1172 472)251104(532

there remains 664. 9. Divide 1893312 by 912.

Ans. 2076. 10. Divide 1893312 by 2076.

Ans. 912. 11. Divide 47254149 by 4674. Ans. 10110

4077 12. What is the quotient of 330098048 divided by 4207?

Ans. 78464. 13. What is the quotient of 761858465 'ivided by 8465?

Ans. 90001. 14. How often does 761858465 contain 90001 ?

Ans. 8465. 15. How many times 38473 can you have in 119184693 ?

Ans, 30973 3 8 12. 16. Divide 280208122081 by 912314.

Quotient, 307140513
MORE EXAMPLES FOR EXERCISE.
Divisor. Dividend.

Remainder.
234063)590624922(Quotient)83973
47614)327879186

) 9182 987654(9886416541 ) ---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 hard 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 will have the true remainder

3 84 73

EXAMPLES,

1. Divide 4673625 by 21400. 214(00) 46736)25(2182127 true quotient by Restitution.

428..

393
214

1796
1712

8900

8125 true reui. 2. Divide :379132075 by 6500.

Ans. 583741976 3. Divide 121400000 by 49000. Ans. 8600. 4. Divide 11059112 by 89000. Ans. 31.!!2 5. Divide 9187642 by 9170000. Ans. 1517 614 7

MORE EXAMPLES.
Divisor. Dividend.

Remains.
125000) 136250000( Quotient.) 0
120000) 149596478

76.178 901000)65847230

)2212:30 720000)987651000

)531000

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

Rule.-Consider low many times the divisor is contained in the first figure or figures of the dividend, put the result under, and carry as many lens to the next figure as there are ones over. Divide every figure in the same manner till the wholo is finisher.

EXAMPLES. Divisor. Dividend.

2)113415 3)85494 4)39407 5)94379

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Contractions in Division. When the divisor is such a number, that any two iigures in the Table, being multiplied together, will produce it, divide the given dividend by one of those figures ; the quotient 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 first remainder.

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51

2258-7
2258-8

63

first rem. +? True Quotient 225895.

True rein. 65 2. Divide 178464 by 16.

Ans. 11154, 3. Divide 467412 by 24.

Ans. 19175!. 4. Divide 94.2341 by 35.

Ans. 2692 135. 5. Divide 70638 by 30.

Ans, 22125 6. Divide 144872 by 48.

Ans. 3018 7. Divide 937387 by 54.

Ans. 17359 8. Divide 93975 by 84.

Ans. 11181. 9. Divide 145260 by 108.

Ans. 134.. 10. I'vide 1575360 by 144.

Ans, 10910. 2. To divide by 10, 100, 1000, &c. Rule.-Cut off as many figures from the right hand of the ilividend as there are ciphers in the divisor, and these figures so cut oft' are tho remainder; and the other figures of the dividend are the quotient.

EXAMPLES, 1. Divide 365 by 10. Ins. 36 and 5 remains. 2. Divide 5762

by 100,

Ans. 57 3. Divide_763753 by 1000. Ans. 763

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02 rem. - 753 rena

1

EXAMPLES,

84.

1. What will 9 tuns of hay come to, at 14

SUPPLEMENT TO MULTIPLICATION. To multiply by a mixt number; that is, a whole number joined with a fraction, as 8, 5, 67, &c.

RULE.—Multiply by the whole number, and take t, d, 1, &c. of the multiplicand, and add it to the product. Multiply 37 by 23.

Multiply 48 by 23. 2)37

48 23

21 181

24= 111

12=;

96 869, Answer.

132 Ans. 3. Multiply 211 by 501.

Ans. 10655!. 4. Multiply 2464 by

Ans. 20533 5. Multiply 345 by 191.

Ans. 65981 6. Multiply 6497 by 51.

Ans. 334131.
Questions to exercise Multiplication and Division.

dollars a

Ans. $136}. 2. If it take 320 rods to make a mile, and every rod contains 51 yards; how many yards are there i1. 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 yards ; how many yards 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 calendar month ?

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

Ans. £7735.

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9. What number multiplied by 9, will make 225 ?

Ans. 25. 10. The quotient of a certain number is 457, and the divisor 8; what is the dividend ?

Ans. 3656. 11. What cost 9 yards of cloth, at 3s. per yard ?

Ans. 27s. 12. What cost 45 oxen, at 81.

per head ? Ans. £360. 13. What cost 144 lb. of indigo, at 2 dols. 50 cts, or Ib.

Ans. 360. 14. Write down four thousand six hundred and seventeen, multiply it by twelve, divide the product by nine, and add 365 to the quotient, then from that sum subtract five thousand five hundred and twenty-one, and the remainder will be just 1000. Try it and see.

250 cents per

COMPOUND ADDITION, IS the adding of several numbers together, having different denoininations, but of the same generic kinil, as pounds, shillings and pence, &c. Tuns, hundreds, quar

ters, &c.

RULE.-1. Place the numbers so that those of the same denomina. tion may stand directly under each other.

2. Add the first column or denomination together, as in whole num. bers; then divide the sum by as many of the same denomination as make one of the next greater; setting down the remainder under the column added, and carry the quotient to the next superior denomination, continuing the same to the last, which add, as in simple addition*

1. STERLING MONEY, Is the money of account in Great-Britain, and is reckon. ed in Pounds, Shillings, Pence and Farthings. See the Pence Tables.

* The reason of this rule is evident: For, addition of this money, as in the pence is equal to 4 in the farthings ; 1 in the shillings, to 12 in the pence; and 1 in the pounds, to 20 in the shillings; therefore carrying as die rected, is the arranging the money, arising from each column, properly in the scale of denominations : and this reasoning will hold good in the addition of compound numbers of any denomination whatever.

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