decimal of a pound, or 0,001 of a pound"; therefore when the farthings are more than 12, it is more than one half of another farthing, or another 0,001 of a pound, and must be increased by 1 ; and if the farthings are more than 36, they are more than 11 of 0,001 of a pound, and must be increased by 2. Again, 1 pound, being 20 shillings, is 3 dollars and one third of a dollar. Now it is vident that if you multiply pounds by 3, the product will be in dollars ; and as 3} X 3 = 10, if you multiply any number by 10 and divide the product by 3, the quotient will be the same as though you multiplied by 3}, and the work is easier. In reducing N. Y. Currency to Federal Currency, the given sum is prepared in the same manner as before : The reason of multiplying by 10 and dividing by 4, is this ; £1 N. Y. Currency is $2,50 ; therefore if you multiply by 2, you get the answer in dollars, cents and mills ; and as 4 is contained in 10, 21 times, if you multiply by 10 and divide by 4, you get the same number as by multiplying by 23. To reduce N. Jersey, Pennsylvania, Delaware, and Maryland Currencies to Federal Money. Reduce the given number to pence, annex a cipher, divide by 9, and add the quotient to the pence. From the sum point off 3 figures, which will be cents and mills; those to the left hand will be dollars. If there are farthings in the given sum, annex, in the place of the cipher, 2 for 1 farthing, 5 for 2 farthings, 7 for 3 farthings. If the given sum be pounds only, multiply by 8, annex 3 ciphers to the product, and divide by three; the quotient will be the answer in mills. Reduce f. 86 6s. 5d. 1qr. to Federal Money. 86 6 5 1 20 1726 12 9)207172 23019 Ans. $230,191 Reduce £. 736 to Federal Money. 736 8 3)5888000 Ans. $ 1962,666 Reduce £. 42 12s. 8d. to Federal Money. Ans. $ 113,688: Reduce £. 684. 6s. 8d. to Federal Money. Ans. $ 1824,888 &c. One dollar in N. Jersey, &c. Currency is 79. 6d. which, reduced to pence, is 90d. ; and as 90 pence make one dollar, it is plain that increasing it one ninth of itself will bring it into cents, as į of 90 = 10, which, added to 90, make 100, the number of cents in a dollar, and the same with any other number of pence. The reason for annexing a cipher is, that the answer may be in mills, and a more exact expression obtained. In reducing pounds only, you multiply by 8 and divide hy 3, for the following reasons. 1 pound is equal to $2,666, which is equal to $2; multiplying by 8 and dividing by 3, is the same as multiplying by 2}, which you will understand from what I have before told you. Pup. These rules appear very plain, and I think I shall have no difficulty in reducing any of the currencies to Federal Money. Tut. The rules which I have given you for reducing the several currencies to Federal Money, will probably be sufficient for your business ; but there are other currencies which it may be necessary for you to reduce to Federal Money, and your knowledge of the preceding rules will be sufficient to suggest to you a rule for their. reduction. Questions. What is compound addition ? How does it differ from simple subtraction ? By which of the simple rules is. reduction ascending performed ? By which is reduction descending performed ? How do you reduce a compound number to a vulgar fraction ? How does it appear that this will give a true expression of the compound number? How do you reduce a compound number to a decimal ? Why should this give a true decimal expression ? How do you reduce a decimal to the terms of an integer ? Why should this give the true value of the decimal ? How do you reduce N. E. Currency to Federal money? Why do you take half the number of shillings ? Why do you reduce the pence to farthings, and in. crease them if they exceed 12 or 36 ? Why do you multiply by 10 and divide by 3 ? Why do you divide by 4, in the reduction of N. Y. Currency? How do you reduce Pennsylvania Currency to Federal money? Why do you reduce the given sum to pence? Why do you divide by 9, and add the quotient to the dividend ? When the given number is pounds only, why do you multiply by 8, and divide by 3? Examples for Practice. 1. A merchant fitted a vessel for sea with the followa ing cargo; 25 tons of iron ; 16 tons, 14 cwt. 2 qrs. steel; 7 cwt 3 qrs. sugar; 50 tons bar iron ; what was the weight of the whole cargo? Ans. 92 T. 2 cwt. I qr. 2. What is the difference between 126 d. 12 h. 40' 02", and 86 d. 18 h. 48' 58" ? Aps. 39 d. 17 h. 51' 4". 3. In 12 pipes how many pints? Ans. 12096 G2 4. "How many inches from Newburyport to London, it being 2700 miles ? Ans. 171072000. 5. In 190080 inches how many yards ? Ans. 5280. 6. How many rods from the sun to the earth, it being 95,000,000 miles ? Ans. 304,000,000,000. 7. Reduce 7 cwt. 3 qrs. 171b. 10 oz. 12 dr. to the decimal of a ton. Ans. 0,39538. 8. Reduce 3 qrs. 3 nls. to the decimal of a yard. Ans. 0,9375. 9. What is the value of 0,387 of a yard? Ans. 1 qr. 2 nls. 10. What is the value of 0,4689 of a day? Ans. 11h. 15' 11". 11. Suppose a man to be 32 years old, how many seconds has he lived, allowing 365 d. 6 h. 48'48” to a year? Ans. 1,009,936,896. 12. How many minutes from the creation to the christian era, it being 4004 years? Ans. 2,104,840,032. 13. How many times does the wheel which is 18 feet, 6 inches in circumference, turn round in the distance of 150 miles ? Ans. 42810 times, and 180 inches over. 14. In 5529600 solid inches, how many cords of wood ? Ans 25. 15. How many square feet in a square mile ? Ans. 27878400. 16. Reduce £825, 16s. 4d. N. E. currency to Federal Money. Ans. $2752,723. 17. Reduce £64, 12s. N. Y. currency to Federal Money. Ans. $161,50. 18. Reduce £120, 15s. 4d. N. E. and N. Y: currencies to Federal Money? Ans. $ 102,556 N. E. [$310,917. N. Y. 19. Reduce £126 12s, 6d. N. Y. Penn and N. E. currencies to Federal Money. Ans. $ 316,562 N. Y. ($ 422,083 N. E. $ 337, 66 Penn, 20. Reduce £150 135, 4d. Penn. currency to Federal Money. Ans. $ 401,777 CONVERSATION V. COMPOUND MULTIPLICATION, COMPOUND DIVISION, AND DUODECIMALS. Tut. You have been taught in the preceding conversation that compound numbers may be multiplied and divided by each other, by first reducing them to the same denomination, and then proceeding as with simple numbers. But when a compound number is to be multiplied by a simple number, the best method is to multiply the compound number by the simple number, without reducing it to one denomination; for which we have the fol. lowing rule for COMPOUND MULTIPLICATION. Write the compound number, and under its lowest denomina.. tion write the simple number by which it is to be multiplied. Begin with the lowest denomination and multiply it by the multiplier ; divide this product by that number which it takes of the number multiplied to make one of the next higher denomination; write the remainder after division under the number multiplied, and add the quotient to the product of the simple number and the next higher denomination, and proceed in this manner with all the denominations to the last, which must be multiplied as a simple number. Multiply 12 lb. 8 oz. 6 pwt. 16 grs. by 8. Pup. I do not perfectly understand the reason of dividing the product by that number which it takes to make one of the next higher denomination ; I should like to have you explain it. Tut. In order to give you a distinct understanding of the whole work, I will multiply each denomination of |