A SHORT RULE. Nore. The value of 100 lbs. of any article will be just as many dollars as the article is cents a pound. Før 100 lb. at 1 cent per lb.=100 centi:=1 dollar. 100 lb. of beef at 4 cents a bb. 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 reinains; and is a concise way of performing several subtractions. Four principaı 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. S. 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 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 te dividend used) when found, place the figure in the quotient ; multiply the di. visor by this quotient figure; place the product under that part of the dividend used; then subtract it there. from, and bring down the next figure of the dividend tu the right hand of the remainder; after which, you must seek, multiply and subtract, till you have brought down every figure of the dividend. Proor. Multiply the divisor and quotient together and add the remainder if there be any to the product ; the work be right, the sum will be equal to the divirlenil.* * Another method which some make use of to prove division is as follows: viz. Add the rernainder and all the preducts of the several quotient figures multiplied by the divisor A 1. EXAMPLES. 1. How many times is 4 2. Divide 3656 dollars contained in 9391? equally among 8 men. Divisor, Div.Quotient. Divisor, Div.Quotient. 4)9991(2547 8)3656(457 32 Remains 18 0 Rem, 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 band. 2. Do the same with the quotient and place it on the right Dand. 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. Nore. If the sun is right the top and bottom figures will be alike Diriser, Div.Quotient. 95)85595(901 61 )286097469 756)863256(1172 472)251104(552 there remains 664 9. Divide 1893312 by 912. Ans. 2076. 10. Divide 1893312 by 2076. Ans. 912. 11. Divide 47254149 by 4674. Ans. 1011010 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 58473 can you have in 1191846:15 ? Ans. 3097}{371. 16. Divide 280208122081 by -912314. Quotient 307140, 13TT. Remainder. 91.82 987654) 988641654 ..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. EXAMPLES. 1. Divide 4673625 by 21400. 214(00)46756) 25(218,84287 true quotient by Restitution. 428., 393 1796 8425 true rem. 112 Ans. 1317goog 2. Divide 379432675, by 6500 Ans, 583741975 3. Divide 421400000 by 49000. Ans. 8600 4. Divide 11659112 by 89000 5. Divide 9187642 by 9170000. MORE EXAMPLES. Remains. )221230 720000)9876540001 534000 CASE II. Short Division is when the divisor does not exceed 12. 1 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 Divide every figure in the same manner till the whole is finished. EXAMPLES. Divisor. Dividend. 2)113415 3)85494 4)39407 5)94379 Quotient 56707—1 6)120616 7)152715 8) 96872 9)118724 are ones over. 11)6986197 12)14814096 12)570196382 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 drst remainder. 4." 22587 2258-8 63 first rem. +2 True Quotient 22589 True rem, 65 2. Divide 178464 by 16. ins. 11154 3. Divide 467412 by 24, Ans. 1947511 4. Divide 942341 by 35. Ans. 2692475 5. Divide 79638 by 56. Ans. 2212 6, Divide 144872 by 48. Ans. 301835 7. Divide 937387 by 54. Ans. 175595 8. Divide 93975 by 84. Ans. 111898 9. Divide 145260 by 108. Ans. 1945 10. Divide 1575560 by 144. Ans. 10940 2. To divide by 10, 100, 1000, &c. RULE. 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 the other figures of the dividend are the quotient. EXAMPLES. 1. Divide 365 by 10. Ans. 36 and 5 remains 2. Divide 5762 by 100. Ans. 57 3. Divide 763753 by 1000. Ans. 763 - 753 rema 62 rem. SUPPLEMENT TO MULTIPLICATION, To multiply by a mixt number ; that is a whole num per joined with a fraction, as 81, 51, 61, &c. RULE. Multiply by the whole number, and take 4, , , &c. of the Multiplicand, and add it to the product. |