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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 Ib. comes to 400 cents 4 dollars, &c.
DIVISION OF WHOLE NUMBERS. SIMPLE 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 di. visor, and of the same name 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 tħe 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.
PROJF. 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 ; vix. Add the remainder and all the products of the several guntieni figures multiplied by the divisor together, according to the
1. How many times is 4 2. Divide 3656 dollari contained in 9391 ? equally among 8 men. Divisor, Div. Quotient. Divisor, Div. Quotient. 4)9391(2347
order in which they stand in the work; and this sum, when the work is sigit will be equal to the dividend. A third method of procf by excess of nilies is as follows, viz.
1. Cast the rines 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 tiie nines, and place the excess at top. 4. Case the nines out of the dividend and place the excoss at bottom Noty-ftho sum is right, the top and bottom figures will be a ke
Dwisur, Div. Quotient 95)85595(901
81)28609(467) 736)863256(1172 472)251104(532
there remains 664 9. Divide 1893312 by 912.
Ans. 2076 10. Divide 1813312 by 2076.
Ans. 912 11. Divide 47254119 by 4674.
12. What is the quotient of 330098048 divided by 4207?
Ans. 78104. 12. What is the quotient of 761858465 diviiled hy $165 ?
Ans. 90001. 14. How often does 761858465 contain 90001 ?
Ans. 8465. 15. How many times 38473 can you have in 110184693?
Ans. 309733443 16. Divide 280208122081 by 912314.
Quotient. 307140 12
47614)327879186( ) 9182
..0 CASE II. When there are cyphers at the right hand of the divisor; cut off the cyphers 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.
1. Divide 4673625 by 21400. 214(00)46736)25218,42 true quotient by Restitution
842) true rem.
2. Divide 379432675 by 6500. Ans.5837459773
CASE III. Sliort Division is when thie 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.
2)113415 3)85494 4)39407 5)94379
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 225893
65 2. Divide 178464 by 16.
Ans. 11154 3. Divide 467412 by 24.
Ans. 1947513 4. Divide 942341 by 35.
Ans. 26924.' 5. Divide 79638 by 36.
Ans. 221236 6. Divide 144872 by 48.
Ans. 3018 7. Divide 937387 by 54.
Ans. 17359 8. Divide 93975 by 84.
Ans. 11189 9. Divide 145260 by 108.
Ans. 1345 10. Divide 1575370 by 144.
Ans. 10940 2. To divide by 10, 100, 1000, &c.
Cut off as many figures from the right hand of the dividend as there are cyphers in the divisor, and these figures so cut off are the remainder ; and tne other fi. gures of the dividend are the quotient.
1. Divide 365 by 10. Ans. 36 and 5 remains 2. Divide 5762
Ans. 57-- 62 rem. 3. Divide 763753 by 1000. Ans. 763—753 rem.
SUPPLEMENT TO MULTIPLICATION. To multiply by a mixt number ; that is a whole numver joined with a fraction, as 81,51, 6, &c.
RULE. Multiply by the whole number, and take , 1, 1, &c of the multiplicand, and add it to the product.