18. Shipped off 316 barrels of pork, at 7 dolls. 25 cts. per barrel; custom-house charges, 183 cents per barrel; porterage and carterage, 61 cents a barrel. How much does the pork stand me in all? Ans. 2370 dollars. 19. Received 72 barrels of whiskey; for 20 of them I am to pay at the rate of 6 dolls. 25 cts. apiece, for 30 of them, 7 dolls. 12 cts. apiece, and for the remainder, 8 dollars 64 cents apiece. How much money do they all come to ? Ans. 516 dolls. 12 cts. 20. Sold 24 dozen of men's hats, at 5 dollars 183 cents apiece; how much do they come to? Ans. 1494 dolls. 21. Thomas received of his father, a certain quantity of apples, and he gave James half of what he received, and half an apple over; to John he gave half of what remained, and half an apple over; to William he gave half of the remainder, and half an apple over; then he had but two left for himself. How many apples did his father give him at first? Ane. 23 apples. 22. A farmer put a certain number of geese into his stubble fields, and on the second day he found one-half of them dead, and half a one over; and when he counted them again, one-half of what survived at first was dead, and half a one over; and the next day, one-half of what remained was dead, and half a one over. He then drove the remainder into his pasture field, and found them to be 28. How many had he at first? Ans. 231 geese. DIVISION Shews how often one number is contained in another, and what remains. It is a short way of performing the continual subtraction of several equal numbers. Four principal parts are to be noticed in Division: first, the dividend, or number given to be divided; second, the divisor, or number given to be divided by; third, the quotient, or answer to the question, which shews how often the divisor is contained in the dividend; and fourth, the remainder, which must be always less than the divisor, and of the same name with the dividend. RULE. First place your divisor to the left hand of the dividend, and then seek how many times the divisor is contained in as many figures of the dividend as are necessary. Find the greatest figure that the divisor can be multiplied by, so as to produce a product that shall not exceed that part of the dividend used, and when found, place the figure in the quotient. Multiply the divisor by that quotient figure, and place the product under that part of the dividend used; then subtract it therefrom, and bring down the next figure of the dividend, and place it on the right hand of the remainder found by the last subtraction. After which you must seek as before multiply and subtract, till you have brought down all the figures in the dividend.. PROOF. Multiply the divisor and quotient together, and add in the remainder, (if there be any.) If the work be right, this product or sum will be equal to the dividend. Proof by the cross. Cast the 9's out of the divisor, and place the excess on the left hand of the cross; do the same with the quotient, and place the excess on the right hand. Multiply these two figures together, add their product to the remainder, cast the 9's out, and place the excess at top. Cast the 9's out of the dividend, and place that excess at bottom. If the work is right, the top and bottom figures will be alike. 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 of the dividend in the same manner, till the whole be divided. LONG DIVISION Is when the divisor exceeds 12. RULE. Try how often the divisor is contained in the same number of figures of the dividend, and proceed as is shewn in the first rule. But if you cannot put the divisor into the same number of figures of the dividend, annex another figure of the dividend, and seek how many times your divisor will go into them, and proceed as directed. When the divisor is such a number, that any two figures multiplied together will make the said divisor, it is shorter to divide the given number by one of those figures, and that quotient by the other, as 6 times 7 is 42. Then, to find your true remainder, you must multiply the first divisor into the last remainder, and to the product add the first remainder. When there are ciphers at the right hand of the divisor, cut off the ciphers in the divisor, and as many figures from the right hand of the dividend; then divide the remaining ones as before directed, and to the remainder, (if any) annex those figures cut off from the dividend, and you will have the true remainder. When the divisor is 10, 100, 1000, &c. cut off as many figures from the right hand of the dividend, as there are ciphers in the divisor; and those figures, so cut off, are the remainder, and the other figures of the dividend are the quotient. RULE. If the given number to be divided consists of eagles, dollars, dimes, cents and mills, bring down the given number, and divide as in whole numbers, and the quotient will be the same name as the given sum in its reduced state, before it was divided; then point off the quotient figures in the following manner: Point off one figure to the right hand for mills, one to the left of that for cents, one to the left of that for dimes, one to the left of that for dollars, and all to the left of dollars are eagles. If dollars and cents are to be divided, divide as in whole numbers, and point off two figures to the right for cents, and all to the left of cents are dollars. If the cents in the given sum to be divided consist of but one figure, as 2 dolls. 6 cts. be always certain you put a cipher on the left hand of the cents given; or, in other words, in the tens places of cents, as 2 dolls. 06 cts. otherwise your work will not be right. Here I bring down the 26 dollars, and annex two ciphers, making 2600 cents; then divide 4 into that number, and the quotient is 650 cents, in which I point off two figures to the right hand for cents, and all to the left of cents are dollars; and so proceed. dolls. cts. m. dolls. cts. m. 1 Divide 765 50 5 by 5 Ans. 153 10 1 1234567 4868022 49 43+6=1 17 33+2= 395,50 104 4 142 216 10 21 60 370 12 12 30 83+4=4 Questions for exercise. 1. Paid 20 labourers 50 dollars; receive? 2. Bought 18 hogs for 22 dollars apiece ? 3. Sold 24 pounds of tallow for 3 pound? what money doth each Ans. 1 dol. 25 cts. dollars; what is that a Ans. 12 cents. 4. Bought 4 dozen and 6 chickens for 3 dollars 37 cents; what is that apiece? Ans. 64 cents. 5. Paid for 12 bushels of apples, 3 dollars 75 cents; how much is that a bushel? Ans. 31 cents. 6. Sold 34 sheep at auction, for 38 dollars 25 cents; what does the sheep average? Ans. 1 dol. 124 cts. |