Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

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 add the remainder, if there be any, to the product; if the work be right, the sum will be equal to the dividend.*

[blocks in formation]

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

to the dividend.

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

1. Cast the nines out of the 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 remainder, 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 will be alike.

[blocks in formation]

11. Divide 47254149 by 4674.

Ans. 912.

Ans. 10110

4674.

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

13. What is the quotient of 761858465

Ans. 78464. ivided by 8465?

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. 3097314.

MORE EXAMPLES FOR EXERCISE.

Quotient, 307140

12

Remainder.

9182

) - - - 0

CASE II.

Divisor. Dividend.

47614)327879186(

234063)590624922(Quotient)83973

987654(988641654(

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) annex those figures cut off from the dividend, and you will have the true remainder

EXAMPLES.

1. Divide 4673625 by 21400.

214(00)46736)25(218 true quotient by Restitution.

428

842 21400

[blocks in formation]

Short Division is when the Divisor does not exceed 12.

RULE.-Consider how many times the divisor is contained in the first figure or figures of the dividend, put the result under, and carry as many tens to the next figure as there are ones over.

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

[blocks in formation]

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 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.

[blocks in formation]

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

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

[merged small][merged small][merged small][merged small][merged small][ocr errors][merged small]

SUPPLEMENT TO MULTIPLICATION.

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 1, 1, 4, &c. of the multiplicand, and add it to the product.

[blocks in formation]
[ocr errors]

1. What will 92 tuns of hay come to, at 14 dollars a tun ? 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 3 of her; what was my part of the money?

4. In 276 barrels of raisins, each 31 hundred weight?

5. In 36 pieces of cloth, each piece yards; how many yards in the whole?

Ans. $8637. cwt. how many Ans. 966 cwt. containing 243 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 among them, amounted to 1197. per man Ans. £7735. what is the value of the prize?

D

« ΠροηγούμενηΣυνέχεια »