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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 ona 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 nun,ber 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 divisòr, 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 follovag : viz. Add the remainder and all the products of the several quotient figures multiplied by the divisor togethor, according to the
order in wbich they stand in the works , and this sum, when the work is night will be equal to the dividend A third method of proof by excess of aines 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 land. 3. Multiply these two figures ogether, and add their product
the remainder, and reject the nines, and place the excess at bp.
4. Cast the nines out of the lividend ind place the excess al bttom Note-If the suna U right, the top and bottom figures will
Divisor, Div. Quotient. 95)85595(901 61 )28609(467
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 10TI 12. What is the quotient of 330098048 divided by 4207?
Ans. 78464. 13. What is the quotient of 761858465 divided by 8465 ?
Ans. 90001. 14. How often does 761858465 contain 90001 ?
Ans. 8465. 15. How many times 38473 can you have in 119184693?
Ans. 309731113. 16. Divide 280208122081 by 912314.
Quotient 307140 JTHITT
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 riglit 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. 214600)46736)25(218,14 * Jue quotient by Restitution.
8425 true reID
2. Divide 379432675 by 6500.
Ans. 58374? 675 2. Divide 421400000 by 49000.
8600 4. Divide 11659112 by 89000.
131112 5. Divide 9187642 by 9:70000. Ans. lg176670
CASE III. 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 inished.
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 tigures ; the quotient thence arising by the other; and the last quot ent will be the answer.
Note. The total remainúer is found by multiplying the last remainder by the first divisor, and adding in the first remainder.
first rem. +9 True Quotient 225843
True rem. 6: - 2. Divide 178464 by 16.
Ans. 11154 3. Divide 467412 by 24.
Ans. 1947512 4. Divide 942341 by 35.
Ans. 2692435 5. Divide 79638 by 36.
Ans. 2212366 6. Divide 144872 by 48.
Ans. 30187 7. Divide 237387 by 54.
Ans. 1735935 8. Divide 93975 by 84.
Ans. 111843 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 many figures from the right hand of the divi. dend as there are cyphers 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.
- 62 ren. Ans. 763 753 rem.
SUPPLEMENT TO MULTIPLICATION. To multiply by a mixt number ; that is a whole number joined with a fraction, as 84, 5, 6, &c.
RULE Multiply by the whole number, and take }, , , &c. of the multiplicand, and add it to the product.