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A SHORT RULE. Note. The value of 100 lbs. of any article will be just as many dollars as the article is cents a pound.
For 100 lb. at 1 cent per lb.=100 cents=1 dollar.
100 lb. of beef at 4 cents a lb. comes to 400 cents=4 dollars, &c.
DIVISION OF WHOLE NUMBERS. SIMPLE
IMPLE DIVISION teaches to find how many times one whole number is contained in another; and also what remains ; and is a concise way of performing several subtractions.
Four principal parts are to be noticed in Division : 1. The Dividend, or number given to be divided. 2. The Divisor, or number given to divide by.
3. The Quotient, or answer to the question, which shows how many times the divisor is contained in the dividend.
4. The Remainder, which is always less than the divisor, and of the same naine with the Dividend.
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.*
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 togethar, according to the
order in which they stand in the work ; and this sum, when the work 13 right will be equal to the dividend. A this 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 ihe excess at bot tom.
Nate. If the sun is right, the top and bottom figures will be alike,
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 077 12. What is the quotient of 330098048 divided by 42077
Ans. 78464. 13. What is the quotient of 761858465 divided by 8465 ?
Ans. 90001. 14. How often docs 761858465 contain 90001 ?
Ans. 8465. 15. How inany times 38473 can you have in 119184693?
Ans. 309734313 16. Divide 280208122081 by 912314.
) 9182 987654)988641654
0 CASE II. When there are ei phers 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 have the true remainder.
1. Divide 4673625 by 21400. 214(00) 46736)25(218,44% true quotient by Restitution.
9435 true rem
2. Divide 379432675 by 6500.
Ans. 58374197% 3. Divide 421400000 by 49000.
Ans. 8600 4. Divide 11659112 by 89000. Ans. 13151} 5. Divide 9187642 by 9170000. Ans. 1.134777
221230 720000) 987654000
CASE III. Short Division is when the Divisor does not exceed 12.
RULE. Consider how many times the divisor is contained in He first figure or figures of the dividend, put the result under, and carry as many tens to the next figure as there are
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 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.
first rem. +2 True Quotient 225895
True rem. 65 2. Divide 178464 by 16.
Ans. 11154 3. Divide 467412 by 24.
Ans. 194751 "4. Divide 942341 by 35.
Ans. 269248' 5. Divide 79638 by 36.
Ans. 2212.16 6. Divide 144872 by 48.
Ans. 30184 7. Divide 937387 by 54.
Ans.173593 8. Divide 93975 by 84.
Ans. 1118.53 9. Divide 145260 by 108.
Ans. 1345 10. Divide 1575360 by 144.
Ans. 10940 2. To divide by 10, 100, 1000, &c.
RULE. Cut off as inany 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.
1. Divide 365
Ans 36 and 5 remains.
SUPPLEMENT TO MULTIPLICATION. To multiply by a mixt number ; that is a whole number joined with a fraction, as 81,5), 63, &c.
RULE: Multiply by the whole number, and take , 1, 1, &c. of *k1e multiplicand, and add it to the product.