ing the fraction four fold, the one effect completely counterbalances the other, and leaves the value of the fraction unchanged. It is evident, then, whether these numbers be considered as fractions or as compound numbers, that, when we wish to change their form from one of a greater to one of a less value, it must be performed by multiplication; because the greater number of less value will be equivalent to the less number of greater value. And, on the contrary, when we wish to change their form from a denomination of less value to one of greater, it must be performed by division, since the smaller number of greater value will be equivalent to the greater number of less value. Thus, to change 4 pounds to shillings, the 4 must be multiplied by 20 (the number of shillings in a pound), since 80 shillings 4 pounds. And, to change 80 shillings into pounds, the 80 must be divided by 20, since 4 pounds=80 shillings. Hence, also, it results that questions of this sort may be proved by changing the number back to its original denomination.] ☞ Federal money being arranged on the decimal scale, no other operation is necessary, in changing a number from one denomination to another, than a mere change of the separatrix. Thus, to change 5 eagles through all the inferior denominations, and vice versa, 5=50-500-5000=50,000=5000'0=500'00=50'000=5'0000 Exemplification for the Black-board. 1. Change £3 5s. 6d. 3q. to farthings. £ S. d. q. 3 5 6 3 960 48 4 2880+240+24+3=3147 farthings. Suggestive Questions.-How many farthings in one pound? Why, then, are the three pounds multiplied by 960? Of what denomination, then, is the 2880? How many farthings in one shilling? Why, then, are the 5s. multiplied by 48? Of what denomination, then, is 240? How many farthings in one penny? Why, then, are the pence multiplied by 4? Of what denomination, then, is 24? Of what denomination is the 3? Of what denomination, then, are all the four numbers? How many farthings, then, in all? 2. Change 3147 farthings to pounds, shillings, and pence. Farthings, 3147(960 Divisor. Divisor, 48)267 £3 5s. 6d. 3q. total quotient. 3 Suggestive Questions.- How many farthings make one pound? Why, then, are the whole number of farthings divided by 960? What is the quotient of 3147 divided by 960? Of what denomination, then, is the 3? Of what denomination is the remainder, 267? How many farthings make one shilling? What is the quotient of 267 by 48? Of what denomination, then, is the 5? Of what denomination is the remainder, 27 ? Why divided by 4? Of what denomination, then, is the quotient, 6? Of what denomination is the remainder, 3? What, then, do 3147 farthings amount to in pounds, shillings, and pence? 3. How many grains in 24 lb. 3 oz. 15 dwt. of silver? Suggestive Questions.-How many grains of silver in a pound? In an ounce? In a pennyweight? Why, then, are the pounds, ounces, and pennyweights, severally multiplied by these numbers? Of what denomination, then, are the three products? 4. How many pounds, &c., in 140040 grains of silver? Suggestive Questions.-Why are the grains of silver divided by 5760? What is the quotient? Of what denomination? What is the remainder? Why divided by 480? Why is the remainder of that division divided by 24? 5. Change £ to the fraction of a penny. X240=480 6. Change the same sum, namely, £, to pence. X240-480-531 pence. or (as 240=3×80) 3ק×80=160=53}, as before. 7. Change 480 pence to the fraction of a pound. d.482÷240=Z£. 8. Change the same sum, namely, 53 pence, to the fraction of a pound. 9. Change of of a cwt. to the fraction of a pound. 4×3×100=300=15 lb. ; or 1.3 100 15 4.5' 1 10. What part of g of a cwt. is 15lbs. ? = 15÷100-15÷3=%=1; or -=1· 1 Ans. of of 100 lbs. or a cwt. 11. Change £ s. d. to the fraction of a penny. Changing to least common denominator, Suggestive Questions.-Why are the given numbers changed to least common denominator? Ans. Because they are to be Why are the pounds multiplied by 240, and the shillings by 12? Of what denomination, then, are the products? 12. Change 253d. to fractions of pounds, shillings and pence. 5)953 12)1903 15s. 103d., or £15=£3 12s.=žs. gd. 13. Change 3s. to the fraction of a pound, and then back to shillings. S. £ 14. Change £4 15s. 9d. to the fraction of a pound. £ S. d. 4 15 9 240 12 d. 960+180+9=11494383 80 15. Change £383 to determinate fractions; that is, to pounds, shillings, and pence. [This is nothing more than to get rid of the common fraction by performing the division indicated.] 80)383(£4 15s. 9d. 16. Change 15s. to the decimal of a pound. 18=£0.75. 17. Change £0'75 to a determinate fraction. £75×20=15s. 18. Change 12s. 6d. 3q. to the decimal of a pound. 576+24+3=888=£0.628125. 19. Change £0 628125 to determinate fractions. £0.628125 20 s. 12.562500 d. 6.7500 9. 3.00 Suggestive Questions.-Does the given number amount to more or less than a pound? Why is it multiplied by 20? How many shillings are there in the product? How much remainder? Ans. 5625 tens of thousandths of a shilling. Why are the ciphers neglected? Why is the remainder multiplied by 12? What is the integer in the product? What is its denomination? Why is the remainder multiplied by 4? What is the denomination of the product? What, then, is the answer? Remark.-A more concise method has been devised of changing shillings, pence, and farthings, to the decimal of a pound, and of changing decimals of a pound to shillings, pence, and farthings, sufficiently correct for all practical purposes, which is called finding the decimal of shillings, pence, and farthings, by inspection. It will be readily understood by the aid of the following questions: What part of a pound is two shillings? Is every 2s. or '1 of a pound, then? If any number of shillings be divided by 2, then, will the quotient be the number of tenths of a pound? What is the only possible remainder when a number is divided by 2? What is the half of a tenth? Ans. 5. What decimal of a pound, |